Real-Time Optimal Control of Dynamical Systems

Abstract

A problem of synthesis of optimal feedbacks for linear and nonlinear control systems is under consideration. At first, based on fast algorithms of constructing optimal open-loop controls, an algorithm of calculating current values of optimal feedback in linear optimal control problem in real time is described. The idea of closed-loop solution is based on constructing a realization of optimal feedback in any concrete control process under unknown but bounded disturbances. The realization of the algorithm of closed-loop solution is oriented on fast corrections of optimal open-loop control subject to small variations of initial state. This is possible due to storage a small amount of additional information allowing to avoid the complete integration of primal or adjoint system. Then, this result is generalized for piecewise linear systems and for control systems with nonlinear dynamics. In the case of piecewise linear systems, algorithms are supplemented by procedures of parametric optimization. In addition, asymptotic methods of correcting solutions for linear or piecewise linear optimal control problems are used for nonlinear systems. Efficiency of described algorithms is illustrated by examples.