Abstract
This paper presents an approach for approximate solution of the target control problem for a class of nonlinear systems on a finite time interval. The main idea is to use a comparison principle from dynamic programming theory together with a special class of piecewise affine value functions for the piecewise linearized form of the original system of ODEs. Two cases are considered: with continuous value function and with discontinuous one. The resulting feedback control functions are also piecewise affine, continuous or discontinuous respectively. For both cases the theorems on sufficient conditions for solving the feedback control problem are formulated and proved. The appropriate computational procedures complement theoretical results.
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