Advances in Statistical Control, Algebraic Systems Theory, by Chang-Hee Won, Cheryl B. Schrader, Anthony N. Michel

By Chang-Hee Won, Cheryl B. Schrader, Anthony N. Michel

This volume—dedicated to Michael ok. Sain at the celebration of his 70th birthday—is a suite of chapters overlaying fresh advances in stochastic optimum keep an eye on idea and algebraic platforms conception. Written via specialists of their respective fields, the chapters are thematically geared up into 4 parts:

* half I makes a speciality of statistical regulate theory, the place the associated fee functionality is seen as a random variable and function is formed via expense cumulants. during this appreciate, statistical regulate generalizes linear-quadratic-Gaussian and H-infinity control.

* half II addresses algebraic platforms theory, reviewing using algebraic platforms over semirings, modules of zeros for linear multivariable platforms, and zeros in linear time-delay systems.

* half III discusses advances in dynamical platforms characteristics. The chapters specialize in the steadiness of a discontinuous dynamical approach, approximate decentralized mounted modes, direct optimum adaptive keep watch over, and balance of nonlinear structures with constrained information.

* half IV covers engineering education and features a particular bankruptcy on theology and engineering, certainly one of Sain's most modern study interests.

The e-book should be an invaluable reference for researchers and graduate scholars in platforms and keep watch over, algebraic platforms conception, and utilized arithmetic. Requiring in basic terms wisdom of undergraduate-level regulate and platforms concept, the paintings can be used as a supplementary textbook in a graduate direction on optimum regulate or algebraic platforms theory.

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D. Dissertation, Department of Electrical Engineering, University of Notre Dame, 2006. R. W. Diersing, M. K. -H. Won, Bi-Cumulant Games: A Generalization of H-infinity and H2/H-infinity Control, IEEE Transactions on Automatic Control, submitted, 2007. J. L. , 1953. J. Doyle, K. Glover, P. Khargonekar, and B. Francis, State-Space Solutions to Standard H2 and H∞ Control Problems, IEEE Transactions on Automatic Control, Vol. 34, No. 8, pp. 831–847, 1989. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, New York: Springer-Verlag, 1975.

Hendel, A Nash Game Approach to Mixed H2 /H∞ Control, IEEE Transactions on Automatic Control, Vol. 39, Number 1, pp. 69–82, January 1994. Minimum entropy H∞ control, Vol. 146 of Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1990. B. Øksendal, Stochastic Differential Equations, An Introduction with Applications, Second Edition, New York: Springer-Verlag, 1989. M. A. Peters and P. A. Iglesias, Minimum Entropy Control for Time-Varying Systems, Systems and Control: Foundations & Applications, Birkh¨auser, Boston, 1997.

This enlarged state vector grows at every new stage but retains the feature of being a discrete linear system with additive white Gaussian noise. The continuous time terminal LEQG problem is also briefly discussed in [SDJ74], and the solutions are achieved by taking a formal limit of the discrete case solutions. In 1976, Speyer considered the noisy measurement case again in continuous time, but with zero state weighting in the cost function [Spe76]. Unlike the method of the previous work [SDJ74], the Hamilton–Jacobi–Bellman equation was used to produce the solutions in [Spe76].

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