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

ISBN-10: 0817647945

ISBN-13: 9780817647940

This volume—dedicated to Michael ok. Sain at the get together of his 70th birthday—is a set of chapters masking contemporary advances in stochastic optimum regulate idea and algebraic structures conception. Written by way of specialists of their respective fields, the chapters are thematically prepared into 4 parts:

* half I specializes in statistical keep an eye on theory, the place the associated fee functionality is considered as a random variable and function is formed via price cumulants. during this appreciate, statistical keep an eye on 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 structures, and zeros in linear time-delay systems.

* half III discusses advances in dynamical structures 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 restricted information.

* half IV covers engineering education and encompasses a specified bankruptcy on theology and engineering, one in all Sain's most up-to-date examine interests.

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

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Additional info for Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics: A Tribute to Michael K. Sain

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124–131, 1973. M. R. James, Asymptotic Analysis of Nonlinear Stochastic Risk-Sensitive Control and Differential Games, Mathematics of Control, Signals, and Systems, 5, pp. 401–417, 1992. M. R. James, J. S. Baras, and R. J. Elliott, Risk-Sensitive Control and Dynamic Games for Partially Observed Discrete-Time Nonlinear Systems, IEEE Transactions on Automatic Control, AC-39, No. 4, pp. 780–792, 1994. R. E. Kalman, Contributions to the Theory of Optimal Control, Bol. de Soc. Math. Mexicana, p. 102, 1960.

D. Pham, M. K. Sain, and S. R. Liberty, Cost Cumulant Control: StateFeedback, Finite-Horizon Paradigm with Applications to Seismic Protection, Special Issue of Journal of Optimization Theory and Applications, Edited by A. Miele, Kluwer Academic/Plenum Publishers, New York, Vol. 115, No. 3, pp. 685–710, December 2002. K. D. Pham, M. K. Sain, and S. R. Liberty, Infinite Horizon Robustly Stable Seismic Protection of Cable-Stayed Bridges Using Cost Cumulants, Proceedings American Control Conference, Boston, MA, USA, pp.

Then the optimal state-feedback kCC control is achieved by the gain k K ∗ (α ) = −R−1 (α )BT (α ) ∑ μˆ r H ∗ (α , r), α ∈ [t0 ,tF ], (35) r=1 where the real constants μˆ r = μi /μ1 represent parametric control design freedom and {H ∗ (α , r) ≥ 0}kr=1 are symmetric solutions of the backward differential equations d ∗ H (α , 1) = −[A(α ) + B(α )K ∗(α )]T H ∗ (α , 1) − H ∗(α , 1)[A(α ) + B(α )K ∗ (α )] dα −K ∗T (α )R(α )K ∗ (α ) − Q(α ), d ∗ H (α , r) = −[A(α ) + B(α )K ∗(α )]T H ∗ (α , r) − H ∗ (α , r)[A(α ) + B(α )K ∗ (α )] dα r−1 2r!

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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

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