An Approach to Discrete-Time Incentive Feedback Stackelberg Games

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1 472 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL. 32, NO. 4, JULY 2002 An Approach to Discrete-Time Incentive Feedback Stackelberg Games Ming Li, Jose B. Cruz, Jr., Life Fellow, IEEE, and Marwan A. Simaan, Fellow, IEEE Abstract A substantial effort has been devoted to various incentive Stackelberg solution concepts. Most of these concepts work well in the sense that the leader can get his desired solution in the end. Yet, most incentive strategies developed thus far include either the follower s control, which may not be realistic in practice, or delays in the state, which makes stabilization more difficult to achieve. In this paper, we obtain the team-optimal state feedback Stackelberg strategy (with no delays) of an important class of discrete-time two-person nonzero-sum dynamic games characterized by linear state dynamics and quadratic cost functionals. Index Terms Games, incentive, Stackelberg, stability, team-optimal. I. INTRODUCTION IN 1930, H. von Stackelberg [1] originally suggested the leader follower solution concept, also known as the Stackelberg solution concept, for static economic competition. Then, in the 1970s, Chen and Cruz [2], and Simaan and Cruz [3], [4] presented dynamic versions of this solution concept in a control framework. The dynamic Stackelberg solution is appropriate in nonzero-sum dynamic games when a hierarchy in decision-making exists. By hierarchy, we mean the decision makers hold nonsymmetrical roles in the decision-making process. One of the players (the leader) has the ability to announce his strategy in advance and announce it to the other player (the follower). By taking into account the projected rational response of the follower, the leader seeks that policy which leads to a most favorable outcome for him. A. Solution Concept Based on different information structures, there are several solution concepts in dynamic Stackelberg games. Under open-loop information, necessary conditions for the Stackelberg solution have been obtained, and explicit forms of the optimal strategies are given in the case of linear quadratic (LQ) Manuscript received July 2, This work was supported by the Defense Advanced Research Projects Agency (DARPA) and Air Force Research Laboratory (AFRL), Air Force Material Command, USAF, under Agreement F The results of this paper are part of the M.S. thesis of M. Li at The Ohio State University, Columbus. The theoretical portion of the research was supported by the DARPA project. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the DARPA, the AFRL, or the U.S. Government. This paper was recommended by Associate Editor M. Shahidehpour. M. Li is with the Electronics Department, MPC Products Corporation, Skokie, IL USA. J. B. Cruz, Jr. is with the Department of Electrical Engineering, The Ohio State University, Columbus, OH USA. M. A. Simaan is with the Department of Electrical Engineering, University of Pittsburgh, Pittsburgh, PA USA. Digital Object Identifier /TSMCA games [2], [3]. However, with the complication induced by the dynamic nature of the games, it is not reasonable to assume that the players only have access to open-loop information. When players have access to closed-loop information, generally the principle of optimality does not hold. This leads to the introduction of a different solution concept called feedback Stackelberg strategy [4], [14] [19]. Under this concept, the two cost-to-go functionals retain their optimal feedback Stackelberg properties after any number of stages. Hence, dynamic programming holds. This property seems attractive, but the feedback Stackelberg strategy is not a Stackelberg strategy except for a one-stage game. Fortunately, if the equilibrium solution is also a team-optimal solution, then the resulting strategy is a Stackelberg equilibrium solution. B. Incentive Format The idea of declaring a reward (punishment) for a decision maker according to his particular choice of action in order to induce certain desired behavior on the part of the other decision maker is known as incentive (threat) [5] [10], [13], [16], [20]. At least three kinds of incentive policies were investigated in the literature. The first approach results in a punishment (value of follower s objective function is worse) when the follower s control deviates from the desired value [5], [6], and it is a linear form, where is the control of the leader; is the control of the follower; and superscript represents the desired value for the leader. In most cases, these desired values of the controls are chosen to be the same as the team-optimal values. This approach is effective, and it has already been proved that under certain kind of constraints on the objective functions and the system matrices, an incentive matrix could always be found so that the desired values are