Model-Reference Adaptive Control of Finite State Machines With Respect to States: A Matrix-Based Approach

To control a system with model uncertainty, adaptive control is an available approach. In this brief we investigate adaptive control in the field of finite state machines with respect to states. The task of the adaptive control is to synthesize an unfixed-parameter controller that invokes an adaptive law to realize a desired behavior. Especially, the adaptive law relies on a reference model. Thus, the title of model-reference adaptive control is adopted. We derive a sufficient and necessary condition for the existence of such an adaptive controller. Based on the condition, the corresponding controller design problem is resolved. As the design process, semi-tensor product of matrices is the core mathematical tool. Thus, for finite state machines with respect to states, model-reference adaptive control is incorporated into the framework of semi-tensor product of matrices.