Online parameter identification for optimal feedback control of nonlinear dynamical systems

Abstract

This research aims to enhance current methods for the optimal feedback control of complex nonlinear dynamical systems via online parameter identifications. Accurate knowledge of the system parameters is essential in numerous practical applications to ensure effective control. A considerable number of advanced control algorithms use model-based approaches. However, the model parameters may often be unknown or subject to change over time. This could result in deviations from the feedback control objective, increased expected costs, and even divergence of the controller. The main objective of this thesis is to develop a combined online parameter identification and model-based controller approach that allows continuously estimating the model parameters of a nonlinear system. The available real-time measurements of the system are used to compute an approximation of the searched parameters. This repeated parameter estimation enables the control algorithm to adapt to the changing system dynamics and maintain optimal control accuracy. This study investigates three approaches. First, a coupled algorithm is developed that employs parameter identifications during operation to adapt a linear quadratic regulator using techniques from parametric sensitivity analysis. Additionally, an approach is presented that also examines the information quality in the data used to predict the probability of success of the parameter estimation. An adaptive control algorithm using nonlinear model predictive control (NMPC) and online parameter identification is proposed as a third alternative. All proposed techniques rely on highly efficient numerical methods for solving nonlinear optimization problems (NLP) and the potential to transfer related problems from optimal control into an NLP by discretization. The proposed approaches are extensively evaluated by conducting simulations and comparing them to the existing standard control methods.