Topic
Optimal control
About: Optimal control is a research topic. Over the lifetime, 68020 publications have been published within this topic receiving 1280283 citations.
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Papers
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01 Jan 1967TL;DR: This complete and authoritative presentation of the current status of control theory offers a useful foundation for both study and research.
Abstract: : This complete and authoritative presentation of the current status of control theory offers a useful foundation for both study and research. With emphasis on general nonlinear differential systems, the book is carefully and systematically developed from elementary motivating examples, through the most comprehensive theory, to the final numerical solution of serious scientific and engineering control problems. The book features reviews of the most recent researches on processes described by partial differential equations, functional- differential, and delay-differential equations; the most recent treatment of impulse controllers, bounded rate controllers, feedback controllers, and bounded phase problems; and many unpublished new research results of the authors. In addition to an exhaustive treatment of the quantitative problems of optimal control, the qualitative concepts of stability, controllability, observability, and plant recognition receive a complete exposition. (Author)
2,035 citations
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01 Jan 2000TL;DR: In this paper, a Markov chain is used to approximate the solution of the optimal stochastic control problem for diffusion, reflected diffusion, or jump-diffusion models, and a general method for obtaining a useful approximation is given.
Abstract: A powerful and usable class of methods for numerically approximating the solutions to optimal stochastic control problems for diffusion, reflected diffusion, or jump-diffusion models is discussed. The basic idea involves uconsistent approximation of the model by a Markov chain, and then solving an appropriate optimization problem for the Murkoy chain model. A general method for obtaining a useful approximation is given. All the standard classes of cost functions can be handled here, for illustrative purposes, discounted and average cost per unit time problems with both reflecting and nonreflecting diffusions are concentrated on. Both the drift and the variance can be controlled. Owing to its increasing importance and to lack of material on numerical methods, an application to the control of queueing and production systems in heavy traffic is developed in detail. The methods of proof of convergence are relatively simple, using only some basic ideas in the theory of weak convergence of a sequence of probabi...
1,767 citations
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01 Nov 2001TL;DR: The root locus method frequency domain analysis classical control design methods state-space design methods optimal control digital control system identification adaptive control robust control fuzzy control is presented.
Abstract: Introduction to automatic control systems mathematical background mathematical models of systems classical time-domain analysis of control systems state-space analysis of control systems stability the root locus method frequency domain analysis classical control design methods state-space design methods optimal control digital control system identification adaptive control robust control fuzzy control. Appendices: Laplace transform tables the Z-transform transform tables.
1,767 citations
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TL;DR: By relaxing the definition of quadratic stability, it is shown how to construct logarithmic quantizers with only finite number of quantization levels and still achieve practical stability of the closed-loop system.
Abstract: We show that the coarsest, or least dense, quantizer that quadratically stabilizes a single input linear discrete time invariant system is logarithmic, and can be computed by solving a special linear quadratic regulator problem. We provide a closed form for the optimal logarithmic base exclusively in terms of the unstable eigenvalues of the system. We show how to design quantized state-feedback controllers, and quantized state estimators. This leads to the design of hybrid output feedback controllers. The theory is then extended to sampling and quantization of continuous time linear systems sampled at constant time intervals. We generalize the definition of density of quantization to the density of sampling and quantization in a natural way, and search for the coarsest sampling and quantization scheme that ensures stability. Finally, by relaxing the definition of quadratic stability, we show how to construct logarithmic quantizers with only finite number of quantization levels and still achieve practical stability of the closed-loop system.
1,703 citations