+                                University
                                   of the
                                 Phi...
+
 Why So Much Focus on Energy?

 Rapid depletion of fossil fuels
 during the past 100 years, from
 accumulations of foss...
+
        How Did This Arise?

    Engineering inventions, and
    advances in science and
    technology during the 20th...
NAE List of 20th Century Greatest
+
    Engineering Achievements
                 In rank order

 1    Electrification
 2 ...
NAE List of 20th Century Greatest
+
    Engineering Achievements
              In rank order

 6    Radio and Television
 ...
+ NAE List of 20th Century Greatest
    Engineering Achievements
              In rank order

 11    Highways
 12    Space...
+ NAE List of 20th Century Greatest
    Engineering Achievements
               In rank order

 16    Health Technologies
...
+Consequences of Our Modern
              Way of Living

    Electrification led to other great
     engineering achievem...
+Consequences of Our Modern
          Way of Living

 The total energy demanded by
 the technologically transformed
 worl...
+Consequences of Our Modern
         Way of Living

 Continued  high rate of burning of
fossil fuels using current
techno...
+
    Energy Expenditures (USA)
          (From EIA AEO 2008)




                                11
+
 Energy Production and Consumption
          (From EIA AEO 2008)




                                     12
+
    Energy Production by Fuel
          (From EIA AEO 2008)




                                13
+
    Energy Consumption by Fuel
           (From EIA AEO 2008)




                                 14
+ Characteristics of Large-Scale
            Systems

  Presence of more than one
  stakeholder and decision-
  maker
  ...
+
          What Is a Dynamic System?
    Simplest Class: Modeled by an ordinary differential equation,
     where the in...
+
       Discrete-time Dynamics
    Difference equations rather than
    differential equations are used.
    Example: A...
+ What is Game Theory?

  Game  Theory is a body of knowledge concerning
  decision-making in a system with two or more
 ...
Very Brief History of Game Theory
+
    Mathematical foundation of game theory:

  John   von Neumann and O. Morgenstern...
+
Different Solution Concepts in Game
Theory
 Players   are assumed to be rational.
 Zero-sum,   min-max, max-min:
  Pu...
+
       Dynamic Game Theory
                            1   1       1
For DM1 :Find {u ,u ,...,u  0   1       N −1
      ...
+ For Energy Systems, What
Game Concept Is Appropriate?

• The government is one of the DMs and
it will be a dominant play...
+ Static Stackelberg Game
• Let there be two players, Player 1 and Player 2.
• ui is the decision variable of Player i,
  ...
+ Static Stackelberg Game -2

• Reaction Set of Player 1: D1 = {(u1,u2 ) ∈U1 × U2 :
  T: U2 → U1, u1 = Tu2 , J1(Tu2 ,u2 ) ...
+ Historical Roots of Dynamic
 Games
4. R. P. Isaacs, Differential Games: a Mathematical
   Theory with Applications to Wa...
+ Dynamic Games
The evolution of a discrete-time dynamic system is modeled by difference
equations x(k + 1) = f (x(k),u1(k...
Stackelberg Strategies for Dynamic Games*
+
     First considered by Chen and Cruz, and Simaan and Cruz:

 7.    C.I. Che...
+ Dynamic Stackelberg Games
• A player, say Player 2, called the Leader, commits to a strategy
for the entire horizon of t...
+ Dynamic Stackelberg Games - 2
• Define the reaction set of the Follower as the set of of u1
sequence for each possible a...
2-stage 3-state dynamic game
+
example              0,0
                         5,1

                        X=2         ...
Determining a Stackelberg
+
Closed Loop Strategy
 At
   the initial state x = 1, each Player chooses a
 decision of 0 or ...
+
       16 Choices for Players

           ci1
 ci2
 ci3
   ci4
   ci5
   ci6
   ci7
   ci8
   ci9
   Ci
   Ci
   Ci
   C...
Reaction Sets
+
  R1c = {(c115 ,c 21 ), (c18 , c 22 ), (c113 , c 23 ), (c16 , c 24 ), (c111, c 25 ),
  (c14 , c 26 ), (c19...
Choices for Player 1 when
+
u2=(0,1,0,1)              5,1
 u1 = (0,0,1,1)
                           X=2                  ...
+ Stackelberg Example


There are two closed loop Stackelberg controls with Player 2 as
Leader, (c15 , c 211 ) and (c16 , ...
+ Stackelberg Example -2

 Thisexample shows that the closed loop
 Stackelberg strategy violates Bellman’s
 principle of ...
+ Stackelberg Example -3

 Forthe same example in [9] it was shown
 that the open loop strategy for a game
 starting at t...
+ Stackelberg Example - 4
 This
     violation of the principle of optimality is
 known as time-inconsistency in economic...
+ Feedback Stackelberg
 Strategies
  Principal
           property: The principle of
  optimality holds. (Time-consistenc...
+        Dynamic Stackelberg
             Strategies

     Feedback Stackelberg
     strategies proposed for the
     fir...
Dynamic Stackelberg Strategies
+
Are Pervasive in Macroeconomics

  Kydland and Prescott published a paper in
 1977 showi...
Dynamic Stackelberg Strategies
+
Are Pervasive in Macroeconomics

  Kydland and Prescott won the Nobel
 prize in economic...
Related Developments in
+
Economics
12. Finn Kydland, “Equilibrium Solutions in Dynamic
  Dominant Player Models,” Journal...
Related Developments in Economics
+

