Any classical control design starts by first satisfying stability and then looking towards satisfying transient requirements. Similarly, a Model Reference Adaptive Control (MRAC) Method should start with a stability analysis. Lyapunov function analysis is first used to justify the stability of the adaptive scheme. Next, a numerical study is conducted to predict the stability behavior of three different MRAC methods in the presence of large unanticipated changes in the dynamics of an aircraft. The Model reference adaptive control methods studied are: Method:1, an adaptive gain method; Method:2, a Neural Network (NN) approximation technique; and, Method:3, a linear approximation technique. For comparison purposes, the aircraft is assumed to have Linear Time Invariant, LTI dynamics. Each algorithm is given full state feedback, an inaccurate reference model and a poor Linear Quadratic Regulator, LQR design for the true plant. It is seen that when the LQR stabilizes the true plant, the three algorithms all achieve the same steady state error to a step command. Numerical results predict the different types of stability behavior that the algorithms provide. It is seen that the Methods: 2 and 3 can only provide a bounded stability, whereas Method: 1 can provide an asymptotic stability. A robust static controller can satisfy stability, but a robust static controller that accommodates variations in plant dynamics might not always be able to match transient requirements as expected. Although there may be no analytical guarantee from adaptive controllers of transient performance, one might look at anecdotal performances.
On Fractional Model Reference Adaptive Control
