Output regulation of rational nonlinear systems with input saturation

This thesis deals with the output regulation of rational nonlinear systems with input saturation. The output regulation problem considers a controlled plant subject to non-vanishing perturbations or reference signals produced by an exogenous autonomous system, where the goal is to ensure asymptotic convergence to zero of the plant output error. This work develops systematic methodologies for stability analysis and design of anti-windup compensated dynamic output feedback stabilizing controllers able to solve the output regulation problem for rational nonlinear systems with saturating inputs. In order to obtain these results, the proposed method employs the differential-algebraic representation, a theoretical framework that treats rational nonlinear systems by a differential equation combined with an equality relation. This tool is utilized in order to cast the stability analysis and control synthesis into optimization problems subject to linear matrix inequality constraints. Towards ensuring asymptotic output regulation, it is initially assumed the prior knowledge of an exact solution to the regulator equations, which represent an invariant and zero-error steady-state manifold. This assumption is later relaxed, where the results are extended for the practical regulation problem. In this last scenario, any numerically approximated solution to the regulator equations may be considered and the devised methodology ensures ultimate boundedness of the output error. Overall, the main innovation of this thesis is the application of the differential-algebraic representation into the nonlinear output regulation context, in turn providing a solution to a new set of problems intractable by state-of-the-art nonlinear methods.Esta tese trata da regulação de saída de sistemas não-lineares racionais com saturação na entrada. O problema de regulação de saída considera uma planta sujeita a sinais persistentes de distúrbio ou referência produzidos por um sistema exógeno autônomo, onde o objetivo é garantir a convergência assintótica do erro de saída da planta para zero. Este trabalho desenvolve metodologias sistemáticas para análise de estabilidade e projeto de controladores estabilizantes dinâmicos de realimentação de saída com compensadores anti-windup para sistemas não-lineares racionais com saturação no contexto de regulação de saída. O método proposto utiliza principalmente a representação algébrico-diferencial, uma abordagem teórica que trata sistemas não-lineares racionais por meio de uma equação diferencial combinada com uma igualdade algébrica. Para assegurar a regulação assintótica de saída, inicialmente assume-se o conhecimento de um modelo interno e uma solução exata para as equações do regulador, que representa um conjunto invariante de regime permanente onde o erro de saída é zero. Esta suposição é posteriormente relaxada, onde os resultados são estendidos para o contexto de regulação de saída prática. Os desenvolvimentos principais desta tese estão divididos nos seguintes capítulos: Regulação de Saída de Sistemas Não-Lineares Racionais; Regulação de Saída de Sistemas Não-Lineares Racionais com Saturação de Entrada e Extensão para Regulação de Saída Prática. O primeiro capítulo mencionado introduz a proposta de base deste trabalho, que consiste no emprego da representação algébrico-diferencial para a dinâmica do erro de regulação entorno do conjunto invariante descrito pelas equações do regulador. Com base nesta formulação, teoremas de estabilidade e desempenho são obtidos com condições na forma de desigualdades matriciais, permitindo o uso de otimização numérica para análise e síntese de controladores estabilizantes. No próximo capítulo, a formulação é estendida para a presença de saturação no sinal de controle, onde uma nova condição de setor é proposta para tratar esta não-linearidade adicional. Desta forma, novos teoremas são obtidos tanto para análise quanto para síntese de controladores estabilizantes incluindo compensadores anti-windup. No capítulo final da metodologia, considera-se uma abordagem de regulação prática onde soluções numéricas aproximadas podem ser consideradas para as equações do regulador. Novos teoremas de estabilidade voltados para análise e síntese também são obtidos dentro deste panorama prático, onde garante-se um conjunto terminal para a trajetória do erro de saída. Em geral, a grande importância deste trabalho é a possibilidade de solucionar um novo conjunto de problemas de regulação de saída não-linear, anteriormente intratáveis por métodos do estado-da-arte

Reinforcement Learning, Intelligent Control and their Applications in Connected and Autonomous Vehicles

Reinforcement learning (RL) has attracted large attention over the past few years. Recently, we developed a data-driven algorithm to solve predictive cruise control (PCC) and games output regulation problems. This work integrates our recent contributions to the application of RL in game theory, output regulation problems, robust control, small-gain theory and PCC. The algorithm was developed for $H_\infty$ adaptive optimal output regulation of uncertain linear systems, and uncertain partially linear systems to reject disturbance and also force the output of the systems to asymptotically track a reference. In the PCC problem, we determined the reference velocity for each autonomous vehicle in the platoon using the traffic information broadcasted from the lights to reduce the vehicles\u27 trip time. Then we employed the algorithm to design an approximate optimal controller for the vehicles. This controller is able to regulate the headway, velocity and acceleration of each vehicle to the desired values. Simulation results validate the effectiveness of the algorithms