10. Finn Kydland, “Noncooperative and Dominant
 Player Solution in Discrete Dynamic G...
+ Introduction to Current Joint Work
    with R R Tan and A B Culaba, DLSU
     Energy consumption is closely coupled wit...
+ Some Examples of Nascent
   Energy Supply Chains

     Biofuel           production systems from dedicated energy
     ...
+ Motivating Case
 In  the Philippines, Jatropha curcas has been
   touted as a promising dedicated energy
   crop for bi...
+
    The Basic Model
    (Cruz et al., 2009)


         Axt = yt                                 Material and energy bala...
+ Key Assumptions
 MatrixA reflects scale-invariant physical
 relationships such as process yields
 Matrix B reflects ec...
+
    The Basic Model
    (Cruz et al., 2009)
                                                  (I – BA) defines the
     ...
The Extended Model

                                                            Material and energy balances
             ...
+
    The Extended Model
                                                  The extended
                                  ...
Case Study 1
   (Scenario 1, Cruz et al., 2009)


                                                  Energy crop

         ...
+
         Case Study 1
                 (Cruz et al., 2009)




Presented at the 29th APAMS, July 13 - 15, 2009
Case Study 2
   (Scenario 4, Cruz et
   al., 2009)




Presented at the 29th APAMS, July 13 - 15, 2009
Case Study 2
   (Scenario 4, Cruz et
   al., 2009)




Presented at the 29th APAMS, July 13 - 15, 2009
Case Study 3
   (Scenario 5, Cruz et
   al., 2009)
                                  Farm
    Farm                        ...
Case Study 4

   We revisit Case 3, but
   introduce time lags with:

   ( 1, 2,            3)
                           ...
+ Key Implications

     Undesirable  dynamic characteristics in nascent
       energy supply chains may arise due to fee...
+
    Conclusions

      We  have extended our dynamic input-output
       model for nascent energy supply chains to
    ...
+
    Conclusions

      We  have extended our dynamic input-output
       model for nascent energy supply chains to
    ...
Pending Collaboration with UPLB




+
    Virgilio T.
    Villancio
    Program Leader
  Integrated R&D on Jatropha curcas...
+
OPPORTUNITIES

  Growing demand for
   biofuels
  Unstable prices of
   crude oil
  Rising prices of
   vegetable oil...
+
+
      It is locally known as Tubang
      bakod, Tuba-tuba, Kasla, Tubang
      aso, Tubang silangan, tawa-tawa
        ...
+

    •  2,000‐5,000
kg/
hectare/
year

       (depending
on
the
quality
of
Jatropha

       seed
and
soil)


    •  0.3‐...
+
                                         PROCESSING
AND
UTILIZATION

      FEEDSTOCK
PRODUCTION

                       ...
+
FLOWERING
AND
FRUITING
PHYSIOLOGY

+
+
+

           •  
3
fruit
clusters
per
branch

              per
fruiBng
season

Matured

pods
      •  
12
fruits
per
bun...
+




    Map for Jatropha suitability
+   Godilano, 2008
+




    JATROPHA PLANTATION AT ZAMBOANGUITA, DUMAGUETE
+     R & D Plan for OSU,
          DLSU, UPLB
    Investigate Total Dynamic Supply Chain.
    Investigate genetic reeng...
+




    Opo! Game Theory pa!
+
    The Engineer of 2020


    A Study by the National
    Academy of Engineering



                              77
The premise
Past: Engineering and engineering education
were reactive, responding to change.
Today: Rapid change signals t...
The process

Phase I: Imagining the future
and the challenges it will
present to engineering: Woods
Hole Workshop.
Phase I...
Steering Committees
     Phase I                                 Phase II
Wayne Clough, Chair, Ga Tech           Wayne Clo...
Context for engineering
          Breakthroughs in technology
          Demographics
          Challenges
          Econom...
Sustainable Technology      Breakthroughs


                                                     Microelectronics/
       ...
Demographics
8 billion people; a 25% increase since 2000.
Balance tipped toward urbanization.
Youth “bulge” in underdevelo...
Challenges
Fresh water shortages
Aging infrastructure
Energy demands
Global warming
New diseases
Security
Economic/societal forces
High speed communications /
Internet
Removal of trade barriers
Terrorist attacks; wars in Iraq,
A...
Social, global and professional
context of engineering practice
Population is more diverse.
Social, cultural, political fo...
Aspirations for the Engineer of 2020

         Engineering’s image
 Public that understands and appreciates the
 impact of...
Aspirations for the Engineer of 2020

 Engineering without boundaries
 Embrace potentialities offered by creativity,
 inno...
Aspirations for the Engineer of 2020

Engineering a sustainable society
   Lead the way toward wise, informed,
   economic...
Aspirations for the Engineer of 2020

 Educating the engineer of 2020
 Reconstitute engineering curricula and related
 edu...
Attributes of the engineer of 2020
    Strong analytical skills
    Practical ingenuity, creativity; innovator
    Good co...
To succeed
Attract best and brightest with
a forward-looking educational
experience – Phase II.
Educate them to be ready:
...
Thoughts from the Phase II summit
 Some needs have not changed:
    A sound grounding in science
    The learning experien...
Thoughts from the Phase II summit
 Research/co-op experience with real problems
 Experience with real-world tools and team...
Highlights from Phase II summit
Break out of the present mold
Education, not just curriculum
Career, not just jobs
Multipl...
More highlights from Phase II summit
Emphasis on innovation
Systems approach
Larger context for engineering
and technology...
+ References
    The National Academies Summit on America’s
     Energy Future: Summary of a Meeting, National
     Resea...
+
    References

