Worst‐case control policies for (terminal) linear–quadratic control problems under disturbances |
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Authors: | E. Kostina O. Kostyukova |
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Affiliation: | 1. Department of Mathematics and Computer Science, University of Marburg, Hans‐Meerwein‐Strasse, 35032 Marburg, Germany;2. Institute of Mathematics, National Academy of Sciences of Belarus, Surganov str. 11, 220072 Minsk, Belarus |
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Abstract: | We consider linear control systems under uncertainties. For such systems we solve the problem of constructing worst‐case feedback control policies that are allowed to be corrected at m fixed intermediate time moments. We propose two types of the approximative control policies. All of them guarantee that for all admissible uncertainties the terminal system state lies in a prescribed neighborhood of a given state x* at a given final moment, and the value of the cost function does not exceed a given estimate. It is shown that computation of the estimate for each policy is equivalent to solving a corresponding convex mathematical programming (MP) problem with m decision variables. Based on the solution of the MP problem, we derive simple explicit rules (which can be easily implemented on‐line) for constructing the corresponding control policy in the original control problem. Copyright © 2009 John Wiley & Sons, Ltd. |
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Keywords: | linear– quadratic control problems worst‐case optimal feedback policies approximative feedback policies |
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