Adaptive control of a class of nonlinear systems using multiple models

Abstract

A common approach to control complex dynamic systems is to design a set of controllers, each of which for a particular operating region or performance objective, and then to switch among the controllers in real time to achieve the overall control objective. Many physical systems are hybrid in the sense that they have continuous behaviors and discrete phenomena. Most nonlinear controllers are derived from the dynamic equations of the system. A single controller acting on a system works well if the system parameters remain fixed during the operation. To cope with the variation of the system parameters, adaptive control methods has been widely used. For a slowly varying system, adaptive controllers work very well by adapting unknown/varying parameters of the system. However, an adaptive controller consumes some time until it finds the optimal parameters when the system parameters undergo a step change. In this case, a large transient response is resulted during adaptation. Moreover, there are unavoidable large transient errors at the time of task variation. Task change has a similar effect on system dynamics; System dynamics undergoes changes when a different task is applied. For example, if a robot manipulator has to perform task 1, task 2, task 1, task 2, repeatedly in this order, an adaptive controller will always adapt itself to the new task, repeatedly, causing the system to forget the control skill acquired previously. Although task 1 is encountered for the second time, the adaptive controller recognizes it as a new task as the controller has already been adapted to task 2. However, if the dynamic parameters and control skills are stored for each task, this information can be utilized to recognize the tasks when the tasks encounter repeatedly at a later time. It also makes the system be able to cope with the repeating tasks quickly. In control system with multiple models, switching strategy and stability of the closed-loop system under switching are very im...