      The
         Engineer of 2020: Visions of
     Engineering in the New Century,
     National Acad...
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Dals Up 09 Cruz

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Dals Up 09 Cruz

  1. 1. + University of the Philippines Distinguished Systems Thinking in Alumni Lecture Dynamic Planning of College of Series Energy Systems Engineering Diliman, Jose B. Cruz, Jr. Quezon City The Ohio State University Engineering Columbus, Ohio USA Theatre 17 July 2009
  2. 2. + Why So Much Focus on Energy?  Rapid depletion of fossil fuels during the past 100 years, from accumulations of fossils during the past hundreds of millions of years.  Negative impact of burning fossil fuels on the environment – global warming. 2
  3. 3. + How Did This Arise?   Engineering inventions, and advances in science and technology during the 20th century have transformed society into one with intense and pervasive use of electrical energy. 3
  4. 4. NAE List of 20th Century Greatest + Engineering Achievements In rank order 1  Electrification 2  Automobile 3  Airplane 4  Water Supply and Distribution 5  Electronics 4
  5. 5. NAE List of 20th Century Greatest + Engineering Achievements In rank order 6  Radio and Television 7  Agricultural Mechanization 8  Computers 9  Telephone 10  Air Conditioning and Refrigeration 5
  6. 6. + NAE List of 20th Century Greatest Engineering Achievements In rank order 11  Highways 12  Spacecraft 13  Internet 14  Imaging 15  Household Appliances 6
  7. 7. + NAE List of 20th Century Greatest Engineering Achievements In rank order 16  Health Technologies 17 Petroleum and Petrochemical Technologies 18  Laser and Fiber Optics 19  Nuclear Technologies 20  High-performance Materials 7
  8. 8. +Consequences of Our Modern Way of Living   Electrification led to other great engineering achievements.  Each of the 19 other achievements is closely coupled to the availability of electricity. Each implies greater use of energy. 8
  9. 9. +Consequences of Our Modern Way of Living  The total energy demanded by the technologically transformed world can not be met without the availability of high energy density fossil fuels (coal and oil). 9
  10. 10. +Consequences of Our Modern Way of Living  Continued high rate of burning of fossil fuels using current technologies releases carbon dioxide and other gases, contributing to global warming, and placing earth and humanity at great risk. 10
  11. 11. + Energy Expenditures (USA) (From EIA AEO 2008) 11
  12. 12. + Energy Production and Consumption (From EIA AEO 2008) 12
  13. 13. + Energy Production by Fuel (From EIA AEO 2008) 13
  14. 14. + Energy Consumption by Fuel (From EIA AEO 2008) 14
  15. 15. + Characteristics of Large-Scale Systems  Presence of more than one stakeholder and decision- maker  Presence of dynamics (next state depends on current state and current action) 15
  16. 16. + What Is a Dynamic System?   Simplest Class: Modeled by an ordinary differential equation, where the independent variable is time.   Example: Vertical motion of an automobile tire moving on a rough road d2y dy m +d + ky = f . This is usually written dt 2 dt in vector-matrix form as dx ⎡ 0 1 ⎤ ⎡ 0 ⎤ =⎢ ⎥x + ⎢ ⎥ dt ⎢ −k / m −d / m ⎥ ⎣ ⎦ ⎢ f /m ⎣ ⎥ ⎦ ⎡ x ⎤ where x = ⎢ 1 ⎥ , x = y, x = dy ⎢ x ⎥ 1 2 dt ⎣ 2 ⎦ when simulating in MATLAB 16
  17. 17. + Discrete-time Dynamics   Difference equations rather than differential equations are used.   Example: Autoregressive Moving Average (ARMA) yk + an−1 yk −1 + ... + a0 yk −n = bmuk + bm−1uk −1... + b0uk −m Vector-Matrix Representation: x k +1 = Axk + Bu 17
  18. 18. + What is Game Theory?   Game Theory is a body of knowledge concerning decision-making in a system with two or more Decision Makers.   A player is a decision maker or a controller.   A player chooses a decision, strategy, or control.   A decision choice is based on available information.   Associated with each player is a cost or pay-off function.   A cost depends on one or more decisions.   Much of game theory deals with how a player selects a decision. 18
  19. 19. Very Brief History of Game Theory +   Mathematical foundation of game theory:   John von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, 1944 [1].   Game theory cuts across multiple disciplines of mathematics, operations research, economics, political science, control theory, and engineering.   For a recent brief history see   Jose B. Cruz, Jr. and Xiaohuan Tan, Dynamic Noncooperative Game Models for Deregulated Electricity Markets, Nova Publishers, 2009 [2,Section 2.1]. 19
  20. 20. + Different Solution Concepts in Game Theory  Players are assumed to be rational.  Zero-sum, min-max, max-min:  Pure strategies (deterministic choice)  Mixed strategies (choice of random distribution)  Nash equilibrium for nonzero sum games.  Pareto optimality.  Stackelberg equilibrium. 20
  21. 21. + Dynamic Game Theory 1 1 1 For DM1 :Find {u ,u ,...,u 0 1 N −1 } to "optimize" J1 2 2 2 For DM2 :Find {u ,u ,...,u 0 1 N −1 } to "optimize" J2 N −1 i Ji = L (xN ) + N ∑ L (xk ,u ,u ) i k 1 k 2 k k =0 21
  22. 22. + For Energy Systems, What Game Concept Is Appropriate? • The government is one of the DMs and it will be a dominant player. • The dynamic Stackelberg strategy (Leader-Follower) is appropriate. • The dominant player is the Leader and announces its sequence of strategies first. 22