obtained. However, one limitation of this form is that it requires the leader s exact knowledge of the follower s control, which is acceptable in team problems, but problematic in dynamic games in general. The second approach was proposed by Basar and Selbuz [7]. It uses the one-step-delay memory representation, implying that at each stage, the leader s control depends not only on the state information at the present stage,but also on the previous stage. This approach could be extended to -step delay memory representation easily. However, guaranteeing stability was not considered in [7]. The third approach, using a no-memory state feedback representation and the only attempt so far that includes stability analysis, is the one by Salman and Cruz [8]. A sufficient condition /02$ IEEE

2 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL. 32, NO. 4, JULY (with system stability guaranteed) for the leader to enforce his team optimum was proposed. However, the result only applies to the continuous case (without proof). With the importance of digital control, discrete-time problems are important as well. In this paper, we consider discrete-time dynamic Stackelberg games. We design an incentive policy for the leader, while the follower s rational reaction guarantees system stability, using a no-memory state feedback representation. For simplicity, pure state feedback strategies in LQ games are investigated. We investigate the finite-time case in Section II. Then, we extend the problem to the infinite-time case in Section III with stabilization consideration. A proposition for two-person discrete-time LQ incentive state feedback Stackelberg games is given and proven in Section III. We develop a numerical example in Section IV to illustrate the effectiveness of the incentive policy. Finally, we draw conclusions and enumerate some possible future expansions in Section V. B. Solution Since the ultimate goal of the leader is to induce the follower to act in a way that the leader s team optimum is achieved, the team-optimal solution is calculated first as a basis for any further derivations. After that, the rational reaction of the follower is calculated under the incentive strategy of the leader. The leader chooses incentive matrix such that the optimal reaction of the follower is. 1) Team-Optimal Solution: In the team optimization part, both of the players optimize the leader s objective. Using standard optimal control theory, the team-optimal control is II. FINITE-TIME CASE A. Problem Formulation Consider a linear discrete-time system described as (3) where (1) (4) where is the state vector; and for are the control or decision vectors chosen by Players 1 and 2, respectively. We assume that each player has a quadratic cost function Similarly, the team-optimal control where is (5) where subscripts represent different players, respectively; is symmetric and positive semi-definite matrix, and and are symmetric positive definite matrices for any time step. The dimensions of each matrix or vector are indicated as where We assume that each player only has access to perfect state information. At time step, the information available to the players is and. Each player chooses his strategy from the space of admissible strategies, such that it minimizes its objective through the realization for. Our goal is to introduce an incentive strategy that will achieve the leader s team optimum under certain constraints. We call the corresponding leader team-optimal controls of the leader and follower and, respectively, and the state trajectory. Without loss of generality, we assume that Player 1 is the leader. (2) with matrix satisfying the following recursive equation and boundary condition: The associated team-optimal state trajectory is 2) Incentive Feedback Strategy: After obtaining the team optimum of the leader, let us now investigate how the follower can be induced to cooperate so that the optimum reaction control for minimizing is exactly, resulting in and. Assume that the leader uses the following incentive strategy: The problem is to find a sequence of matrices team-optimal solution of the leader is achieved. (6) (7) (8) (9) (10), so that the

3 474 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL. 32, NO. 4, JULY 2002 The follower optimizes his own objective function From the state equation where is given by (10). First, form the Hamiltonian (11) Using the minimum principle we obtain the expression for (20) in terms of with boundary condition and (12) (13) Substituting (21) and (16) into (12) we obtain (21) (14) (15) Assume that takes the form (16) where and are matrices of proper dimensions, then (22) Suppose that condition holds: (17) can be chosen such that the following Since the above condition is true for any initial values of and, the corresponding coefficients of and on both sides of the equation are equal. For the term (18) (This gives rise to one of the conditions of Proposition 1 in Section III.) Then, can be related to by (19) (23)

