H∞-Optimal Control of Singularly Perturbed Systems with Sampled-State Measurement
One of the important recent developments in control theory has been the recognition of the close relationship that exists between H ∞-optimal control problems, (originally formulated in the frequency domain  , and then extended to state space formulations      ) and a class of linear-quadratic differential games     , which has not only led to simpler derivations of existing results on the former, but also enabled us to develop worst-case (H ∞-optimal) controllers under various information patterns, such as (in addition to perfect and imperfect state measurements) delayed state and sampled state measurements  . An up-to-date coverage of this relationship and the derivation of H ∞-optimal controllers under different information patterns can be found in the recent book , which also contains an extensive list of references on the topic.
KeywordsDifferential Game Conjugate Point Disturbance Input Fast Subsystem Slow Subsystem
Unable to display preview. Download preview PDF.
- B. A. Francis, A Course in H ∞ Control Theory, vol. 88 of Lecture Notes in Control and Information Sciences. New York, NY: Springer-Verlag, 1987.Google Scholar
- A. A. Stoorvogel, The H∞ Control Problem: A State Space Approach. Prentice Hall, 1992.Google Scholar
- T. Başar, “A dynamic games approach to controller design: Disturbance rejection in discrete time,” in Proc. IEEE 29th Conf. on Decision and Control, (Tampa, FL), pp. 407–414, December 13–15, 1989. Also appeared in the IEEE Transactions on Automatic Control, vol. 36, no. 8, pp. 936–952, August 1991.Google Scholar
- T. Başar, “Game theory and H∞-optimal control: The continuous-time case,” in Differential Games: Developments in Modelling and Computation, Springer-Verlag, August 1991. R. P. Hamalainen and H. K. Ehtamo, eds. Lecture Notes in Control and Information Sciences, vol. 156, pp. 171–186.Google Scholar
- D. Limebeer, B. Anderson, P. Khargonekar, and M. Green, “A game theoretic approach to H∞ control for time varying systems,” in Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems, (Amsterdam, The Netherlands), 1989.Google Scholar
- T. Başar and P. Bernhard, H∞-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Boston, MA: Birkhäuser, 1991.Google Scholar
- Z. Pan and T. Başar, “H∞-optimal control for singularly perturbed systems. Part I: Perfect state measurements,” Automatica, vol. 29, March 1993.Google Scholar
- Z. Pan and T. Başar, “H∞-optimal control for singularly perturbed systems. Part II: Imperfect state measurements,” in Proceedings of the 31st IEEE Conference on Decision and Control, (Tucson, AZ), pp. 943–948, December 1992.Google Scholar
- Z. Pan and T. Başar, “A tight bound for the H∞ performance of singularly perturbed systems,” CSL Report, University of Illinois, Urbana, IL, March 1992.Google Scholar