  23. 23. + Static Stackelberg Game • Let there be two players, Player 1 and Player 2. • ui is the decision variable of Player i, ui ∈Ui , i = 1, 2. • Ji (u1,u2 ) is the scalar cost function of Player i, i = 1, 2. • One player, called the Leader, declares its decision strategy first. • The other player is called the Follower. • H. von Stackelberg, The Theory of the Market Economy, Oxford University Press, English translated ed., 1952 [3]. 23
  24. 24. + Static Stackelberg Game -2 • Reaction Set of Player 1: D1 = {(u1,u2 ) ∈U1 × U2 : T: U2 → U1, u1 = Tu2 , J1(Tu2 ,u2 ) ≤ J1(u1,u2 ) for all u1 ∈U1, for each u2 ∈U2 }. • Stackelberg strategy pair with Player 2 as Leader, Player 1 as Follower: (u1S 2 ,u2S 2 ) ∈{(u1S 2 ,u2S 2 ) ∈D1 : J2 (u1S 2 ,u2S 2 ) ≤ J2 (u1,u2 ) for all (u1,u2 ) ∈D1 }. • Similarly Player 1 may be the Leader and Player 2 the Follower. 24
  25. 25. + Historical Roots of Dynamic Games 4. R. P. Isaacs, Differential Games: a Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. New York: John Wiley and Sons, 1955. First book on dynamic games. 5. Y.C. Ho, “Differential Games, Dynamic Optimization, and Generalized Control Theory,” Journal of Optimization Theory and Applications, Vol. 6, No. 3, 1970. Clarified connections of control theory to dynamic game theory. 6. T. Basar and G.J. Olsder, Dynamic Noncooperative Game Theory, 2nd Edition (revised), the Society for Industrial and Applied Mathematics, 1998. Comprehensive and extensive treatment of dynamic games. 25
  26. 26. + Dynamic Games The evolution of a discrete-time dynamic system is modeled by difference equations x(k + 1) = f (x(k),u1(k),u 2 (k),k), where x(k) is the state vector, ui (k) is the control or decision vector of Player i, and k is discrete time or time stage, k = 0,1, 2,...,N, and f is a mapping from x, u1, u 2 , and t to the space of x. The sequence {x(k)} describes the evolution of the state as a consequence of the application of decisions u1, u 2 applied at preceding time stages. A continuous time model is described by a set of ordinary differential equations x = f (x(t),u1(t),u 2 (t)), t ∈[t0 ,tf ], x(t0 ) = x0 and the  symbols are defined similarly. An open loop control is a time sequence ui = {ui (0),ui (1),...,ui (N − 1)}, starting at a given state x(0) = x0 . A closed loop control is a sequence {ui (k,x(k))} = {ui (0,x(0)),ui (1,x(1)),...,ui ((N − 1),x(N − 1))}. 26
  27. 27. Stackelberg Strategies for Dynamic Games* +   First considered by Chen and Cruz, and Simaan and Cruz: 7. C.I. Chen and J.B. Cruz, Jr., “Stackelberg Solution for Two-Person Games with Biased Information Patterns,” IEEE Trans. on Automatic Control, Vol. AC-17, No. 6, December 1972, pp. 791-798. 8. M. Simaan and J.B. Cruz, Jr., “On the Stackelberg Strategy in Nonzero-Sum Games,” Journal of Optimization Theory and Applications, Vol. 11, No. 5, May 1973, pp. 533-555. 9. M. Simaan and J.B. Cruz, Jr., “Additional Aspects of the Stackelberg Strategy in Nonzero-Sum Games,” Journal of Optimization Theory and Applications, Vol. 11, No. 6, June 1973, pp. 613-626. 27
  28. 28. + Dynamic Stackelberg Games • A player, say Player 2, called the Leader, commits to a strategy for the entire horizon of the game and announces it before the start of the game. • The other player, Player 1, called the Follower is aware of the Leader's commitment and as a rationale decision maker proceeds 1 2 to optimize its cost function J1(u ,u ) with respect to its choice for a control sequence u1, taking into account the Leader's commitmnt to 2 a specific control sequence u . • The Leader notes how the Follower will react, and chooses u to 2 optimize J2 (u1,u 2 ) under the condition that u1 is a reaction to u 2 . 28
  29. 29. + Dynamic Stackelberg Games - 2 • Define the reaction set of the Follower as the set of of u1 sequence for each possible announced commitment of u2 sequence by the Leader: R1 = {(u1,u 2 ) : J1(u1,u 2 ) ≤ J1(v 1,u 2 ) for all v 1 ∈U 1 and for each u 2 ∈U 2 } • If Player 1 is the Leader a similar reaction set for the Follower is defined: R 2 = {(u1,u 2 ) : J2 (u1,u 2 ) ≤ J2 (u1,v 2 ) for all v 2 ∈U 2 and for each u1 ∈U 1 } • The Leader selects its decision from the reaction set of the Follower that results in the minimum of its cost function. 29
  30. 30. 2-stage 3-state dynamic game + example 0,0 5,1 X=2 1,0 0,1 X=2 6,3 5,-3 2,5 0,1 1,1 7,7 8,3 0,0 3,3 0,1 0,0 X=1 X=1 1,1 5,5 X= 0,6 1,0 1 1,1 9,0 1,7 1,0 4,5 3,1 0,0 0,1 16,10 1,0 2,0 X= X=0 1,1 0 12,2 30
  31. 31. Determining a Stackelberg + Closed Loop Strategy  At the initial state x = 1, each Player chooses a decision of 0 or 1.  At time 1, state x = 2, each player chooses a decision of 0 or 1.  At time 1, state x = 1, each player chooses a decision of 0 or 1.  At time 1, state x = 0, each player chooses a decision of 0 or 1.  Each decision maker or Player has 16 choices 31
  32. 32. + 16 Choices for Players ci1
 ci2
 ci3
 ci4
 ci5
 ci6
 ci7
 ci8
 ci9
 Ci
 Ci
 Ci
 Ci
 Ci
 Ci
 Ci
 10
 11
 12
 13
 14
 15
 16
 ui(0,1)
 0
 0
 0
 0
 0
 0
 0
 0
 1
 1
 1
 1
 1
 1
 1
 1
 ui(1,2)
 0
 0
 0
 0
 1
 1
 1
 1
 0
 0
 0
 0
 1
 1
 1
 1
 ui(1,1)
 0
 0
 1
 1
 0
 0
 1
 1
 0
 0
 1
 1
 0
 0
 1
 1
 ui(1,0)
 0
 1
 0
 1
 0
 1
 0
 1
 0
 1
 0
 1
 0
 1
 0
 1
 32
  33. 33. Reaction Sets + R1c = {(c115 ,c 21 ), (c18 , c 22 ), (c113 , c 23 ), (c16 , c 24 ), (c111, c 25 ), (c14 , c 26 ), (c19 , c 27 ), (c12 , c 28 ), (c115 , c 29 ), (c116 , c 210 ), (c15 , c 211 ), (c111, c 212 ), (c16 , c 213 ), (c112 , c 214 ), (c11, c 215 ), (c12 , c 216 )} R2c = {(c11, c 211 ), (c12 , c 211 ), (c13 , c 2 ), (c14 , c 211 ), (c15 , c 211 ), (c16 , c 211 ), (c17 , c 211 ), (c18 , c 211 ), (c19 , c 211 ), (c110 , c 23 ), (c111, c 211 ), (c112 , c 23 ), (c113 , c 211 ), (c114 , c 23 ), (c115 , c 211 ), (c116 , c 23 )} For example, for u 2 = c 26 (0,1,0,1) Player 1 minimizes J1 and gets u1 = c14 ,(0, 0, 1 ,1). This is repeated for each u 2 = c 2 j , thus obtaining R1c . 33
