HJB-INEQUALITIES IN ESTIMATING REACHABLE SETS OF A CONTROL SYSTEM UNDER UNCERTAINTY

Tatiana F. Filippova     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108, Russian Federation)

Abstract


Using the technique of generalized inequalities of the Hamilton--Jacobi--Bellman type, we study here the state estimation problem for a control system which operates under conditions of uncertainty and nonlinearity of a special kind, when the dynamic equations describing the studied system  simultaneously contain the different forms of nonlinearity in state velocities. Namely, quadratic functions and uncertain matrices of state  elocity coefficients are presented therein. The external ellipsoidal bounds for reachable sets are found, some approaches which may produce internal estimates for such sets are also mentioned. The example is included to illustrate the result.


Keywords


Control, Nonlinearity, Uncertainty, Ellipsoidal calculus, State estimation

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References


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DOI: http://dx.doi.org/10.15826/umj.2022.1.004

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