Output Regulation Theory Research Articles

Distributed output regulation of leader–follower multi‐agent systems

SUMMARYIn this paper, distributed leader–follower control algorithms are presented for linear multi‐agent systems based on output regulation theory and internal model principle. By treating a leader to be followed as an exosystem, the proposed framework can be used to generalize existing multi‐agent coordination solutions to allow the identical agents to track an active leader with different dynamics and unmeasurable variables. Moreover, the obtained results for multi‐agent coordination control are an extension of previous work on centralized and decentralized output regulation to a distributed control context. Necessary and sufficient conditions for the distributed output regulation problem are given. Finally, distributed output regulation of some classes of multi‐agent systems with switching interconnection topologies are discussed via both static and dynamic feedback. Copyright © 2011 John Wiley & Sons, Ltd.

Robust Attitude Regulation of a 3-DOF Helicopter Benchmark: Theory and Experiments

This paper presents the design and experimental results of the robust attitude regulation for a 3-DOF Quanser helicopter benchmark. The control objective is to asymptotically track the desired elevation and pitch reference signals generated by an exogenous system, while keeping all the closed-loop states bounded, even if there exist unknown uncertainties. Based on the output-regulation theory and signal compensation technique, a new design method of state feedback robust controller is proposed. This method permits the existence of unknown uncertainties and external disturbances in both the helicopter and the exosystem. Only knowledge about the bounds of these uncertainties is required. The experimental results demonstrate the desired performance of the proposed controller implemented on the Quanser helicopter.

Output Consensus of Heterogeneous Uncertain Linear Multi-Agent Systems

This technical note studies the output consensus problem for a class of heterogeneous uncertain linear multi-agent systems. All the agents can be of any order (which might widely differ among the agents) and possess parametric uncertainties that range over an arbitrarily large compact set. The controller uses only the output information of the plant; moreover, the delivered information throughout the communication network is also restricted to the output of each agent. Based on the output regulation theory, it is shown that the output consensus is reached if the (state) consensus is achieved within the internal models among the agent's controllers (even though the plant's outputs, rather than the internal model's outputs, are communicated). The internal models can be designed and embedded into the controller, which provides considerable flexibility to designers in terms of the type of signals that are agreed on among the agents.

Robust control of a submarine snorkel system

AbstractThis paper illustrates a control strategy for a submarine snorkel able to assure that the water surface profile can be tracked by the extremity of the device, called “fluctuating head”. The proposed solution is based on adaptive output regulation theory. More precisely, it is assumed that wave profile can be approximated as a linear combination of a number of harmonics of unknown amplitude, phase and frequency and we look for an internal model-based adaptive regulator able to enforce the top of the mast to track the reference profile. The effectiveness of the proposed adaptive scheme is shown through simulations.

Adaptive neural output regulation control of a solar power plant

This work proposes an indirect adaptive nonlinear control scheme based on a recurrent neural network and the output regulation theory. The neural model is first trained off-line, being further improved by means of an on-line learning strategy using the Lyapunov and nonlinear observation theories. The regulation problem is solved by an iterative strategy, formulated as an eigenvalue assignment problem, ensuring the convergence of the regulation equations. The strategy was tested on a distributed collector field of a solar power plant (Plataforma Solar de Almería, Spain). Experimental results, collected on the solar power plant, show the effectiveness of the proposed approach.

On Synchronous Steady States and Internal Models of Diffusively Coupled Systems

We investigate the problem of synchronizing non-identical nonlinear dynamical systems by means of generalized diffusive couplings. The focus is not on the actual solution to the problem but on the derivation of necessary conditions for the existence of such a solution despite the systems possessing non-identical models. We show that for the problem to be solvable a synchronous steady state needs to exist. This condition leads to the requirement that all individual system models need to embed an internal model of some virtual exosystem. The latter condition is expressed in terms of nonlinear partial differential equations. The conditions derived in this paper are related to those known from the theory of output regulation.

A Remark on Sensor Disturbance Rejection of Nonlinear Systems

When disturbances enter sensors, the states of a plant cannot be precisely measured and the state feedback controllers are not implementable. Instead, the so-called measurement feedback controllers become interesting. For nonlinear systems, the output regulation theory is widely used for handling actuator and plant disturbances. This note gives a remark how the output regulation theory can be applied for sensor disturbances, and hence provides a novel measurement feedback design approach.

Attitude Tracking and Disturbance Rejection of Rigid Spacecraft by Adaptive Control

In this technical note, we deal with the attitude tracking and disturbance rejection problem of spacecraft for a class of persistent disturbances with unbounded energy which include the sinusoidal disturbance as a special case. The approach involves the integration of techniques from robust control, adaptive control, and robust output regulation theory.

Uniform Practical Nonlinear Output Regulation

In this paper, we present a solution to the problem of asymptotic and practical semiglobal regulation by output feedback for nonlinear systems. A key feature of the proposed approach is that practical regulation is achieved uniformly with respect to the dimension of the internal model and to the gain of the stabilizer near the zero error manifold. This property renders the approach interesting for a number of real cases by bridging the gap between output regulation theory and advanced engineering applications. Simulation results regarding meaningful control problems are also presented.

State-space Approach to Pricing Design in OSNR Nash Game

The static nature of the noncooperative power control game model in optical networks makes it difficult to study and design an appropriate pricing scheme. In this paper, we derive a first-order best response dynamics from the game-theoretical model and formulate a general multi-input and multi-output (MIMO) state-space model. We use classical linear system theory to explain the controllability of the pricing and the observability of the power states. We use the output regulator theory to design a pricing policy for the network for a given optical signal-to-noise ratio (OSNR) target.

