Synthesis of optimally sensitive control for systems with time-varying parameters†

Abstract

Recently, optimally sensitive controls have been synthesized for systems that contain uncertain constant parameters in the plant dynamics. In this paper the concept of optimally sensitive control is extended to a class of problems containing unknown time-varying parameters. The optimal sensitivity equations are derived and closed-loop controls are synthesized based on these equations. It is shown that for the class of problems considered the optimally sensitive control structure is equivalent to that control obtained from the second variational method of deterministic control theory. Several numerical examples are presented to illustrate the effectiveness of this technique for the closed-loop control of stochastic systems. The examples also point out that the optimally sensitive systems are relatively insensitive to error in the a priori statistics of the stochastic inputs.