A wide range of multi-agent coordination problems including reference tracking and disturbance rejection requirements can be formulated as a cooperative output regulation problem. The general framework captures typical problems such as output synchronization, leader-follower synchronization, and many more. In the present paper, we propose a novel distributed regulator for groups of identical and non-identical linear agents. We consider global external signals affecting all agents and local external signals affecting only individual agents in the group. Both signal types may contain references and disturbances. Our main contribution is a novel coupling among the agents based on their transient state components or estimates thereof in the output feedback case. This coupling achieves transient synchronization in order to improve the cooperative behavior of the group in transient phases and guarantee a desired decay rate of the synchronization error. This leads to a cooperative reaction of the group on local disturbances acting on individual agents. The effectiveness of the proposed distributed regulator is illustrated by a vehicle platooning example and a coordination example for a group of four non-identical 3-DoF helicopter models.
Reference tracking and disturbance rejection problems can be formulated in the general framework of output regulation which was developed in the 1970s, @cite_20 @cite_35 . The basic setup consists of a so-called , an autonomous system that generates all external signals (references as well as disturbances) acting on the plant, and a description of the plant. The signal generated by the exosystem is referred to as the . The tracking and regulation requirements are formulated in terms of a regulation error depending on the plant state and the external signals. The objective is to find a control law, also called , which ensures internal stability of the plant and asymptotic convergence to zero of the regulation error for all initial conditions. For the details on the output regulation theory, the reader is referred to the books @cite_15 , @cite_32 , and @cite_24 .
@cite_35 @cite_32 @cite_24 @cite_15 @cite_20
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Necessary structural criteria are obtained for linear multivariable regulators which retain loop stability and output regulation in the presence of small perturbations, of specified types, in system parameters. It is shown that structural stability thus defined requires feedback of the regulated variable, together with a suitably reduplicated model, internal to the feedback loop, of the dynamic structure of the exogenous reference and disturbance signals which the regulator is required to process. Necessity of these structural features constitutes the ‘internal model principle’. Control Theory for Linear Systems deals with the mathematical theory of feedback control of linear systems. It treats a wide range of control synthesis problems for linear state space systems with inputs and outputs. The book provides a treatment of these problems using state space methods, often with a geometric flavour. Its subject matter ranges from controllability and observability, stabilization, disturbance decoupling, and tracking and regulation, to linear quadratic regulation, @math and @math control, and robust stabilization. Each chapter of the book contains a series of exercises, intended to increase the reader's understanding of the material. Often, these exercises generalize and extend the material treated in the regular text. Preface 1. Linear output regulation 2. Introduction to nonlinear systems 3. Nonlinear output regulation 4. Approximation method for the nonlinear output regulation 5. Nonlinear robust output regulation 6. From output regulation to stabilization 7. Global robust output regulation 8. Output regulation for singular nonlinear systems 9. Output regulation for discrete-time nonlinear systems Notes and references Appendices Bibliography Index. 1 The problem of output regulation.- 1.1 Introduction.- 1.2 Problem statement.- 1.3 Output regulation via full information.- 1.4 Output regulation via error feedback.- 1.5 A particular case.- 1.6 Well-posedness and robustness.- 1.7 The construction of a robust regulator.- 2 Disturbance attenuation via H?-methods.- 2.1 Introduction.- 2.2 Problem statement.- 2.3 A characterization of the L2-gain of a linear system.- 2.4 Disturbance attenuation via full information.- 2.5 Disturbance attenuation via measured feedback.- 3 Full information regulators.- 3.1 Problem statement.- 3.2 Time-dependent control strategies.- 3.3 Examples.- 3.4 Time-independent control strategies.- 3.5 The local case.- 4 Nonlinear observers.- 4.1 Problem statement.- 4.2 Time-dependent observers.- 4.3 Error feedback regulators.- 4.4 Examples.- 5 Nonlinear H?-techniques.- 5.1 Introduction.- 5.2 Construction of the saddle-point.- 5.3 The local scenario.- 5.4 Disturbance attenuation via linearization.- A Matrix equations.- A.l Linear matrix equations.- A.2 Algebraic Riccati equations.- B Invariant manifolds.- B.l Existence theorem.- B.2 Outflowing manifolds.- B.3 Asymptotic phase.- B.5 A special case.- B.6 Dichotomies and Lyapunov functions.- C Hamilton-Jacobi-Bellman-Isaacs equation.- C.l Introduction.- C.2 Method of characteristics.- C.3 The equation of Isaacs.- C.4 The Hamiltonian version of Isaacs' equation. For the multivariable control system described by [ x = Ax + Bu, y = Cx, z = Dx, ] necessary and sufficient conditions are found for the existence of state feedback @math such that @math and @math as @math . It is assumed that @math is A-invariant, or equivalently that a dynamic observer is utilized. A constructive version of the existence conditions is obtained under the further assumption that auxiliary integrating elements can be introduced by way of dynamic compensation, and a bound is given for the number of such elements required.