Output Tracking of Piecewise-Linear Systems via Error Feedback Regulator With Application to Synchronization of Nonlinear Chua's Circuit

This paper considers the output tracking problem of general piecewise discrete-time linear systems via error feedback scheme. A number of sufficient conditions are obtained based on piecewise-quadratic Lyapunov functions in the framework of output regulation theory. The resulting closed-loop system is guaranteed to be stable and the output tracking is achieved asymptotically. Moreover, the proposed piecewise-linear model based regulator has been successfully applied to the chaos synchronization of general nonlinear Chua's circuits. Simulation results are also given to illustrate the performance and advantages of the proposed approach.

Experimental Output Regulation for a Nonlinear Benchmark System

Research on the nonlinear output regulation problem is mainly focused on theoretical developments and studies on simulation level. In this brief, we present experimental results on the local output regulation problem for a nonlinear benchmark mechanical system, the so-called translational oscillator with a rotational actuator system. The presented results show the effectiveness of the nonlinear output regulation theory in practice. As follows from the conducted experiments, issues such as the convergence rate, stability, and performance robustness with respect to (non) parametric uncertainties, the size of the region of attraction, and actuator saturation should be accounted for in tuning the controller gains. This design problem has not been addressed in the existing literature on the nonlinear output regulation problem and it, therefore, raises a new direction for research crucial to the future application of output regulation theory in practice.

Output tracking and synchronization of chaotic Chua’s circuit with disturbances via model predictive regulator

In this paper, we consider the output tracking and synchronization problem for a piecewise linear chaotic Chua’s circuit, which is expected to follow the reference signal generated by another autonomous chaotic Chua’s circuit. A novel model predictive regulator is proposed to guarantee the chaos synchronization in the presence of external disturbance. Moreover with this regulator, the optimal transient tracking performance for synchronization is ensured even when the piecewise autonomous and controlled Chua’s circuits switch asynchronously. The proposed approach is highly efficient in the sense that the regulation conditions can be satisfied by solving a set of linear matrix inequalities and several Sylvester equations instead of many partial differential regulator equations in the well-known nonlinear output regulation theory.

A New Approach to Adaptive Nonlinear Regulation

This paper shows how the theory of adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The main result obtained in this way is a new method for the synthesis of adaptive internal models, which substantially enhances the existing theory of adaptive output regulation by allowing nonlinear internal models and more general classes of controlled plants.

Feedback and Feedforward Output Regulation of Bounded Uniformly Continuous Signals for Infinite‐Dimensional Systems

This article presents a state space output regulation theory for linear infinite‐dimensional systems (with bounded control, observation, and feedthrough operators) in which the reference and disturbance signals are bounded and uniformly continuous. Output regulation problems are posed and solved for both feedforward and error feedback controllers. Furthermore, under certain assumptions necessary conditions are obtained for those controllers which solve these output regulation problems. One consequence of these necessary conditions is a generalization of the well‐known internal model principle. A key feature in our theory is that the exogenous system generating the reference and disturbance signals is infinite‐dimensional.

Output feedback stabilization and approximate and restricted tracking for a class of cascaded systems

In this note, we discuss the problems of output feedback stabilization for a class of cascaded systems and of (approximate and restricted) output regulation for general nonlinear systems. It is shown that (global) output feedback stabilization for a class of systems in feedforward form can be achieved with a dynamic feedback law, yielding bounded control, and relying on the introduction of a reduced-order observer. The above result, together with standard tools borrowed from the output regulator theory, is instrumental to construct dynamic control laws achieving (approximate) disturbance rejection and output tracking in the presence of (small) disturbance/reference signals generated by a known exosystem.

INTERNAL MODEL BASED FRAMEWORK FOR TRACKING AND FAULT TOLERANT CONTROL OF A PERMANENT MAGNET SYNCHRONOUS MOTOR

In this paper an adaptive internal model based control scheme is designed to deal with tracking and input disturbance suppression problems for a permanent magnet synchronous motor. More in detail we show how to design a controller able to guarantee the perfect asymptotic tracking of unknown exogenous trajectories belonging to a certain family, embedding in the regulator the internal model of this family; the theoretical machinery exploited in order to prove the global asymptotical stability of the solution exposed is the nonlinear output regulation theory, specialized for the energy-based port-Hamiltonian formalism.

An internal model-based approach to certain pursuit-evasion problems

In this paper we propose a novel framework for dealing with certain pursuit-evasion control problems. The distinctive feature of the framework relies in fact that the evader trajectory is not assumed perfectly known in advance but it is just assumed to belong to a pre-specified possible set of maneuvers. By taking inspiration from the output regulation theory we design a controller which embeds an internal model of the allowed evader maneuvers and which is able to achieve asymptotic perfect tracking robustly with respect to uncertainties affecting the pursuer dynamic and the evader trajectories.

Implicit fault-tolerant control: application to induction motors

In this paper we propose an innovative way of dealing with the design of fault-tolerant control systems. We show how the nonlinear output regulation theory can be successfully adopted in order to design a regulator able to offset the effect of all possible faults which can occur and, in doing so, also to detect and isolate the occurred fault. The regulator is designed by embedding the (possible nonlinear) internal model of the fault. This idea is applied to the design of a fault-tolerant controller for induction motors in presence of both rotor and stator mechanical faults.

Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation

In this paper, we lay the foundations for a nonequilibrium theory of nonlinear output regulation, giving a more general (nonequilibrium) definition of the problem, deriving necessary conditions, and, using these necessary conditions, we present a set of sufficient conditions and a design methodology for the solution of the problem in question. Our analysis leads to a nonequilibrium enhancement of the internal model principle.