A Structural Condition for Model Reference Adaptive Control Systems to Enforce Partial Performance Constraints

A fundamental challenge in model reference adaptive control synthesis is to achieve a- priori, user-defined performance guarantees. To this end, a new architecture entitled set- theoretic model reference adaptive control has been recently developed, where the key feature of this control synthesis methodology is to allow the weighted Euclidean norm of the system error vector, which represents the error between the state vector of an uncertain dynamical system and the state vector of a reference model (capturing a desired closed-loop system performance), to be less than a-priori, user-defined scalar performance bound. Although this architecture has the capability to enforce performance constraints on the entire system error vector, this vector can contain, for example, system error states resulting from internal compensator dynamics or simply a subset of vehicle dynamics that one does not necessarily need to enforce any performance constraints. Motivated from this standpoint, this paper presents a structural condition that allows the set-theoretic model reference adaptive control architecture to enforce partial performance constraints — enforcing performance constraints to a desired subset of the system error vector when this condition holds. An illustrative numerical example is also presented on an aircraft short period dynamics to complement the proposed theoretical contribution.