Optimal Control Modification Adaptive Law with Covariance Adaptive Gain Adjustment and Normalization

In the presence of large uncertainty, a controller needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly. However, a large adaptive gain can lead to high-frequency oscillations which can adversely affect robustness of an adaptive control law. As the adaptive gain increases, the time delay margin for a standard model-reference adaptive control decreases, hence loss of robustness. Optimal control modification is a new adaptive control method developed recently to achieve fast adaptation with robustness. Its formulation is based on the minimization of the L2 norm of the tracking error, posed as an optimal control problem. Computer simulations as well as pilot-in-the-loop high-fidelity simulations in a motion-based flight simulator demonstrate the effectiveness of the new adaptive law. In this study, we extend the optimal control modification to include a covariance-like adjustment mechanism of a time-varying adaptive gain to prevent persistent learning which can reduce robustness. The covariance update law can also include a forgetting factor in a similar context as a standard recursive least-squares estimation algorithm. The covariance adaptive gain adjustment allows an initial large adaptive gain to be set arbitrarily and provides the ability to drive the adaptive gain to a lower value as the adaptation has achieved sufficiently the desired tracking performance. Alternatively, a normalized adaptive gain may be used to reduce adaptation when the amplitude of an input basis function becomes large. Flight control simulation results demonstrate that both approaches can achieve significant robustness as measured by the time delay margin. Furthermore, a recent flight test program of the optimal control modification with normalization on a NASA F-18 aircraft demonstrates the effectiveness of the adaptive law.