Adaptive Output Feedback Design Using Asymptotic Properties of LQG/LTR Controllers

This technical note introduces an observer-based adaptive output feedback tracking control design for multi-input-multi-output dynamical systems with matched uncertainties. The reported methodology exploits asymptotic behavior of LQG/LTR regulators. Sufficient conditions for closed-loop stability and uniform ultimate boundedness of the corresponding tracking error dynamics are formulated. This method is valid for systems whose nominal linearized dynamics are controllable and observable. We assume that the number of the system measured outputs (sensors) is greater than the number of the control inputs (actuators) and that the system output-to-input matrix product has full column rank. In this case, the system can be “squared-up” (i.e., augmented) using pseudo-control signals to yield relative degree one minimum-phase dynamics. Since it is known that the “squaring-up” problem is solvable for any controllable observable triplet (A, B, C), the proposed design is applicable to systems whose regulated output dynamics may be non-minimum phase or have a high relative degree. A simulation example is presented to demonstrate key design features.