Learning-Based Economic Control for Repetitive Systems

Abstract

For many engineering applications, the behavior of a system is largely repetitive as it performs a given task many times. Although control strategies have traditionally sought to enable improved behavior of these repetitive dynamic systems through enhanced reference tracking, system performance is often dictated by a non-tracking, or economic, performance objective such as the maximization of efficiency or safety, or minimization of energy expenditure or monetary cost. Modern control strategies often consider these economic objectives directly by leveraging tools available from the field of mathematical optimization, but their success in practice is frequently hindered by the presence of uncertainty in the system dynamics. To mitigate the harmful impacts of uncertainty on the quality of decisions made by economic controllers, learning-enhanced control has become a popular field of investigation.

The consideration of repetitive system dynamics within the field of learning-based control is the focus of iterative learning control (ILC) and repetitive control (RC) research efforts. Here, repetition facilitates performance improvements, as information about a system's behavior from previous task executions can be used to inform how to appropriately apply control in the future.

However, despite developments in the fields of ILC and RC, several limitations remain that have prevented a more widespread adoption in practice. Namely, the simultaneous presence of economic performance objectives, nonlinear plant dynamics, and system constraints has not been thoroughly considered in the controller design.

This dissertation presents various methodologies for improving the economic performance of constrained, nonlinear, repetitive systems through learning-based techniques. First, this dissertation establishes a connection between repetitive system behavior and the iterative nature of numerical optimization algorithms. Based on this insight, a controller is designed based on a sequential quadratic programming algorithm wherein sensor measurements obtained from previous trials are used to iteratively improve the system's behavior with regards to economic performance and constraint satisfaction without the requirement of a high-fidelity system model. Conditions for which a control trajectory can be identified that satisfies the constraints of the true system, and a subsequent assessment of the optimality of the resulting converged closed-loop performance are presented.

Moreover, while ILC and RC are designed to mitigate the impacts of modeling errors, closed-loop performance is nonetheless predicated upon the presence of uncertainty. Here, whereas ILC and RC have traditionally facilitated learning at the signal level through direct manipulation of the control input from trial to trial, benefits may be achieved through the additional incorporation of learning at the system level wherein historical data is leveraged to reduce the amount of uncertainty that exists.

Consequently, a controller is developed for application to repetitive systems commonly studied within the scope of RC, wherein uncertainty is reduced through the use of a novel adaptive control scheme based on a parametric set membership update law. Specifically, by reducing the impacts of periodic parametric uncertainties on the nominal system dynamics, improvements in economic performance are achieved. Finally, this methodology is then extended to a class of repetitive systems investigated within the ILC literature subject to state-varying parametric uncertainty. Here, the simultaneous use of signal-level and system-level learning is used to enhance economic performance. Conditions are then established for guaranteeing the robust satisfaction of hard state and input constraints. The recursive feasibility and robustly optimal closed-loop performance of these predictive controllers is additionally guaranteed and demonstrated using a set of simulation case studies.