Towards High Speed Aerial Tracking of Agile Targets

In order to provide a novel perspective for videography of high speed sporting events, a highly capable trajectory tracking control methodology is developed for a custom designed Kadet Senior Unmanned Aerial Vehicle (UAV). The accompanying high fidelity system identification ensures that accurate flight models are used to design the control laws. A parallel vision based target tracking technique is also demonstrated and implemented on a Graphical Processing Unit (GPU), to assist in real-time tracking of the target. Nonlinear control techniques like feedback linearization require a detailed and accurate system model. This thesis discusses techniques used for estimating these models using data collected during planned test flights. A class of methods known as the Output Error Methods are discussed with extensions for dealing with wind turbulence. Implementation of these methods, including data acquisition details, on the Kadet Senior are also discussed. Results for this UAV are provided. For comparison, additional results using data from a BAC-221 simulation are also provided as well as typical results from the work done at the Dryden Flight Research Center. The proposed controller combines feedback linearization with linear tracking control using the internal model approach, and relies on a trajectory generating exosystem. Three different aircraft models are presented each with increasing levels of complexity, in an effort to identify the simplest controller that yields acceptable performance. The dynamic inversion and linear tracking control laws are derived for each model, and simulation results are presented for tracking of elliptical and periodic trajectories on the Kadet Senior

Modeling and Control of a Magnetic Drug Delivery System

Therapeutic operation risk has been reduced by the use of micro-robots, allowing highly invasive surgery to be replaced by low invasive surgery (LIS), which provides an effective tool even in previously inaccessible parts of the human body. LIS techniques help delivering drugs effectively via micro-carriers. The micro-carriers are divided into two groups: tethered devices, which are supported by internally supplied propulsion mechanism, and untethered devices. Remote actuation is the critical issue in micro-device navigation, especially through blood vessels. To achieve remote control within the cardiovascular system, magnetic propulsion offers an advantage over other proposed actuation methods. In the literature, most research has focused on micro-device structural design, while there is a lack of research into design and analysis of combined structure and control. As the main part, integrating the principle of electromagnetic induced force by feedback control design will lead to the desired automatic movement. An actuator configuration should thus first be designed to initiate the desired force. The design is basically defining the type and placement of a set of coils to achieve an operational goal. In this project, the magnetic actuation is initiated by a combination of four electromagnets and two sets of uniform coils. Preliminary studies on 2D navigation of a ferromagnetic particle are used to show the effect of actuator structure on controller performance. Accordingly, the performance of the four electromagnets combination is compared to the proposed augmented structure with uniform coils. The simulation results show the improved efficiency of the augmented structure. In more general cases, the arrangement and number of electromagnets are unknown and should be defined. An optimization method is suggested to find these variables when the working space is maximized. Finally, the problem of robust output regulation of the electromagnetic system driven by a linear exosystem, is also addressed in this project. The exosystem is assumed to be neutrally stable with unknown frequencies. The parallel connection of two controllers, a robust stabilizer and an internal model-based controller, is presented to eliminate the output error. In the latter one, an adaptation is used to tune the internal model frequencies such that a steady-state control is produced to maintain the output-zeroing condition. The robust regulation with a local domain of convergence is achieved for a special class of decomposable MIMO nonlinear minimum-phase system. The simulation results show the effectiveness and robustness of this method for the electromagnetic system when two different paths are considered

Robust controllers design for unknown error and exosystem: a hybid optimization and output regulation approach

This thesis addresses the problem of robustness in control in two main topics: linear output regulation when no knowledge is assumed of the modes of the exosystem, and hybrid gradient-free optimization. A framework is presented for the solution of the first problem, in which asymptotic regulation is achieved in case of a persistence of excitation condition. The stability properties of the closed-loop system are proved under a small-gain argument with no minimum phase assumption. The second part of the thesis addresses, and proposes, a solution to the gradientfree optimization problem, solved by a discrete-time direct search algorithm. The algorithm is shown to convergence to the set of minima of a particular class of non convex functions. It is, then, applied considering it coupled with a continuous-time dynamical system. A hybrid controller is developed in order to guarantee convergence to the set of minima and stability of the interconnection of the two systems. Almost global asymptotic is proven for the proposed hybrid controller. Shown to not be robust to any bounded measurement noise, a robust solution is also proposed. The aim of this thesis is to lay the ground for a solution of the output regulation problem in case the error is unknown, but a proxy optimization function is available. A controller embedding the characteristics of the two proposed approaches, as a main solution to the aforementioned problem, will be the focus of future studies