4 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL. 32, NO. 4, JULY For the term By applying the boundary condition (13) on (16), we obtain the boundary conditions on (29) Substituting (24) into (23) results in an equation without (24) Equation (29) is valid for any value of, therefore (30) Thus (25) (31) Now let us consider the effect of the matrix. Does the constraint on given by (24) affect the follower s control? The answer is No. Substituting (21) into (19), we obtain the follower s control as (26) Note that when, (10) gives and (26) results in. In order to have a well-posed problem, the initial value of the true state should be equal to that of the desired state, i.e.,. This yields From the state equation, we obtain. Similarly, we can get,, for,and,for.thus, for any stage, the term remains zero. Hence, the value of does not affect the follower s control. Furthermore, note that a crucial property of the follower s optimal control is that under, the follower s reaction is. Hence, any term may be added to (26) as long as still implies. A special case is to change into, where can be any function such that when. If is chosen as, where is any matrix such that the system is asymptotically stable, the resulting control of the follower is still optimal. Also, can be added to the right-hand side of (26) III. INFINITE-TIME CASE A. Problem Formulation For the infinite-time case, the system matrices in the state equation and the weighing matrices in the objective functions are assumed to be time-invariant, i.e., the system described by (1) and (2) becomes with the objective functions (32) (33) with similar constraints on the weighting matrices,, and as described in Section II. As time goes to infinity, assume all the matrices converge: 1) Proposition 1: If there exists a matrix such that: a) is stabilizable; b) ; where is constrained by with, and satisfying then the leader s strategy where is defined as (27) and the follower s strategy Hence, has no effect on the follower s optimal control. (28) constitute an incentive state feedback Stackelberg equilibrium for any. Furthermore, can be chosen by the follower to make the system stable.

5 476 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL. 32, NO. 4, JULY ) Proof: As time goes to infinity, with all the relevant matrices convergent, (7) becomes Equation (18) becomes where Equation (25) becomes (34) (35) (36) (37) (38) If the leader can find a matrix that satisfies all of the above equations, then the leader s control and the follower s control (39) (40) constitute a state feedback Stackelberg equilibrium pair that leads to the leader s team optimum, where can be any matrix that asymptotically stabilizes the system. This completes our proof. The foregoing algorithm procedure is summarized as follows: 1. Calculate through (34). 2. Calculate using (35). 3. Calculate through (38). 4. If the system is not stabilizable, then change to where satisfies: and go back to Step 3. If the system is stabilizable, continue to Step Pick that asymptotically stabilizes the system. IV. NUMERICAL EXAMPLE A. Simplified Homeland Security Model A numerical example is given in this section to illustrate the effectiveness of the strategy derived earlier. We consider a simplified linear discrete-time model describing the interplay between maintaining a certain level of homeland security and a healthy level of tourism. International tourism is the world s largest item of trade and represents a major industry in over 100 nations [11]. Recent attacks by terrorists have had a negative impact on travel patterns and the economies of countries. With increased focus on security, there is a dampening effect on tourism. However, security needs to be maintained. The formulation we use here is a rather simplified model of the interplay between two groups of decision makers: the tourism industry and the government. We assume that tourism in a country is affected by the policy of the tourism industry as a whole and the policy of the government to maintain some level of security. The problem is modeled as an LQ feedback Stackelberg game problem. Both players assume a linear relationship between the number of tourists and a surrogate number to represent a level of security to mitigate threat. In the steady state,, where is a positive number and is determined by the steady state values of,, and. Player 1 wants to be small, while Player 2 wants to be large. Thus, Player 1 will use a cost function assuming a level of security that has a small value while Player 2 will use a cost function assuming a level of security that has a large value with, and, being parameters beyond the control of either player. In formulating their own objectives, both players have a budget expectation on the expenses spent on the efforts they undertake. The expenses with regard to tourism are twofold for each player. For Player 1, it undertakes investment in order to increase the number of tourists. On the other hand, it spends money on enforcement of security in order to reduce threat and thus reduce. For Player 2, in an effort to increase,it invests to increase the security level directly, and which has an effect of directly decreasing. (If there is a public perception of increasing, there is a perception of a greater threat, which dampens tourism.) The numbers and are the state variables; and and are the control variables for Player, respectively. 