  34. 34. Choices for Player 1 when + u2=(0,1,0,1) 5,1 u1 = (0,0,1,1) X=2 0,1 X=2 6,3 5,-3 2,5 1,1 7,7 8,3 0,0 3,3 0,0 X=1 X=1 5,5 X=1 0,6 1,0 9,0 1,7 1,0 4,5 3,1 0,1 16,10 X=0 2,0 X=0 1,1 12,2 34
  35. 35. + Stackelberg Example There are two closed loop Stackelberg controls with Player 2 as Leader, (c15 , c 211 ) and (c16 , c 212 ), both leading to J1S 2 = 7 and c J2S 2 = 2 and to the same trajectory x(1) = 2 and x(2) = 1. At time c t = 1, the remaining controls are (u1,u 2 ) = (1,0) and the remaining costs are J1 = 2 and J2 = 5. Supose that Player 2 considers violating its commitment made at time t = 0 regarding its control at time t = 1. Its closed loop Stackelberg strategy for a game starting at t = 1 and x(1) = 2 is (u1,u 2 ) = (0,1) leading to J1 = 6 and J2 = 3. It will be tempted to violate its commitment to reduce its cost. 35
  36. 36. + Stackelberg Example -2  Thisexample shows that the closed loop Stackelberg strategy violates Bellman’s principle of optimality. That is, the continuation of a previously announced closed loop strategy, starting at a later time, is not necessarily a closed loop Stackelberg strategy for a new game starting at the later time.  This example is in Simaan and Cruz [Ref 9]. 36
  37. 37. + Stackelberg Example -3  Forthe same example in [9] it was shown that the open loop strategy for a game starting at t=0, x=1 violates the principle of optimality.  Ifa Leader violates its commitment made at an earlier time and changes its strategy at a later time with a new commitment, there will be a credibility problem. The Follower may not believe a subsequent commitment by the Leader. 37
  38. 38. + Stackelberg Example - 4  This violation of the principle of optimality is known as time-inconsistency in economics.  The credibility problem and the time- inconsistency problem suggest that a Stackelberg-like closed loop strategy that satisfies the principle of optimality would be an acceptable suboptimal alternative.  Such a strategy, called Feedback Stackelberg was introduced in [7], precisely defined and fully described in [9]. It is a suboptimal closed loop Stackelberg-like strategy. But it is time-consistent. 38
  39. 39. + Feedback Stackelberg Strategies  Principal property: The principle of optimality holds. (Time-consistency holds).  Dynamic programming can be applied.  Optimal Cost-to-go at stage k is the sum of the incremental cost at stage k plus the optimal cost-to-go at the next stage k+1, where the optimization is performed stage by stage starting with the last stage, in the sense of Stackelberg. 39
  40. 40. + Dynamic Stackelberg Strategies  Feedback Stackelberg strategies proposed for the first time in Simaan and Cruz 1973 are suboptimal but time- consistent and widely used in macroeconomics.   The same methodology can be applied to energy systems. 40
  41. 41. Dynamic Stackelberg Strategies + Are Pervasive in Macroeconomics   Kydland and Prescott published a paper in 1977 showing that the government strategy is time-inconsistent (violates the principle of optimality of Bellman’s Dynamic Programming). This paper revolutionized the entire field of macroeconomics.   Kydland published a more theoretical paper in 1975, used as a reference in Kydland and Prescott, 1977). 41
  42. 42. Dynamic Stackelberg Strategies + Are Pervasive in Macroeconomics   Kydland and Prescott won the Nobel prize in economics in 2004.   Kydland, 1975 referred to Simaan and Cruz, 1973, where time-inconsistency is proved. Simaan and Cruz, 1973 is a reference in Kydland’s Ph.D. dissertation supervised by Prescott at Carnegie Mellon University in 1974. 42
  43. 43. Related Developments in + Economics 12. Finn Kydland, “Equilibrium Solutions in Dynamic Dominant Player Models,” Journal of Economic Theory, 15, 307-325, 1977. Kydland states that the dominant solution, open loop or closed loop are time-inconsistent. Suggests that a feedback solution is self-enforcing. Cites Simaan and Cruz [8,9]. 13. Guido Taballini, “Finn Kydland and Edward Prescott’s Contribution to the Theory of Macroeconomic Policy,” Scand. J. of Economics, 107(20), 203-216, 2005. Taballini notes that Kydland [12] cites Simaan and Cruz [8,9]. 43
  44. 44. Related Developments in Economics + 10. Finn Kydland, “Noncooperative and Dominant Player Solution in Discrete Dynamic Games, “International Economic Review, Vol. 16, No. 2, June 1975, pp. 321-335. Cites Simaan and Cruz: “The dominant player problem, on the other hand, has only recently received a little attention in the game literature, and the two interesting papers by Simaan and Cruz [24,25] should be mentioned.” 11. Finn E. Kydland and Edward C. Prescott, “Rules Rather Than Discretion: The Inconsistency of Optimal Plans,” The Journal of Political Economy, Vol. 85 No. 3 (June 1977), pp. 473-492. This paper is one of the bases for Kydland and Prescott to be selected for the 2004 Nobel Prize in Economics. 44
  45. 45. + Introduction to Current Joint Work with R R Tan and A B Culaba, DLSU   Energy consumption is closely coupled with both economic growth and greenhouse gas emissions.   Despite the increasing popularity of renewables, the world remains highly dependent on fossil fuels for transportation, power generation and industrial use.   Various novel solutions are at inherent disadvantage compared to entrenched technologies due to network externalities. Presented at the 29th APAMS, July 13 - 15, 2009