Advances In Internal Model Principle Control Theory

In this thesis, two advanced implementations of the internal model principle (IMP) are presented. The first is the identification of exponentially damped sinusoidal (EDS) signals with unknown parameters which are widely used to model audio signals. This application is developed in discrete time as a signal processing problem. An IMP based adaptive algorithm is developed for estimating two EDS parameters, the damping factor and frequency. The stability and convergence of this adaptive algorithm is analyzed based on a discrete time two time scale averaging theory. Simulation results demonstrate the identification performance of the proposed algorithm and verify its stability. The second advanced implementation of the IMP control theory is the rejection of disturbances consisting of both predictable and unpredictable components. An IMP controller is used for rejecting predictable disturbances. But the phase lag introduced by the IMP controller limits the rejection capability of the wideband disturbance controller, which is used for attenuating unpredictable disturbance, such as white noise. A combination of open and closed-loop control strategy is presented. In the closed-loop mode, both controllers are active. Once the tracking error is insignificant, the input to the IMP controller is disconnected while its output control action is maintained. In the open loop mode, the wideband disturbance controller is made more aggressive for attenuating white noise. Depending on the level of the tracking error, the input to the IMP controller is connected intermittently. Thus the system switches between open and closed-loop modes. A state feedback controller is designed as the wideband disturbance controller in this application. Two types of predictable disturbances are considered, constant and periodic. For a constant disturbance, an integral controller, the simplest IMP controller, is used. For a periodic disturbance with unknown frequencies, adaptive IMP controllers are used to estimate the frequencies before cancelling the disturbances. An extended multiple Lyapunov functions (MLF) theorem is developed for the stability analysis of this intermittent control strategy. Simulation results justify the optimal rejection performance of this switched control by comparing with two other traditional controllers

Investigation of feedforward neural networks and its applications to some nonlinear control problems.

Ng Chi-fai.Thesis submitted in: December 2000.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 69-73).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiList of Figures --- p.viiiList of Tables --- p.ixChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation and Objectives --- p.1Chapter 1.2 --- Principles of Feedforward Neural Network Approximation --- p.1Chapter 1.3 --- Contribution of The Thesis --- p.5Chapter 1.4 --- Outline of The Thesis --- p.5Chapter 2 --- Feedforward Neural Networks: An Approximator for Nonlinear Control Law --- p.8Chapter 2.1 --- Optimization Methods Applied in Feedforward Neural Network Approximation --- p.8Chapter 2.2 --- Example in Supervised Learning --- p.10Chapter 2.2.1 --- Problem Description --- p.10Chapter 2.2.2 --- Neural Network Configuration and Training --- p.12Chapter 2.2.3 --- Simulation Result --- p.13Chapter 3 --- Neural Based Approximation of Center Manifold Equations --- p.19Chapter 3.1 --- Solving Center Manifold Equations by Feedforward Neural Network Approx- imation --- p.19Chapter 3.2 --- Example --- p.21Chapter 3.2.1 --- Problem Description --- p.21Chapter 3.2.2 --- Simulation Result --- p.24Chapter 3.2.3 --- Discussion --- p.24Chapter 4 --- Connection of Center Manifold Equations to Output Regulation Problem --- p.29Chapter 4.1 --- Output Regulation Theory --- p.29Chapter 4.2 --- Reduction of Regulator Equation into Center Manifold Equations --- p.31Chapter 5 --- Application to the Control Design of Ball and Beam System --- p.34Chapter 5.1 --- Problem Description --- p.34Chapter 5.2 --- Neural Approximation Solution of Center Manifold Equations --- p.37Chapter 5.3 --- Simulation Results --- p.38Chapter 5.4 --- Discussion --- p.45Chapter 6 --- Neural Based Disturbance Rejection of Nonlinear Benchmark Problem (TORA System) --- p.48Chapter 6.1 --- Problem Description --- p.48Chapter 6.2 --- Neural based Approximation of the Center Manifold Equations of TORA System --- p.51Chapter 6.3 --- Simulation Results --- p.53Chapter 6.4 --- Discussion --- p.59Chapter 7 --- Conclusion --- p.62Chapter 7.1 --- Future Works --- p.63Chapter A --- Center Manifold Theory --- p.64Chapter B --- Relation between Center Manifold Equation and Output Regulation Prob- lem --- p.66Biography --- p.68References --- p.6