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Milad Farsi | Applied Mathematics, University of Waterloo
Model-based Reinforcement Learning of Nonlinear Dynamical Systems
Model-based reinforcement learning (MBRL) techniques accelerate the learning task by employing a transition model to make predictions. In this dissertation, we present novel techniques for online learning of unknown dynamics by iteratively computing a feedback controller based on the most recent update of the model. Assuming a structured continuous-time model of the system in terms of a set of bases, we formulate an infinite horizon optimal control problem addressing a given control objective. The structure of the system along with a value function parameterized in the quadratic form provides a flexibility in analytically calculating an update rule for the parameters. Hence, a matrix differential equation of the parameters is obtained, where the solution is used to characterize the optimal feedback control in terms of the bases, at any time step. Moreover, the quadratic form of the value function suggests a compact way of updating the parameters that considerably decreases the computational complexity. In the convergence analysis, we demonstrate asymptotic stability and optimality of the obtained learning algorithm around the equilibrium by revealing its connections with the analogous linear quadratic regulator. Moreover, the results are extended to the trajectory tracking problem. Assuming a structured unknown nonlinear system augmented with the dynamics of a commander system, we obtain a control rule minimizing a given quadratic tracking objective function. Furthermore, in an alternative technique for learning, a piecewise nonlinear affine framework is developed for controlling nonlinear systems with unknown dynamics. Therefore, we extend the results to obtain a general piecewise nonlinear framework where each piece is responsible for locally learning and controlling over some partition of the domain. Then, we consider the piecewise linear (PWA) system with a bounded uncertainty as a special case, for which we suggest an optimization-based verification technique. Accordingly, given a discretization of the learned PWA system, we iteratively search for a common piecewise Lyapunov function in a set of positive definite functions, where a non-monotonic convergence is allowed. Then, this Lyapunov candidate is verified for the uncertain system. To demonstrate the applicability of the approaches presented in this dissertation, simulation results on benchmark nonlinear systems are included, such as quadrotor, vehicle, solar photo-voltaic systems, etc.