Abstract
In this paper, the decision making problem in continuoustime dynamic systems is considered for the situation with two decision makers and a hierarchical decision structure. The leader-follower strategy is studied. To implement the leader's strategy, we propose to use a sliding mode approach, which allows the leader to constrain the state of the system within some manifold of the state space and forces the follower to choose the strategy preferable for the leader. The corresponding sliding manifolds are derived from the classical variational problem formulation for a class of systems whose right-hand side is affine with respect to the two control inputs. Numerical examples are considered with simulations to illustrate the technique.
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References
Von Stackelberg, H.,The Theory of Market Economy, Oxford University Press, Oxford, England, 1952.
Chen, C. I., andCruz, J. B., Jr.,Stackelberg Solution for Two-Person Games with Biased Information Patterns, IEEE Transactions on Automatic Control, Vol. 17, No. 6, pp. 791–797, 1972.
Basar, T., andSelbuz, H.,Closed-Loop Stackelberg Strategies with Applications in the Optimal Control of Multilevel Systems, IEEE Transactions on Automatic Control, Vol. 24, No. 2, pp. 166–179, 1979.
Zheng, Y. P., Basar, T., andCruz, J. B., Jr.,Stackelberg Strategies and Incentives in Multiperson Deterministic Decision Problems, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 14, No. 1, pp. 10–23, 1984.
Tolwinski, B.,Closed-Loop Stackelberg Solution to a Multistage Linear-Quadratic Game, Journal of Optimization Theory and Applications, Vol. 34, No. 4, pp. 485–499, 1981.
Ho, Y. C., Luh, P. B., andOlsder, G. J.,A Control-Theoretic View on Incentives, Automatica, Vol. 18, No. 2, pp. 167–179, 1982.
Utkin, V. I.,Sliding Modes and Their Application in Variable Structure Systems, MIR, Moscow, Russia, 1978.
DeCarlo, R. A., Zak, S. H., andMatthews, G. P. Variable Structure Control for Nonlinear Multivariable Systems: A Tutorial, IEEE Transactions on Automatic Control, Vol. 76, No. 3, pp. 212–232, 1988.
Drakunov, S. V., andUtkin, V. I.,Sliding Mode Control in Dynamic Systems, International Journal of Control, Vol. 55, No. 4, pp. 1029–1037, 1992.
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The authors wish to express their thanks to Dr. Vadim Utkin for his helpful discussions.
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Cruz, J.B., Drakunov, S.V. & Sikora, M.A. Leader-follower strategy via a sliding mode approach. J Optim Theory Appl 88, 267–295 (1996). https://doi.org/10.1007/BF02192172
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DOI: https://doi.org/10.1007/BF02192172