Toward Verifiable Adaptive Control Systems: High-Performance and Robust Architectures

In this dissertation, new model reference adaptive control architectures are presented with stability, performance, and robustness considerations, to address challenges related to the verification of adaptive control systems. The challenges associated with the transient performance of adaptive control systems is first addressed using two new approaches that improve the transient performance. Specifically, the first approach is predicated on a novel controller architecture, which involves added terms in the update law entitled artificial basis functions. These terms are constructed through a gradient optimization procedure to minimize the system error between an uncertain dynamical system and a given reference model during the learning phase of an adaptive controller. The second approach is an extension of the first one and minimizes the effect of the system uncertainties more directly in the transient phase. In addition, this approach uses a varying gain to enforce performance bounds on the system error and is further generalized to adaptive control laws with nonlinear reference models. Another challenge in adaptive control systems is to achieve system stability and a prescribed level performance in the presence of actuator dynamics. It is well-known that if the actuator dynamics do not have sufficiently high bandwidth, their presence cannot be practically neglected in the design since they limit the achievable stability of adaptive control laws. Another major contribution of this dissertation is to address this challenge. In particular, first a linear matrix inequalities-based hedging approach is proposed, where this approach modifies the ideal reference model dynamics to allow for correct adaptation that is not affected by the presence of actuator dynamics. The stability limits of this approach are computed using linear matrix inequalities revealing the fundamental stability interplay between the parameters of the actuator dynamics and the allowable system uncertainties. In addition, these computations are used to provide a depiction of the feasible region of the actuator parameters such that the robustness to variation in the parameters is addressed. Furthermore, the convergence properties of the modified reference model to the ideal reference model are analyzed. Generalizations and applications of the proposed approach are then provided. Finally, to improve upon this linear matrix inequalities-based hedging approach a new adaptive control architecture using expanded reference models is proposed. It is shown that the expanded reference model trajectories more closely follow the trajectories of the ideal reference model as compared to the hedging approach and through the augmentation of a command governor architecture, asymptotic convergence to the ideal reference model can be guaranteed. To provide additional robustness against possible uncertainties in the actuator bandwidths an estimation of the actuator bandwidths is incorporated. Lastly, the challenge presented by the unknown physical interconnection of large-scale modular systems is addressed. First a decentralized adaptive architecture is proposed in an active-passive modular framework. Specifically, this architecture is based on a set-theoretic model reference adaptive control approach that allows for command following of the active module in the presence of module-level system uncertainties and unknown physical interconnections between both active and passive modules. The key feature of this framework allows the system error trajectories of the active modules to be contained within apriori, user-defined compact sets, thereby enforcing strict performance guarantees. This architecture is then extended such that performance guarantees are enforced on not only the actuated portion (active module) of the interconnected dynamics but also the unactuated portion (passive module). For each proposed adaptive control architecture, a system theoretic approach is included to analyze the closed-loop stability properties using tools from Lyapunov stability, linear matrix inequalities, and matrix mathematics. Finally, illustrative numerical examples are included to elucidate the proposed approaches