Abstract

A method is proposed for computing optimal nonlinear feedback control laws. It is shown that the feedback loop satisfies a system of quasi-linear partial differential equations. This system is of first order when the dimensions of the state and the control vector are the same. Hereby, it degenerates into algebraic equations when the performance index does not depend on the control. These important results offer new ways for determining optimal feedback laws. Connections with the Volterra series and the Hamilton-Jacobi-Bellman equation are treated. Some examples are given to illustrate the advantages of this method.

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