Continuous Suboptimal Control with Partial State Feedback

Abstract

It is well known that the classical optimal control method requires availability of all state variables of the controlled system for control feedback. This requires a measurable system, namely that all state variables may be obtained by measurement of sensors or by estimation of observers. However, some state variables in control feedback actually have a small effect on control performance. Neglecting these state variables does not greatly affect the performance of control. In this paper, we investigate a continuous suboptimal control method with partial-state feedback. First, the state variables with significant effect on the performance of control are determined using second-order sensitivity (i.e. second-order derivative of performance index with respect to control gain). Then, the suboptimal controller is designed utilizing only the determined state variables. Numerical examples are presented to demonstrate the application of the proposed control algorithm. It is shown that the relative importance of each state variable can be indicated clearly by the second-order sensitivity. The suboptimal control method presented is effective in reducing maximum responses of the structure. Furthermore, the continuous suboptimal control method may achieve almost the same level of control effectiveness as the discrete suboptimal control method.