Abstract
A method for synthesizing an optimal control that ensures the existence and stability of sliding modes for a system of nonlinear ordinary differential equations is proposed. This method uses an auxiliary optimal control problem. The solution gives a control in analytical form. It is proved that the trivial solution of the closed-loop system is Lyapunov stable. Application of the proposed method to linear and quasi-linear systems of equations is demonstrated, and an illustrative example is discussed.
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