Adaptive inverse control of unmodeled stable SISO and MIMO linear systems

Adaptive-signal-processing techniques have been employed with great success in such applications as: system identi"cation, channel equalization, statistical prediction and noise/echo cancellation. From a mathematical point of view, there is little di!erence between these applications and the types of operations required by control systems to control a dynamical system. This paper presents an approach to control systems called adaptive inverse control in which adaptive-signal-processing techniques are used throughout. Adaptive inverse control comprises three simultaneous processes. The plant is automatically modeled using adaptive system identi"cation techniques. The dynamic response of the system is adaptively controlled using the resulting model and methods related to channel equalization. Adaptive disturbance canceling is performed using methods similar to noise canceling. The method applies directly to stable single-input single-output (SISO) and multi-input multi-output (MIMO) plants, and does not require an a priorimodel of the system. If the plant is unstable, it must "rst be stabilized using conventional feedback. This implies that at least a rudimentary model need be made if the plant is unstable. Once the plant is stabilized, adaptive inverse control may be applied to the stabilized system. Copyright 2002 John Wiley & Sons, Ltd.