Output Regulation for Time-Delay Systems and Its Application in Trajectory Tracking of Mobile Robots

The output regulation problem, also called the servomechanism problem, is to design afeedback control law for the system such that asymptotic tracking for a class ofreference inputs and disturbance rejection for a class of external disturbances can beachieved while the stability of the closed-loop system can be maintained. One of themost important features of output regulation is that both reference inputs and externaldisturbances do not need to be known exactly. Arising from practical control problems inengineering, such as trajectory tracking of mobile robots, disturbance rejection inairplane taking-off and landing, and vibration suppression of high speed trains, theoutput regulation problem has attracted extensive attention for scientific research forseveral decades.Due to information collection, transmission, and processing, time-delay is ubiquitous inpractical systems. It is well understood that a very small time-delay may devastate thestability of a well-designed control system. However, due to the complexity of involvingtime-delay in analysis and synthesis, most of existing results on output regulation focuson systems without time-delay. More recently, some efforts are devoted to addressingthe output regulation problem for linear time-delay systems. However, they onlyconsider linear systems with known and constant time-delays, which are not the case formany engineering systems in practice.The objective of this project is to investigate several fundamental problems in outputregulation of linear and nonlinear time-delay systems in more practical settings. We aimto explore both feedforward design and internal model design control methodologies anddevelop novel approaches for output regulation of time-delay systems. In particular, wewill investigate controller design for linear systems with time-varying delays, linearsystems with time-varying delays and model uncertainties, linear systems with unknowntime-delays and model uncertainties, and a class of nonlinear systems with time-delays.The theoretical results will also be applied to a practical engineering problem intrajectory tracking and disturbance rejection of mobile robots.Based on deep exploration of the internal model principle for time-delay systems, ageneral framework for handling the robust output regulation problem for time-delaysystems will be established. The success of this research project will enable us to addressa number of critical and fundamental problems in trajectory tracking control anddisturbance rejection control of practical systems. The anticipated theoretic results willexpand the applications of output regulation in more practical situations. This project isthus of both significant academic interest and practical importance.