  46. 46. + Some Examples of Nascent Energy Supply Chains   Biofuel production systems from dedicated energy crops   Fossil-based electricity production with carbon capture and storage   The “hydrogen economy” Presented at the 29th APAMS, July 13 - 15, 2009
  47. 47. + Motivating Case  In the Philippines, Jatropha curcas has been touted as a promising dedicated energy crop for biodiesel production  However, investments in upstream (farm- level) production capacity has not been matched by corresponding growth in downstream (oilseed pressing and conversion) capacity  This imbalance in the J. curcas supply chain is typical of nascent energy systems. Presented at the 29th APAMS, July 13 - 15, 2009
  48. 48. + The Basic Model (Cruz et al., 2009) Axt = yt Material and energy balances of physical streams xt+1 = B(zt – yt) + xt Response of where: production capacity to A = technical coefficient matrix deficits or surpluses xt = sectoral total output vector at t yt = sectoral net output vector at t B = influence matrix Presented at the 29th APAMS, July 13 - 15, 2009
  49. 49. + Key Assumptions  MatrixA reflects scale-invariant physical relationships such as process yields  Matrix B reflects econometrically determined collective behavioral responses of supply chain agents  Vector x reflects total system outputs, including intermediates  Vectoractual y reflects net system outputs, while z gives the desired output level.  Productioncapacities are assumed to respond to surpluses or deficits incurred in the previous time interval. Presented at the 29th APAMS, July 13 - 15, 2009
  50. 50. + The Basic Model (Cruz et al., 2009) (I – BA) defines the dynamic xt+1 = (I – BA)xt + Bzt characteristics of the system. zt = Kxt + zo Adaptive target output level is where: introduced K = control matrix (I – BA + BK) now zo = baseline target output defines the dynamic characteristics of the controlled xt+1 = (I – BA + BK)xt + Bzo system. Presented at the 29th APAMS, July 13 - 15, 2009
  51. 51. The Extended Model Material and energy balances of physical streams Response of production capacity to deficits or Lagged influences surpluses may be interpreted probabilistically Presented at the 29th APAMS, July 13 - 15, 2009
  52. 52. + The Extended Model The extended model is thus Denoting reduced to the same form as the previous one. Presented at the 29th APAMS, July 13 - 15, 2009
  53. 53. Case Study 1 (Scenario 1, Cruz et al., 2009) Energy crop Biofuel Land Farming Biofuel production Presented at the 29th APAMS, July 13 - 15, 2009
  54. 54. + Case Study 1 (Cruz et al., 2009) Presented at the 29th APAMS, July 13 - 15, 2009
  55. 55. Case Study 2 (Scenario 4, Cruz et al., 2009) Presented at the 29th APAMS, July 13 - 15, 2009
  56. 56. Case Study 2 (Scenario 4, Cruz et al., 2009) Presented at the 29th APAMS, July 13 - 15, 2009
  57. 57. Case Study 3 (Scenario 5, Cruz et al., 2009) Farm Farm capacity capacity responds to increases biodiesel with oilseed surplus or surplus deficit Biodiesel production capacity exhibits sluggish response Presented at the 29th APAMS, July 13 - 15, 2009
  58. 58. Case Study 4 We revisit Case 3, but introduce time lags with: ( 1, 2, 3) T = (0.3, 0.5, 0.2)T Presented at the 29th APAMS, July 13 - 15, 2009
  59. 59. + Key Implications   Undesirable dynamic characteristics in nascent energy supply chains may arise due to feedback loops in physical linkages or information flows.   Control theory can be used to systematically design interventions to suppress undesirable system behavior.   Such interventions can come in the form of policy instruments or economic incentives/disincentives. Presented at the 29th APAMS, July 13 - 15, 2009
  60. 60. + Conclusions   We have extended our dynamic input-output model for nascent energy supply chains to incorporate weighted time lags in the capacity response.   This extension allows for added flexibility in modeling real systems wherein changes in production capacity may be subject to time delays. Presented at the 29th APAMS, July 13 - 15, 2009
  61. 61. + Conclusions   We have extended our dynamic input-output model for nascent energy supply chains to incorporate weighted time lags in the capacity response.   This extension allows for added flexibility in modeling real systems wherein changes in production capacity may be subject to time delays. Presented at the 29th APAMS, July 13 - 15, 2009
  62. 62. Pending Collaboration with UPLB + Virgilio T. Villancio Program Leader Integrated R&D on Jatropha curcas for Biodiesel UP Los Banos
  63. 63. + OPPORTUNITIES
   Growing demand for biofuels   Unstable prices of crude oil   Rising prices of vegetable oils   Need for non-food sources of oil   Higher value of by- products as additional source of revenue
  64. 64. +
  65. 65. + It is locally known as Tubang bakod, Tuba-tuba, Kasla, Tubang aso, Tubang silangan, tawa-tawa Planted in fences for hedges, thus the term Tubang bakod Seeds are grounded and used to poison fish thus the term Tuba Leaves are used as herbal medicine for fractures
  66. 66. + •  2,000‐5,000
kg/
hectare/
year
 (depending
on
the
quality
of
Jatropha
 seed
and
soil)
 •  0.3‐
9
kg
/
tree
seed
producBon
 •  Can
bear
fruit
throughout
the
year
 •  Oil
yield
30
–
40%
crude
non‐edible
oil
 •  0.75
–
2
tons
biodiesel
/
hectare

