Nonlinear control of feedforward systems with bounded signals

Published versio

On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

Nonovershooting and nonundershooting exact output regulation

We consider the classic problem of exact output regulation for a linear time invariant plant. Under the assumption that either a state feedback or measurement feedback output regulator exists, we give design methods to obtain a regulator that avoids overshoot and undershoot in the transient response

About stabilization of non-minimum phase systems by output feedback

This thesis work has been motivated by an internal benchmark dealing with the output regulation problem of a nonlinear non-minimum phase system in the case of full-state feedback. The system under consideration structurally suffers from finite escape time, and this condition makes the output regulation problem very hard even for very simple steady-state evolution or exosystem dynamics, such as a simple integrator. This situation leads to studying the approaches developed for controlling Non-minimum phase systems and how they affect feedback performances. Despite a lot of frequency domain results, only a few works have been proposed for describing the performance limitations in a state space system representation. In particular, in our opinion, the most relevant research thread exploits the so-called Inner-Outer Decomposition. Such decomposition allows splitting the Non-minimum phase system under consideration into a cascade of two subsystems: a minimum phase system (the outer) that contains all poles of the original system and an all-pass Non-minimum phase system (the inner) that contains all the unavoidable pathologies of the unstable zero dynamics. Such a cascade decomposition was inspiring to start working on functional observers for linear and nonlinear systems. In particular, the idea of a functional observer is to exploit only the measured signals from the system to asymptotically reconstruct a certain function of the system states, without necessarily reconstructing the whole state vector. The feature of asymptotically reconstructing a certain state functional plays an important role in the design of a feedback controller able to stabilize the Non-minimum phase system

Two nonlinear output regulation problems.

Hu Guoqiang.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.Includes bibliographical references (leaves 87-93).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Nonlinear Control Systems --- p.2Chapter 1.2 --- Output Regulation --- p.5Chapter 1.3 --- Semiglobal Stabilization --- p.7Chapter 1.4 --- A Benchmark Nonlinear Control Problem --- p.8Chapter 1.5 --- Contribution of this Thesis --- p.10Chapter 2 --- Semiglobal Robust Output Regulation of a Class of Nonlinear Systems via Output Feedback Control --- p.12Chapter 2.1 --- Introduction --- p.13Chapter 2.2 --- Semiglobal Backstepping Technique --- p.16Chapter 2.3 --- Output Regulation Converted to Stabilization --- p.18Chapter 2.4 --- Solvability of the Semiglobal Robust Stabilization Problem via Partial State Feedback --- p.23Chapter 2.5 --- Design of the Output Feedback Regulator --- p.35Chapter 2.6 --- An example --- p.39Chapter 2.7 --- Concluding Remarks --- p.46Chapter 3 --- Disturbance Rejection of the RTAC system --- p.50Chapter 3.1 --- Disturbance Rejection Problem Formulated into Output Regulation Problem --- p.51Chapter 3.2 --- Solvability of the Output Regulation Problem via Measurement Output Feedback Control --- p.53Chapter 3.3 --- Parameters Design and Simulation Results --- p.57Chapter 3.4 --- Concluding Remarks --- p.58Chapter 4 --- Robust Disturbance Rejection of the RTAC System --- p.63Chapter 4.1 --- Introduction --- p.63Chapter 4.2 --- A General Framework for Robust Output Regulation --- p.64Chapter 4.3 --- Robust Asymptotic Disturbance Rejection of the RTAC System --- p.69Chapter 4.4 --- Algorithms to Design and Optimize the Parameters Kx and L --- p.73Chapter 4.5 --- Parameters design and Simulation Results --- p.75Chapter 4.6 --- Concluding Remarks --- p.76Chapter 5 --- Conclusions --- p.86Biography --- p.87Bibliography --- p.88Appendix A. ITAE Prototype Design --- p.9