The Optimal Adaptive Control Law for a Linear Plant with Unknown Input Gains

摘要

In an adaptive control system the function of an input to the plant is dual in nature-control of the plant to yield desired outputs, and testing of the plant so that knowledge gained about it can be used to reduce future error. Furthermore, it is often found that the input which is best for immediate control is usually not best for investigation and vice versa. Thus, to find an optimal control law, one must find that coordination of control and investigation which best satisfies the performance criterion. Statistical decision theory is used in conjunction with dynamic programming to derive a dual control algorithm which optically coordinates these two requirements and for a multi-input, multi-output system. Usually, use of the dual control algorithms for determination of the optimal control leads to computational difficulties which are insurmountable. However, in this paper an explicit solution is found for a discrete-time system with unknown gains. (Author)