Transient Performance Bounds for Adaptive Control

In this paper, we develop a methodology to understand and analyze transient performance in adaptive switching control systems that employ hysteresis type switching algorithms. In particular, we quantify the transient performance in terms of percent overshoot bound of the cost function (performance metric). The overshoot essentially measures the amount by which the achieved cost exceeds the robust cost, which is defined as the supremum of minimum controller cost over all possible input-output data and time. Furthermore, we highlight the parameters that can reduce this bound, which in turn improves the transient performance of the system. The efficacy of the proposed ideas are validated using simulation examples.