Model reference adaptive control for state and input constrained linear systems

Abstract

State and input constraints are ubiquitous in all engineering systems and developing adaptive controllers for uncertain linear systems under pre-specified state and input constraints is a problem of fundamental interest. For uncertain linear systems, a computationally inexpensive control method is the model reference adaptive control (MRAC). Although MRAC controllers come with strong stability guarantees they do not guarantee system operation within the pre-defined state and input constraints. Several modifications of the MRAC framework have been proposed to address input constraints in uncertain linear systems. Considering the infeasibility of arbitrary reference trajectories, reference modification has been implemented in the case of input constraints in the literature. The resulting conditions on the reference and input signals are difficult to verify online. Similar results on state and input constraints together have also been proposed, albeit resulting in more complex and unverifiable conditions on the control. In this paper, we have developed a modified MRAC controller that can handle state and input constraints in uncertain linear systems. We have also provided easily verifiable conditions on the control and reference under which our stability results hold. Obtaining such a verifiable condition is crucial in practical implementations on safety–critical systems. A combination of reference modification and barrier Lyapunov methods in adaptive control are employed to arrive at these results.