By Chang-Hee Won, Cheryl B. Schrader, Anthony N. Michel
This volume—dedicated to Michael okay. Sain at the party of his 70th birthday—is a suite of chapters masking contemporary advances in stochastic optimum keep an eye on concept and algebraic structures concept. Written via specialists of their respective fields, the chapters are thematically geared up into 4 parts:
* half I specializes in statistical keep watch over theory, the place the price functionality is considered as a random variable and function is formed via fee cumulants. during this appreciate, statistical keep watch over generalizes linear-quadratic-Gaussian and H-infinity control.
* half II addresses algebraic structures theory, reviewing using algebraic structures 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 soundness of a discontinuous dynamical method, approximate decentralized fastened modes, direct optimum adaptive keep watch over, and balance of nonlinear platforms with restricted information.
* half IV covers engineering education and encompasses a specific bankruptcy on theology and engineering, one in all Sain's most modern learn interests.
The e-book should be an invaluable reference for researchers and graduate scholars in platforms and keep an eye on, algebraic structures thought, and utilized arithmetic. Requiring merely wisdom of undergraduate-level keep watch over and structures conception, the paintings can be utilized as a supplementary textbook in a graduate path on optimum keep watch over or algebraic structures theory.
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Extra resources for Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics: A Tribute to Michael K. Sain
23) (24) Definition 1. A function M(t, x), from T × Rn to R+ , is an admissible mean cost function if it has continuous second partial derivatives with response to x and a continuous partial derivative with respect to t, and if there exists a continuous control law k such that V1 (t, x; k) = M(t, x) (25) for t ∈ T and x ∈ Rn . ∗ satisfies A minimal mean cost (MMC) control law kM ∗ V1 (t, x; kM ) = V1∗ (t, x) ≤ V1 (t, x; k), (26) ∗ . Clearly, M(t, x) ≥ V ∗ (t, x). for t ∈ T , x ∈ Rn , whenever k = kM 1 Definition 2.
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Ray and R. Stengel, A Monte Carlo Approach to the Analysis of Control System Robustness, Automatica, Vol. 29, No. 1, pp. 229–236, 1993. T. Runolfsson, The Equivalence Between Infinite-Horizon Optimal Control of Stochastic Systems with Exponential-of-Integral Performance Index and Stochastic Differential Games, IEEE Transactions on Automatic Control, Vol. 39, No. 8, pp. 1551–1563, 1994. A. P. Sage, Optimum Systems Control. , 1968. M. K. D Thesis, Department of Electrical Engineering and Coordinated Science Laboratory, University of Illinois, Urbana, IL, January 1965.
Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics: A Tribute to Michael K. Sain by Chang-Hee Won, Cheryl B. Schrader, Anthony N. Michel