UC Santa Cruz

Estimating the unknown parameters of a system is critical in many engineering applications, such as the control of power electronics, motion planning for autonomous cars, flight controllers for aircraft, and rendezvous and docking controllers for spacecraft. While modern continuous-time and discrete-time estimation algorithms have found widespread use throughout engineering, the recent rise of hybrid modeling paradigms highlights their limitations. Hybrid systems are characterized by state variables that may evolve continuously (flow) and, at times, evolve discretely (jump). When applied to hybrid systems, the parameter estimation error for purely continuous-time or purely discrete-time estimation algorithms may fail to converge to zero. Motivated by these shortcomings, this dissertation focuses on developing novel parameter estimation algorithms for hybrid dynamical systems.

The first algorithm, developed using hybrid systems tools, is inspired by the continuous-time and discrete-time gradient descent algorithms. Our proposed hybrid parameter estimation algorithm operates during both the flows and jumps of a hybrid system, and guarantees convergence of the parameter estimate to the true value under a notion of hybrid persistence of excitation that relaxes the classical continuous-time and discrete-time persistence of excitation conditions. Key properties of the algorithm are established, including exponential stability, convergence rate, and robustness to measurement noise.

The second algorithm is inspired by the recently proposed integral concurrent learning algorithm. Our proposed hybrid algorithm selectively stores measurements of the inputs and outputs of a hybrid system during flows and jumps. The algorithm guarantees convergence of the parameter estimate to the true value if the stored data satisfies a (hybrid) richness condition. Key properties of the algorithm are established, including exponential stability, convergence rate, and robustness to measurement noise.

The third algorithm uses hybrid systems tools to estimate in finite-time the unknown parameters of a class of continuous-time systems. Our proposed hybrid algorithm ensures convergence of the parameter estimate to the true value when the system inputs are exciting over only a finite interval of time. As a result, the algorithm can also be employed to estimate unknown parameters of hybrid systems if the inputs are sufficiently exciting over a single interval of flow. Key properties of the algorithm are established, including time to convergence and robustness to measurement noise.

The fourth algorithm estimates unknown parameters for hybrid systems whose jump times are known only approximately. By solving an optimization problem to estimate the jump times of the system, our proposed algorithm ensures convergence of the parameter estimate to the true value, except possibly during the intervals wherein the detection of jumps is delayed. Key properties of the algorithm are established, including stability and robustness to perturbations.

The contributions of this dissertation are not limited to the theory of parameter estimation for hybrid systems, as they have implications in adaptive control algorithms for practically relevant engineering control systems. For such systems, we develop methods for the design of algorithms that learn and adapt using real-time data to cope with unknown parameters and features in the environment, to enable autonomous systems to perform near optimal conditions, with robustness. Numerical results validate the findings.