An indirect adaptive control design with anti-windup compensation: Stability analysis

We combine an adaptive law with a control design including a Linear Quadratic (LQ) controller and a Linear Matrix Inequality (LMI) based anti-windup compensator using the certainty equivalence principle for asymptotically stable plants with saturation limits imposed on the control input. If the desired linear performance can be recovered for nominal systems subject to input saturation by implementing an LQ control augmented with an anti-windup compensator, our analysis on its adaptive counterpart reveals the fact that the perturbation terms due to plant parameter errors in the adaptive scheme do not cause any unbounded signals in the closed-loop, and the system remains stable. Continuous-time lumped Hurwitz systems with input saturation nonlinearities and unknown plant parameters can benefit from the resulting indirect adaptive control design.