  67. 67. + PROCESSING
AND
UTILIZATION
 FEEDSTOCK
PRODUCTION
 Mechanical
processing
 Germplasm
Management,
 EnzymaNc
processing
 Varietal
improvement,
seed
 Processing
of
by‐products
 technology,
provenance
tesNng
 Waste
management
 Nursery
development
 Development
of
producNon

 GOALS
 systems,
prototype
plantaNon
 BUSINESS
AND
 ENTERPRISE

 Rural
employment
 Soil
FerNlity
management
 DEVELOPMENT
 Income
generaNon
 Pest
and
diseases
management
 Energy
independence
 Cleaner
environment
 Flowering
and
fruiNng
 MARKET
DEVELOPMENT
 physiology
 Product
development
and
 Post
ProducNon
management
 promoNon
 PNOC FUNDED Technology
promoNon
 Establishment
of
the
value
 DOST-PCARRD chain
 FUNDED CHED FUNDED SOCIAL
 ECONOMICS
 POLICY
 ENVIRONMENTAL
 Capacity
development

  68. 68. +
  69. 69. FLOWERING
AND
FRUITING
PHYSIOLOGY
 +
  70. 70. +
  71. 71. + •  
3
fruit
clusters
per
branch
 per
fruiBng
season
 Matured
 pods
 •  
12
fruits
per
bunch
 •  2.66
seeds
per
fruit
 •  48
branches
per
tree
 •  1,600
trees
per
hectare
 •  1,400
seeds
per
kg
 •  5,250
kg
per
hectare

