Adaptive Control with Unknown High Frequency Gain and Unmatched Uncertainties

Adaptive control, which adapts to a system with unknown or slowly time-varying parameters, is one of the primary control methods for systems with uncertainties in modern control. Utilizing fast adaptation, L1 adaptive control can be extended to systems with general time-varying parameters. Control signal is further low-pass filtered to recover robustness of the resulting closed-loop system. However, the type of uncertainties handled by adaptive control, including L1 adaptive control, is still restrictive in many perspectives. One of the highly concerned restrictions is that the controller should know the sign of high frequency gain in advance. The main contribution of this dissertation has three parts. First of all, this study develops a recursive filtered adaptive state feedback control approach to handle systems with unknown high frequency gain and unmatched uncertainties. It merges the least-squares estimator into L1 adaptive control architecture, which allows the signs of the high-frequency gain to be unknown and thus significantly relaxes the assumptions on it. With the least-squares estimator and projection, the unknown systematic parameters are updated iteratively without losing controllability. It demonstrates the feasibility to extend L1 adaptive control to systems with unknown high frequency gain. The second part focuses on the adaptive attitude control of autonomous underwater vehicles in a dynamic environment. The attitude control problem is one of the fundamental problems to facilitate the advancement of autonomous underwater networks. However, the attitude dynamics have highly-coupled nonlinearity with uncertainties, which are from modeling errors and time-varying external disturbances. To handle uncertainties, an advanced attitude controller, which utilizes L1 adaptive control to get fast and robust adaptation for backstepping control approach, is developed. Moreover, a Lyapunov function-based optimum linearization method is presented to analyze the stability of the uncontrollable channel in the operation region. Finally, this dissertation develops a novel distributed ultrasound temperature sensing system with acoustic multiplexing and Gaussian Radial Basis Functions-based temperature field reconstruction algorithm. This sensing system can provide real-time temperature monitoring for any purpose.