Multiple Model Adaptive Control With Mixing

Despite the remarkable theoretical accomplishments and successful applications of adaptive control, the field is not sufficiently mature to solve challenging control problems where strict performance and robustness guarantees are required. Critical to the design of practical control systems for these challenging applications, and currently lacking in parameter estimation-based adaptive control schemes, is an approach that explicitly accounts for robust-performance and stability specifications. Towards this goal, this paper describes a robust adaptive control approach called
adaptive mixing control
that makes available the full suite of powerful design tools from LTI theory, e.g., mixed-μ synthesis. The stability and robustness properties of adaptive mixing control are analyzed. It is shown that the mean-square regulation error is of the order of the modeling error provided the unmodeled dynamics satisfy a norm-bound condition. And when the parameter estimate converges to its true value, which is guaranteed if a persistence of excitation condition is satisfied, the adaptive closed-loop system converges exponentially fast to a closed-loop system comprising the plant and some LTI controller that satisfies the control objective. A benchmark example is presented, which is used to compare the adaptive mixing controller with other adaptive schemes.