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 set of chapters overlaying contemporary advances in stochastic optimum regulate thought and algebraic platforms concept. Written via specialists of their respective fields, the chapters are thematically equipped into 4 parts:
* half I specializes in statistical regulate theory, the place the price functionality is seen as a random variable and function is formed via fee cumulants. during this admire, statistical keep watch over generalizes linear-quadratic-Gaussian and H-infinity control.
* half II addresses algebraic structures theory, reviewing using algebraic platforms 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 concentrate on the soundness of a discontinuous dynamical approach, approximate decentralized mounted modes, direct optimum adaptive regulate, and balance of nonlinear structures with restricted information.
* half IV covers engineering education and encompasses a detailed bankruptcy on theology and engineering, one among Sain's newest study interests.
The booklet should be an invaluable reference for researchers and graduate scholars in structures and keep an eye on, algebraic platforms conception, and utilized arithmetic. Requiring simply wisdom of undergraduate-level regulate and platforms concept, the paintings can be utilized as a supplementary textbook in a graduate direction on optimum keep watch over or algebraic structures theory.
Read or Download Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics: A Tribute to Michael K. Sain PDF
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During this e-book the writer analyzes and compares 4 heavily comparable difficulties, particularly linear programming, integer programming, linear integration, linear summation (or counting). the point of interest is on duality and the procedure is quite novel because it places integer programming in standpoint with 3 linked difficulties, and allows one to outline discrete analogues of recognized non-stop duality thoughts, and the explanation at the back of them.
This volume—dedicated to Michael ok. Sain at the get together of his 70th birthday—is a set of chapters overlaying fresh advances in stochastic optimum keep an eye on concept and algebraic platforms idea. Written through specialists of their respective fields, the chapters are thematically equipped into 4 parts:* half I specializes in statistical keep watch over conception, the place the fee functionality is considered as a random variable and function is formed via price cumulants.
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This ebook goals to supply a unified remedy of input/output modelling and of keep an eye on for discrete-time dynamical platforms topic to random disturbances. the consequences offered are of extensive applica bility up to the mark engineering, operations examine, econometric modelling and plenty of different parts. There are detailed techniques to mathematical modelling of actual structures: an instantaneous research of the actual mechanisms that include the method, or a 'black field' technique in response to research of input/output facts.
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Additional info for Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics: A Tribute to Michael K. Sain
Thus utility functions can be viewed as a characterization of a decision maker in some sense. The problem of selecting an optimal decision is reduced to the problem of maximizing the expected value of the utility function, U . The utility function can be determined experimentally, or we can use one of the known utility functions. Most utility functions are convex, which implies risk-aversive behavior of a decision maker. In classical LQG optimal control we can view the cost function as having a quadratic utility function.
For μ = 0, the disutility function, DMCV (J), describes a risk-neutral problem. Proof. The disutility function becomes DMCV = λ J − λ M, which is a linear function. Thus by definition, this is a risk-neutral case. ✷ Note that we may also use the first three cumulants and define the disutility function as D3CC (J) = μ1 (J − M) + μ2(J − M)2 + μ3 (J − M)3 . (69) In fact, we could define any linear combination of cumulants, but then we will probably have to place more stringent conditions on J for the utility function to be convex or concave.
Sain, B. F. , and S. R. Liberty, Generalized LQG Techniques for the Wind Benchmark Problem, Special Issue of ASCE Journal of Engineering Mechanics on the Structural Control Benchmark Problem, Vol. 130, No. 4, April 2004. K. D. Pham, M. K. Sain, and S. R. Liberty, Cost Cumulant Control: StateFeedback, Finite-Horizon Paradigm with Application to Seismic Protection, Special Issue of Journal of Optimization Theory and Applications, Edited by A. Miele, Kluwer Academic/Plenum Publishers, New York, Vol.
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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