1) State Equations: The number increases with tourism investments, but decreases with investments for increasing the security level. On the other hand, increases with a flourishing tourism and direct investments in security, but decreases with security enforcement activities. With consideration of natural decay rates of both and, the state equations for the linear model are All of the matrix (41) (42) s are positive numbers, which constitute the system 2) Cost Functions: Assuming an infinite-time planning period, the objective functions of Players 1 and 2 are (43) (44)

6 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL. 32, NO. 4, JULY where the coefficients define different linear relationships between and. It is clear that the larger the value of is, the larger is, as increases. stands for the control variables of Player 1; stands for the control variables of Player 2. and are the budget expectation on investment and enforcement activities of Players 1 and 2, respectively. Since the expectations of the two players are different, there are conflicts. In this example, we first assume that Player 1 is the leader and Player 2 is the follower. Then, we assume that Player 2 is the leader and Player 1 is the follower. All other specifications are the same. B. Solution Before using the algorithm procedure discussed in Section III, we need to change the model into a standard regulator game described by (1) and (2). First, we will calculate the steady-state values of and.in order to have a well-posed problem, the coefficients are set to guarantee that the expected relationship between and could be reached in the steady state. As time goes to infinity Denote then (53) (54) From the state equation (45) (46) we solve for and (47) (48) Note that the steady state values of and depend on the system as well as the budget of both players. With the knowledge of the investment and enforcement budget of the follower the leader can make its own budget decision on the investment and enforcement activities, so that the steady state values of and will go to the desired values. From Player 1 s point of view, there should be a small and a large. Let (49) (50) (55) Note that the constant term in (55) disappears because the coefficients and are chosen in the following way. As time goes to infinity, the states and controls are to be regulated to zero value. This requires that the coefficients and satisfy (56) (57) This will make the constant term in (55) vanish. Similarly, we can obtain From which, and can be expressed in terms of and (51) (52) (58) Equations (55) and (58) are the new state equations under the definition given in (49), (50), (53), and (54).

7 478 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL. 32, NO. 4, JULY 2002 Define (59) (60) (61) (62) Fig. 1. Surrogate for tourists T versus time step n, with Player 1 as leader. (63) (64) then the system is described by (65) with cost functions (66) (67) These are exactly the standard forms discussed in the previous sections. Now we are ready to use the algorithm procedure given in Section III to solve the problem. The numerical values used are The weighting coefficients in the objective functions are chosen to be Fig. 2. leader. Surrogate security level S versus time step n, with Player 1 as Plots of the optimal state trajectory as well as the optimal controls are given in Figs. 1 4, where Player 1 is the leader. No units are specified, and the numerical values should be viewed in relative terms. Next, we consider the case when Player 2 is the leader. All parameter values are the same as before. Figs. 5 8 show corresponding plots for the case when Player 2 is the leader. Note that Player 2 as leader allows a much higher level of security at the start than in the case when Player 2 is the follower. V. CONCLUSIONS AND FURTHER REMARKS A. Conclusions In this paper, we developed an incentive strategy for discrete-time LQ state feedback Stackelberg games, with stability guaranteed by the follower. Sufficient conditions were given to find the incentive matrix. A feasible calculation procedure and a numerical example were discussed to illustrate the effectiveness of our design.

