An Iterative Learning Control Design Method for Nonlinear Discrete-Time Systems with Unknown Iteration-Varying Parameters and Control Direction

An iterative learning control (ILC) scheme is designed for a class of nonlinear discrete-time dynamical systems with unknown iteration-varying parameters and control direction. The iteration-varying parameters are described by a high-order internal model (HOIM) such that the unknown parameters in the current iteration are a linear combination of the counterparts in the previous certain iterations. Under the framework of ILC, the learning convergence condition is derived through rigorous analysis. It is shown that the adaptive ILC law can achieve perfect tracking of system state in presence of iteration-varying parameters and unknown control direction. The effectiveness of the proposed control scheme is verified by simulations

Multiple Model ILC for Continuous-Time Nonlinear Systems

Multiple model iterative learning control (MMILC) method is proposed to deal with the continuous-time nonlinear system with uncertain and iteration-varying parameters. In this kind of control strategy, multiple models are established to cover the uncertainty of system; a switching mechanism is used to decide the most appropriate model for system in current iteration. For system operating iteratively in a fixed time interval with uncertain or jumping parameters, this kind of MMILC can improve the transient response and control property greatly. Asymptotical convergence is demonstrated theoretically, and the control effectiveness is illustrated by numerical simulation

Frequency Domain Based Analysis and Design of Norm-Optimal Iterative Learning Control

In this thesis, novel frequency domain based analysis and design methods on Norm-Optimal Iterative Learning Control (NO-ILC) are developed for Single-Input-Single-Output (SISO) Linear Time Invariant (LTI) systems. Modeling errors in general degrade the convergence performance of NO-ILC and hence ensuring Robust Monotonic Convergence (RMC) against model uncertainties is important. Although the robustness of NO-ILC has been studied in the literature, determining the allowable range of modeling errors for a given NO-ILC design is still an open research question. To fill this gap, a frequency domain analysis with a multiplicity formulation of model uncertainty is developed in this work to quantify and visualize the allowable modeling errors. Compared with the traditional formulation, the proposed new uncertainty formulation provides a less conservative representation of the allowable model uncertainty range by taking additional phase information into account and thus allows for a more complete evaluation of the robustness of NO-ILC. The analysis also clarifies how the RMC region changes as a function of NO-ILC weighting terms and therefore leads to several frequency domain design tools to achieve RMC for given model uncertainties. Along with this frequency domain analysis, rather than some qualitative understanding in the literature, an equation quantitatively characterizing the fundamental trade-off of NO-ILC with respect to robustness, convergence speed and steady state error at each frequency is presented, which motivates the proposed loop-shaping like design methods for NO-ILC to achieve different performance requirements at various frequencies. The proposed analysis also demonstrates that NO-ILC is the optimal solution for general LTI ILC updating laws in the scope of balancing the trade-off between robustness, convergence speed and steady state error.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137007/1/gexinyi_1.pd

Discretization and Approximation Methods for Reinforcement Learning of Highly Reconfigurable Systems

There are a number of techniques that are used to solve reinforcement learning problems, but very few that have been developed for and tested on highly reconfigurable systems cast as reinforcement learning problems. Reconfigurable systems refers to a vehicle (air, ground, or water) or collection of vehicles that can change its geometrical features, i.e. shape or formation, to perform tasks that the vehicle could not otherwise accomplish. These systems tend to be optimized for several operating conditions, and then controllers are designed to reconfigure the system from one operating condition to another. Q-learning, an unsupervised episodic learning technique that solves the reinforcement learning problem, is an attractive control methodology for reconfigurable systems. It has been successfully applied to a myriad of control problems, and there are a number of variations that were developed to avoid or alleviate some limitations in earlier version of this approach. This dissertation describes the development of three modular enhancements to the Q-learning algorithm that solve some of the unique problems that arise when working with this class of systems, such as the complex interaction of reconfigurable parameters and computationally intensive models of the systems. A multi-resolution state-space discretization method is developed that adaptively rediscretizes the state-space by progressively finer grids around one or more distinct Regions Of Interest within the state or learning space. A genetic algorithm that autonomously selects the basis functions to be used in the approximation of the action-value function is applied periodically throughout the learning process. Policy comparison is added to monitor the state of the policy encoded in the action-value function to prevent unnecessary episodes at each level of discretization. This approach is validated on several problems including an inverted pendulum, reconfigurable airfoil, and reconfigurable wing. Results show that the multi-resolution state-space discretization method reduces the number of state-action pairs, often by an order of magnitude, required to achieve a specific goal and the policy comparison prevents unnecessary episodes once the policy has converged to a usable policy. Results also show that the genetic algorithm is a promising candidate for the selection of basis functions for function approximation of the action-value function