Frequency Limited Adaptive Control Using a Quadratic Stability Framework: Stability and Convergence

Model Reference Adaptive Control systems have been receiving a lot of interest in the controls community because they offer the ability to handle larger amounts of uncertainty than linear control approaches. In theory, one usually wants the adaptive control law to adapt as fast a possible to obtain the best performance. However, this can inject high frequency signals into the control channels. These high frequency signals can destabilize unmodeled dynamics and exceed actuator performance limits. Experience suggests that inserting a filter in the control loop can attenuate these effects and this has recently been explored quite a bit in the literature by using the small-gain theorem to prove stability. It is well known that the small-gain theorem leads to conservative results. This paper presents a completely new theoretical framework for analyzing a filtered adaptive control signal using quadratic stability arguments instead. The limiting conditions on quadratic stability can be determined using algorithms developed in a companion paper to this one. Simulations examples illustrate that the new framework potentially captures the stability limit less conservatively than existing results.