8 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL. 32, NO. 4, JULY Fig. 3. Investment and enforcement of Player 1 versus time step n, with Player 1 as leader. Fig. 6. leader. Surrogate security level S versus time step n, with Player 2 as Fig. 4. Investment and enforcement of Player 2 versus time step n, with Player 1 as leader. Fig. 7. Investment and enforcement of Player 1 versus time step n, with Player 2 as leader. B. Further Remarks 1) One important aspect of the incentive feedback Stackelberg solution presented in this paper is that it is also a feedback Nash equilibrium solution for the dynamic game under consideration, since it satisfies the following two inequalities simultaneously: Fig. 5. Surrogate for tourists T versus time step n, with Player 2 as leader. 2) Although sufficient conditions were given to find the matrix, we could not guarantee that this could always be found. No definite calculation procedure was proposed due to the complication induced by the matrix equations. It would be more convenient to express the conditions in Section III directly in terms of the parameters of the problem, but unfortunately, no such general formulation is yet available. Given the value of,

9 480 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL. 32, NO. 4, JULY 2002 Fig. 8. Investment and enforcement of Player 2 versus time step n, with Player 2 as leader. [12] G. P. Papavassilopoulos and J. B. Cruz, Jr., Sufficient condition for Stackelberg and Nash strategies with memory, J. Optim. Theory Appl., vol. 31, pp , June [13] B. Tolwinski, Closed-loop Stackelberg solution to multistage linearquadratic games, J. Optim. Theory Appl., vol. 34, pp , Aug [14] T. Basar and A. Haurie, Feedback equilibria in differential games with structural and modal uncertainties, in Advances in Large Scale Systems, J. B. Cruz, Jr., Ed. Greenwich, CT: JAI, 1984, vol. 1, pp [15] F. Kydland, Noncooperative and dominant player solutions in discrete dynamic games, Int. J. Econ. Rev., vol. 16, pp , Feb [16] T. Basar, A. Haurie, and G. Ricci, On the dominance of capitalistic leadership in a feedback Stackelberg solution of a differential game model of capitalism, J. Econ. Dyn. Contr., vol. 9, pp , Sept [17] J. B. Cruz, Jr., Leader follower strategies for multilevel systems, IEEE Trans. Automat. Contr., vol. AC-23, pp , Apr [18] B. F. Gardner and J. B. Cruz, Jr., Feedback Stackelberg strategy for a two-player game, IEEE Trans. Automat. Contr., vol. AC-22, pp , Apr [19], Feedback Stackelberg strategy for M-level hierarchical games, IEEE Trans. Automat. Contr., vol. AC-23, pp , June [20] V. R. Saksena and J. B. Cruz, Jr., Optimal and near-optimal incentive strategies in the hierarchical control of Markov chains, Automatica, vol. 21, no. 2, pp , in order for to be solvable in the general case, we need the dimension constraints:, which means that Player 1 must have as many control variables as there are state variables. 3) What we have done was based on no-memory state feedback information. What if utilization of delayed state information were allowed? An approach might be to reformulate the feedback problems in terms of a general memory structure. For example, the feedback control may be a function of the states at times,, and. However, this will dramatically increase the dynamic controller dimension, and thus may be impractical. Sufficient conditions for continuous-time Stackelberg and Nash strategies with memory are discussed in [12]. REFERENCES [1] H. von Stackelberg, The Theory of the Market Economy. London, U.K.: Oxford Univ. Press, Transl: A.T. Peacock. [2] C. I. Chen and J. B. Cruz, Jr., Stackelberg solution for two-person games with biased information patterns, IEEE Trans. Automat. Contr., vol. AC-17, pp , May [3] M. Simaan and J. B. Cruz, Jr., On the Stackelberg strategy in nonzero-sum games, J. Optim. Theory Appl., vol. 11, no. 5, pp , [4], Additional aspects of the Stackelberg strategy in nonzero-sum games, J. Optim. Theory Appl., vol. 11, no. 6, pp , [5] Y. C. Ho, P. B. Luh, and G. Olsder, A control-theoretic view of incentives, Automatica, vol. 18, no. 1, pp , [6] M. A. Salman and J. B. Cruz, Jr., An incentive model of duopoly with government coordination, Automatica, vol. 17, no. 6, pp , [7] T. Basar and H. Selbuz, Closed-loop Stackelberg strategies with applications in the optimal control of multilevel systems, IEEE Trans. Automat. Contr., vol. AC-24, pp , Apr [8] M. A. Salman and J. B. Cruz, Jr., Team-optimal closed-loop Stackelberg strategies for systems with slow and fast modes, Int. J. Control, vol. 37, no. 6, pp , [9] Y.