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      Stabilizing Value Iteration with and without Approximation Errors

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          Abstract

          Adaptive optimal control using value iteration (VI) initiated from a stabilizing policy is theoretically analyzed in various aspects including the continuity of the result, the stability of the system operated using any single/constant resulting control policy, the stability of the system operated using the evolving/time-varying control policy, the convergence of the algorithm, and the optimality of the limit function. Afterwards, the effect of presence of approximation errors in the involved function approximation processes is incorporated and another set of results for boundedness of the approximate VI as well as stability of the system operated under the results for both cases of applying a single policy or an evolving policy are derived. A feature of the presented results is providing estimations of the region of attraction so that if the initial condition is within the region, the whole trajectory will remain inside it and hence, the function approximation results will be reliable.

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          Adaptive critic designs

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            Policy Iteration Adaptive Dynamic Programming Algorithm for Discrete-Time Nonlinear Systems

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              Relaxing Dynamic Programming

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                Author and article information

                Journal
                2014-12-17
                2015-05-15
                Article
                1412.5675
                25ce56b8-c0b3-4dad-8e04-d574892269c7

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                In this revision the proof of Lemma 5 is updated. Initial submission date: 12/17/2014. (This study has overlaps on Theorem 6 and Lemma 5 with another work of the author available at arXiv:1412.6095)
                cs.SY math.OC stat.ML

                Numerical methods,Performance, Systems & Control,Machine learning
                Numerical methods, Performance, Systems & Control, Machine learning

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