Nonstationary discrete-time deterministic and stochastic control systems: Bounded and unbounded cases |
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Authors: | Xianping Guo |
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Affiliation: | a The School of Mathematics and Computational Science, Zhongshan University, Guangzhou 510275, PR Chinab Department of Economics, Universidad Carlos III de Madrid, Spainc Mathematics Department, CINVESTAV-IPN, A. Postal 14-740, México D.F. 07000, Mexico |
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Abstract: | This paper is about nonstationary nonlinear discrete-time deterministic and stochastic control systems with Borel state and control spaces, with either bounded or unbounded costs. The control problem is to minimize an infinite-horizon total cost performance index. Using dynamic programming arguments we show that, under suitable assumptions, the optimal cost functions satisfy optimality equations, which in turn give a procedure to find optimal control policies. We also prove the convergence of value iteration (or successive approximations) functions. Several examples illustrate our results under different sets of assumptions. |
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Keywords: | Discrete-time control systems Time-nonhomogeneous systems Time-varying systems Nonlinear systems Nonstationary dynamic programming |
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