-P. Zheng, T. Basar, and J. B. Cruz, Jr., Stackelberg strategies and incentives in multiperson deterministic decision problems, IEEE Trans. Syst., Man, Cybern., vol. SMC-14, pp , Jan./Feb [10] T. Basar and G. J. Olsder, Dynamic Noncooperative Game Theory, 2nd ed. Philadelphia, PA: SIAM, [11] G. Feichtinger, R. F. Hartl, P. M. Kort, and A. J. Novak, Terrorism control in the tourist industry, J. Optim. Theory Appl., vol. 108, pp , Feb Ming Li was born in Puyang, China, on October 22, She received the dual B.S. degrees in automation and economics from Tsinghua University, Beijing, in 1999, and M.S.E.E. degree from The Ohio State University (OSU), Columbus, in From 1999 to 2001, she was a graduate research associate with the Department of Electrical Engineering, OSU. Since 2001, she has been with the Electronics Department of MPC Products Corporation, Skokie, IL. Jose B. Cruz, Jr. (M 57 SM 61 F 68 LF 95) received the B.S. degree in electrical engineering (summa cum laude) from the University of the Philippines in April 1953, the S.M. degree in electrical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, in June 1956, and the Ph.D. in electrical engineering from the University of Illinois, Urbana-Champaign, in October He is a currently Professor of electrical engineering at The Ohio State University (OSU), Columbus. Previously, he served as Dean of the College of Engineering at OSU from 1992 to 1997, Professor of electrical and computer engineering at the University of California, Irvine (UCI), from 1986 to 1992, and at the University of Illinois from 1965 to He was a Visiting Professor at MIT and Harvard University, Cambridge, in 1973 and Visiting Associate Professor at the University of California, Berkeley, in He served as Instructor at UP in , and Research Assistant at MIT from 1954 to He is the author or co-author of six books, 21 chapters in research books, and numerous articles in research journals and refereed conference proceedings. Dr. Cruz was elected as a member of the National Academy of Engineering (NAE) in He is also a Fellow of the American Association for the Advancement of Science (AAAS), elected 1989; recipient, Curtis W. McGraw Research Award of the American Society for Engineering Education (ASEE) 1972; recipient, Halliburton Engineering Education Leadership Award, 1981; Distinguished Member, IEEE Control Systems Society, designated in 1983; recipient, IEEE Centennial Medal, 1984; recipient, IEEE Richard M. Emberson Award, 1989; recipient, ASEE Centennial Medal, 1993; and recipient, Richard E. Bellman Control Heritage Award, American Automatic Control Council (AACC), In addition to membership in NAE, IEEE, ASEE, and AAAS, he is a member of the Philippine American Academy for Science and Engineering (Founding member, 1980, President 1982, and Chairman of the Board, ), Philippine Engineers and Scientists Organization (PESO), National Society of Professional Engineers, Sigma Xi, Phi Kappa Phi, and Eta Kappa Nu. He served as a member of the Board of Examiners for Professional

10 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL. 32, NO. 4, JULY Engineers for the State of Illinois, He served on various professional society boards and editorial boards, and he served as an officer of professional societies, including IEEE, where he was President of the Control Systems Society in 1979, Editor of the IEEE TRANSACTIONS ON AUTOMATIC CONTROL, a member of the Board of Directors from 1980 to 1985, Vice President for Technical Activities in 1982 and 1983, and Vice President for Publication Activities in 1984 and Currently he serves as Secretary of the Engineering Section of the American Association for the Advancement of Science (AAAS). Marwan A. Simaan (S 69 M 72 SM 79 F 88) received the Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign (UIUC) in 1972 and did postdoctoral work at the Coordinated Science Laboratory at the University of Illinois until In 1976, he joined the Department of Electrical Engineering at the University of Pittsburgh, Pittsburgh, PA, where he is currently the Bell of PA/Bell Atlantic Professor. He served as chair of the department from 1991 to He has held research and consulting positions in industry including the English Electric Leo-Marconi Computers Ltd.; Bell Telephone Laboratories; Shell Development Company; Gulf R&D Company; and ALCOA Laboratories. His research interests are mainly in the areas of control and signal processing. He has edited four books and written more than 225 articles in journals, books, conference proceedings and technical reports. He is coeditor of the Journal of Multidimensional Systems and Signal Processing (Kluwer) and a member of the editorial board of the Journal of Optimization Theory and Applications (Kluwer). Dr. Simaan is a member of the U.S. National Academy of Engineering and a Fellow of AAAS. He currently serves and has served on the editorial boards of a number of journals including the PROCEEDINGS OF THE IEEE, the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II, the IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING. He received three Best Paper Awards (1985, 1988, and 1999) and a Distinguished Alumnus Award from the Department of Electrical and Computer Engineering at UIUC in He is a member of AAAI, ASEE, and SEG. He is a Registered Professional Engineer in Pennsylvania and serves as an Electrical Engineering program Evaluator for the Accreditation Board for Engineering and Technology (ABET).