  72. 72. + Map for Jatropha suitability
  73. 73. + Godilano, 2008
  74. 74. + JATROPHA PLANTATION AT ZAMBOANGUITA, DUMAGUETE
  75. 75. + R & D Plan for OSU, DLSU, UPLB   Investigate Total Dynamic Supply Chain.   Investigate genetic reengineering of Jatropha curcas for improved total supply of biodiesel (oil content, continuous harvesting, less water needs).   Develop strategies for various stakeholders   Investigate dynamic policy interventions. 75
  76. 76. + Opo! Game Theory pa!
  77. 77. + The Engineer of 2020 A Study by the National Academy of Engineering 77
  78. 78. The premise Past: Engineering and engineering education were reactive, responding to change. Today: Rapid change signals that it is time to reverse the paradigm. Premise: If we anticipate the future and are proactive about changing engineering and engineering education, we can shape a significant, dynamic role for our profession.
  79. 79. The process Phase I: Imagining the future and the challenges it will present to engineering: Woods Hole Workshop. Phase II: Considering how engineering education should prepare for that future: Washington DC Summit. National Academy of Engineering
  80. 80. Steering Committees Phase I Phase II Wayne Clough, Chair, Ga Tech Wayne Clough, Chair, Ga Tech Alice Agogino, UC Berkeley Alice Agogino, UC Berkeley George Campbell, Cooper Union Mark Dean, IBM James Chavez, Sandia Labs Deborah Grubbe, DuPont David Craig, Reliant Energy Randy Hinrichs, Microsoft Jose Cruz, Ohio State Sherra Kerns, Olin College Peggy Girshman, NPR Alfred Moye, H-P Daniel Hastings, MIT Diana Natalicio, UT at El Paso Michael Heller, UC San Diego Siman Ostrach, Case West Res Deborah Johnson, U Virginia Ernest Smerdon, U Arizona Alan Kay, H-P Karan Watson, Texas A&M Tarek Khalil, U Miami David Wisler, GE Aircraft Engines Robert Lucky, Telcordia Technologies John Mulvey, Princeton Sharon Nunes, IBM Sue Rosser, Georgia Tech Ernest Smerdon, U Arizona
  81. 81. Context for engineering Breakthroughs in technology Demographics Challenges Economic/societal forces
  82. 82. Sustainable Technology Breakthroughs Microelectronics/ telecommunications Nanotechnology Biotechnology/ nanomedicine Logistics Photonics/optics Manufacturing
  83. 83. Demographics 8 billion people; a 25% increase since 2000. Balance tipped toward urbanization. Youth “bulge” in underdeveloped nations while developed nations age. If the world condensed to 100 people: 56 in Asia 7 in Eastern Europe/Russia 16 in Africa 4 in the United States
  84. 84. Challenges Fresh water shortages Aging infrastructure Energy demands Global warming New diseases Security
  85. 85. Economic/societal forces High speed communications / Internet Removal of trade barriers Terrorist attacks; wars in Iraq, Afghanistan Emergence of technology- based economies in other nations Sustained investment in higher education in countries like China, India
  86. 86. Social, global and professional context of engineering practice Population is more diverse. Social, cultural, political forces will shape and affect the success of technological innovation. Consumers will demand higher quality, customization. Growing imperative for environmental sustainability. Increasing focus on managing risk and assessment with view to security, privacy, and safety.
  87. 87. Aspirations for the Engineer of 2020 Engineering’s image Public that understands and appreciates the impact of engineering on socio-cultural systems. Public that recognizes engineering’s ability to address the world’s complex and changing challenges. Engineers will be well grounded in the humanities, social sciences, and economics as well as science and mathematics.
  88. 88. Aspirations for the Engineer of 2020 Engineering without boundaries Embrace potentialities offered by creativity, innovation, and cross-disciplinary fertilization. Broaden influence on public policy and the administration of government, nonprofits, and industry. Recruit, nurture and welcome underrepresented groups to engineering.
  89. 89. Aspirations for the Engineer of 2020 Engineering a sustainable society Lead the way toward wise, informed, economical, and sustainable development. Assist in the creating of an ethical balance in standard of living for developing and developed countries alike.
  90. 90. Aspirations for the Engineer of 2020 Educating the engineer of 2020 Reconstitute engineering curricula and related educational programs to prepare today’s engineering students for the careers of the future. Create a well-rounded education that prepares students for positions of leadership and a creative and productive life.
  91. 91. Attributes of the engineer of 2020 Strong analytical skills Practical ingenuity, creativity; innovator Good communication skills Business, management skills High ethical standards, professionalism Dynamic/agile/resilient/flexible Lifelong learner Able to put problems in their socio-technical and operational context Adaptive leader
  92. 92. To succeed Attract best and brightest with a forward-looking educational experience – Phase II. Educate them to be ready: To implement new technology. To focus on innovation. To understand global trends.
  93. 93. Thoughts from the Phase II summit Some needs have not changed: A sound grounding in science The learning experience of great lectures Studio experiences with open-ended problem solving Other things have really changed: Access to IT creates challenge of coupling deep learning with instant gratification Means and ends of using computers to bring the world to campus and enrich learning Design tools and sophisticated instruments that enable students to experience the excitement of engineering Charles Vest
  94. 94. Thoughts from the Phase II summit Research/co-op experience with real problems Experience with real-world tools and teams Encourage and recognize diversity Social, ethical aspects of engineering What students need to learn instead of what we want to teach Creative and practical thinking Arden Bement
  95. 95. Highlights from Phase II summit Break out of the present mold Education, not just curriculum Career, not just jobs Multiple models, not just one Leadership, not just teamwork More coordination with industry Cross-disciplinary emphasis
  96. 96. More highlights from Phase II summit Emphasis on innovation Systems approach Larger context for engineering and technology Non-engineering career tracks Global perspective Market forces, macroeconomics Sense of urgency
  97. 97. + References   The National Academies Summit on America’s Energy Future: Summary of a Meeting, National Research Council, 2008 http://www.nap.edu/catalog/12450.html   Electricity from Renewable Resources: Status, Prospects, and Impediments, National Research Council, 2009 http://www.nap.edu/catalog/12619.html   J. B. Cruz, Jr., R. R. Tan, A. B. Culaba, J-A. Ballacillo, “A Dynamic Input-Output Model foe Nascent Bioenergy Supply Chains,” Applied Energy, 2009. 78
  98. 98. + References   The Engineer of 2020: Visions of Engineering in the New Century, National Academy of Engineering, 2004.   Educating the Engineer of 2020: Adapting Engineering Education to the New Century, National Academy of Engineering, 2005. 79

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