The Internal Model Principle for Systems with Unbounded Control and Observation

In this paper the theory of robust output regulation of distributed parameter systems with infinite-dimensional exosystems is extended for plants with unbounded control and observation. As the main result, we present the internal model principle for linear infinite-dimensional systems with unbounded input and output operators. We do this for two different definitions of an internal model found in the literature, namely, the p-copy internal model and the $\mathcal{G}$-conditions. We also introduce a new way of defining an internal model for infinite-dimensional systems. The theoretic results are illustrated with an example where we consider robust output tracking for a one-dimensional heat equation with boundary control and pointwise measurements.Comment: 38 pages, 2 figures, in revie

Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

We construct two error feedback controllers for robust output tracking and disturbance rejection of a regular linear system with nonsmooth reference and disturbance signals. We show that for sufficiently smooth signals the output converges to the reference at a rate that depends on the behaviour of the transfer function of the plant on the imaginary axis. In addition, we construct a controller that can be designed to achieve robustness with respect to a given class of uncertainties in the system, and present a novel controller structure for output tracking and disturbance rejection without the robustness requirement. We also generalize the internal model principle for regular linear systems with boundary disturbance and for controllers with unbounded input and output operators. The construction of controllers is illustrated with an example where we consider output tracking of a nonsmooth periodic reference signal for a two-dimensional heat equation with boundary control and observation, and with periodic disturbances on the boundary.Comment: 30 pages, 3 figures, to appear in SIAM Journal on Control & Optimizatio

The output regulation problem : a convergent dynamics approach

+192hlm.;24c

Robust output regulation for voltage control in DC networks with time-varying loads

In this letter, we propose a novel control scheme for regulating the voltage in Direct Current (DC) networks. More precisely, the proposed control scheme is based on the output regulation methodology and, differently from the results in the literature, where the loads are assumed to be constant, we consider time-varying loads whose dynamics are described by a class of nonlinear differential equations. We prove that the proposed control scheme achieves voltage regulation ensuring the stability of the overall network

Robust Output Regulation for Autonomous Robots:self-learning mechanisms, task-space control and multi-agent systems

This thesis focuses on robust output regulation for autonomous robots. The control objective of output regulation is to design a feedback controller to achieve asymptotic tracking and/or disturbance rejection for a class of exogenous reference and/or disturbance while maintaining closed-loop stability. We investigate three research problems that pertain to the constructive design of robust output regulation for fully actuated Euler-Lagrange systems from centralized to distributed fashions. The first one is the global robust output regulation of second-order affine nonlinear systems with input disturbances that encompass the fully-actuated Euler-Lagrange systems. Based on a certainty equivalence principle method, we proposed a novel class of nonlinear internal models taking a cascade interconnection structure with strictly relaxed conditions than before. The second one is the output regulation for robot manipulators working in task-space. An internal model-based adaptive controller is designed to cope with uncertain manipulator kinematic and dynamic parameters, as well as unknown periodic reference trajectories generated by harmonic oscillators. The last one is the formation control of manipulators’ end-effector subject to external disturbances or parameter uncertainties. We present and analyze gradient descent-based distributed formation controllers for end-effectors. Internal models are used to reject external disturbances. Moreover, by introducing an extra integrator and an adaptive estimator for gravitational compensation and stabilization, respectively, we extend the proposed gradient-based design to the case where the plant parameters are not exactly known

Robust output synchronization for complex nonlinear systems.

Zhao, Jin.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 79-83).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Synchronization of Master-slave Systems --- p.1Chapter 1.2 --- Output Regulation --- p.2Chapter 1.3 --- Typical Nonlinear Systems --- p.4Chapter 1.4 --- Organization --- p.4Chapter 2 --- Synchronization of Chua's Circuit and Van der Pol Oscillator via Inter- nal Model Approach --- p.6Chapter 2.1 --- Introduction --- p.6Chapter 2.2 --- Problem Formulation --- p.8Chapter 2.3 --- Preliminaries --- p.10Chapter 2.4 --- Solvability of the Problem --- p.13Chapter 2.4.1 --- The solution of the regulator equations --- p.14Chapter 2.4.2 --- Steady-state generator --- p.15Chapter 2.4.3 --- Internal model --- p.19Chapter 2.4.4 --- Stabilization --- p.20Chapter 2.4.5 --- Simulation --- p.22Chapter 2.5 --- Conclusions --- p.27Chapter 3 --- Robust Output Regulation of Output Feedback Systems with Nonlinear Exosystems --- p.28Chapter 3.1 --- Introduction --- p.28Chapter 3.2 --- Assumptions and Preliminaries --- p.29Chapter 3.3 --- Solvability of the Synchronization Problem --- p.33Chapter 3.4 --- Comparing Two Approaches for Output Regulation --- p.42Chapter 3.4.1 --- Differences between the two approaches for the output regulation problem --- p.42Chapter 3.4.2 --- Solvability of the regulator equations --- p.43Chapter 3.4.3 --- Solvability of stabilization --- p.47Chapter 3.5 --- Conclusions --- p.49Chapter 4 --- Applications of Robust Regional Synchronization via Output Regulation Techniques --- p.50Chapter 4.1 --- Problem Formulation --- p.50Chapter 4.2 --- Duffing Oscillator Synchronizes with Chua's Circuit --- p.51Chapter 4.2.1 --- Transfer the synchronization problem into the stabilization problem --- p.53Chapter 4.2.2 --- Boundedness of Chua's circuit --- p.57Chapter 4.2.3 --- Stabilization --- p.59Chapter 4.2.4 --- Simulation Results --- p.64Chapter 4.3 --- The Chaotic SMIB Power System Synchronizes with Van der Pol Oscillator --- p.64Chapter 4.3.1 --- Transfer the synchronization problem into the stabilization problem --- p.68Chapter 4.3.2 --- Stabilization --- p.71Chapter 4.3.3 --- Simulation Results --- p.74Chapter 4.4 --- Conclusions --- p.76Chapter 5 --- Conclusions --- p.77Bibliography --- p.7