Adaptive control for enhanced performance of devices and algorithms

The objective of this dissertation is to explore the use of adaptive feedback control algorithms in control-based continuation of periodic solutions of a priori unknown dynamical systems under continuous variations in system parameters, independently of their stability. The control-based continuation paradigm applies a numerical continuation algorithm to a reference input of the control block that ensures that the family of periodic orbits of the original plant persists and is stabilized by the presence of control feedback. Provided that such a reference input can be found in the absence of a system model, the control-based continuation paradigm can be applied to black-box models and physical experiments. Although the control-based continuation technique has been explored for more than a decade, the feedback design of choice in the literature is a linear controller, e.g., a proportional- derivative control law with fixed control gains. In the absence of a detailed system model, such a control design requires careful tuning of the control gains and offers no guaranteed performance bounds. This dissertation aims to remedy this shortcoming by considering the application of suitably formulated adaptive control formulations. To this end, several candidate nonlinear adaptive control strategies are investigated for both continuous-time and discrete-time systems. Rigorous proofs for the predicted response when applied to unknown linear systems are accompanied by extensive numerical validation. Extensions to nonlinear systems are considered through a combination of theory and simulation. In the case of continuous-time systems, a control formulation inspired by the L1 adaptive control framework is found to be robust to time delays in the control input with a time-delay margin that is independent of the adaptive gain (in contrast to a proposed model-reference adaptive control design). Since time delay is ubiquitous in physical systems, and unmodeled dynamics can be equivalently represented by a delay in the plant input, delay robustness is an important feature also for control-based continuation. This dissertation reviews an analysis of delay robustness for an L1 adaptive control strategy applied to a particular class of systems with unknown matched nonlinearities, jointly authored with Kim Doang Nguyen and Harry Dankowicz. These results extend beyond the control-based continuation framework, including potential applications in robotics and vehicle dynamics