Time Invariant Optimal Control for Systems with Control Delay and Input Derivative

Abstract

In many physical systems, the mathematical model contains derivative of the input. The present paper considers optimization of such a model but in addition, for a delayed system, where only control is delayed. The problem is transformed to a usual one through a transformation. The optimization problem leads to two types of optimization: one infinite-time optimization after the delay period and another finite-time optimization within the delay interval where a quadratic tracking is solved; together these give rise to a time invariant control law. Some examples are illustrated to show the effect of input derivatives.

Indexing Terms:

• Optimal Control
• Time Delay
• Input Derivative