Approximation of Feedback Control Systems

Optimal feedback controls under stochastic uncertainty can be obtained in general by approximate methods only. In this chapter approximate feedback controls are obtained by Taylor expansion of the state function with respect to the gain matrix or the gain parameters. Since the state function is the solution of the state equation, hence, a first-order system of differential equations, corresponding systems of differential equations for the partial derivatives of the state function with respect to the gain matrix, the gain parameters, resp., can be obtained by partial differentiation of the state equation with respect to the gain matrix, the gain parameters. Corresponding approximate optimal stochastic feedback control problems are then derived.