Adaptive control of uncertain systems with gain scheduled reference models and constrained control inputs

This paper develops a new state feedback model reference adaptive control approach for uncertain systems with gain scheduled reference models in a multi-input multi-output (MIMO) setting with constrained control inputs. A single Lyapunov matrix is computed for multiple linearizations of the nonlinear closed-loop gain scheduled reference system, using convex optimization tools. This approach guarantees stability of the closed-loop gain scheduled reference model. Adaptive state feedback control architecture is then developed, and its stability is proven for the case with constrained control inputs. The resulting closed-loop system is shown to have bounded solutions with bounded tracking error, with the proposed stable gain scheduled reference model. Sufficient conditions for ultimate boundedness of the closed-loop system are derived. A semi-global stability result is proved with respect to the level of saturation for open-loop unstable plants while the stability result is shown to be global for open-loop stable plants. Simulation results show that the developed adaptive controller can be used effectively to control a degraded turboshaft engine for large thrust commands, with guaranteed stability and proper tracking performance.