Harmonic internal models for structurally robust periodic output regulation

Introduction: the basic ingredients of asymptotic output regulation the computation of the steady-state response highlights of output regulation for linear systems. Output regulation of nonlinear systems: the regulator equations the internal model necessary and sufficient conditions for local output regulation the special case of harmonic exogenus inputs approximate regulation. Existence conditions for regulator equations: linear regulator equations and transmission zeros the zero dynamics of a nonlinear system existence of solutions of the nonlinear regulator equations. Robust output regulation: structurally stable local regulation robust local regulation the special case of systems in triangular form a globally defined error-zeroing invariant manifold semiglobal robust regulation.

This paper studies a robust output regulation problem with nonlinear exosystems without the assumption that the solution to the regulator equations along the trajectory of the exosystems should be polynomial. Based on the extended concepts of steady-state generator and internal model, a set of sufficient conditions for the solvability of the problem are given. Thus, the result developed in this paper can allow the robust output regulation problem with nonlinear exosystems to accommodate much more general nonlinear given plants including those which contain nonpolynomial nonlinearity.

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

This article investigates the robust optimal output regulation problem for the constrained uncertain nonlinear systems. A two‐step design framework is proposed to overcome the difficulties brought by uncertainties, constraint and performance optimization. First, the feedforward controller is designed by the internal model principle, and the robust output regulation problem is transformed into the robust stabilization problem. Then, the optimal control problem with input saturation is further considered in the robust feedback controller design process. With the help of a non‐quadratic cost functional, actor‐critic algorithm and robust redesign technique are brought together to design the constrained robust optimal feedback controller. Finally, stability analysis based on Lyapunov method shows that all the signals of the closed‐loop system remain bounded, and the tracking error is uniformly ultimately bounded with arbitrarily small ultimate bound. Simulation results illustrate the effectiveness of the proposed methodology.

The problem of global robust output regulation for a class of switched nonlinear systems with nonlinear exosystems is investigated in this paper where not all subsystems are stabilizable. First, as an extension of the concept of non‐switched internal model, this paper defines a switched internal model, which together with the plant is called the switched augmented system. Also, we show that the problem of output regulation for the switched nonlinear system can be converted into a global robust regulation problem of the switched augmented system. Second, based on the average dwell time method, the global robust regulation problem under a class of switching signals with average dwell time is solved, which leads to the solution of the problem of global robust output regulation. Finally, an example is provided to demonstrate the effectiveness of the proposed design approach.

This article develops a robust adaptive boundary output regulation approach for a class of complex anticollocated hyperbolic partial differential equations subjected to multiplicative unknown faults in both the boundary sensor and actuator. The regulator design is based on the internal model principle, which amounts to stabilize a coupled cascade system, which consists of a finite-dimensional internal model driven by a hyperbolic distributed parameter system (DPS). To this end, a systematic sliding mode equipped with a backstepping approach is developed such that the robust state feedback control can be realized. Moreover, since the available information is a faulty boundary measurement at the right side point, state estimation is required. However, due to the presence of boundary unknown faults, we need to solve an issue of joint fault-state estimation. Restrictive persistent excitation conditions are usually required to guarantee the exact estimation of faults but are unrealistic in practice. To this end, a novel concurrent learning (CL) adaptive observer is proposed so that exponential convergence is obtained. It is the first time that the spirit of CL is introduced to the field of DPSs. Consequently, the observer-based adaptive boundary fault tolerant control scheme is developed, and rigorous theoretical analysis is given such that the exponential output regulation can be achieved. Finally, the effectiveness of the proposed methodology is demonstrated via comparative simulations.

The topic of this paper is the backstepping-based solution of the robust state feedback regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients. Thereby, a large class of outputs is considered, i.e., mixed distributed and pointwise in-domain or boundary outputs. The state feedback regulator design is based on the $\boldsymbol {p}$ -copy internal model principle. This results in a stabilization problem for a cascade of $\boldsymbol {m+p}$ boundary controlled transport partial differential equations (PDEs) with $\boldsymbol {p}$ ordinary differential equations (ODEs). For this, a systematic backstepping approach is presented, in which all design equations are explicitly solvable in backstepping coordinates. Furthermore, the solvability conditions for the considered output regulation problem can be evaluated in closed form utilizing the plant transfer behavior. Robust output regulation is verified for nondestabilizing model uncertainties and unknown disturbance input locations. A $\boldsymbol {4 \times 4}$ hyperbolic system with uncertain transport velocities and couplings in the transport PDEs illustrates the results of this paper.

A preliminary analysis of the local regulator problem is presented. It is then demonstrated that it is possible to isolate the main ingredients of a global solution to the output regulation problem. The authors then summarize some recent advances in the design of globally stabilizing feedback laws that were made possible by suitable use of the notion of passivity and, in particular, by the solution to the problem of when a given nonlinear system can be rendered passive via state feedback. Some of the results obtained are applied to the problem of deriving globally/asymptotically stabilizing feedback laws for certain classes of nonlinear systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper formulates a robust output regulation problem for a linear timeinvariant system with uncertain parameters whose controlled output may be different from the measurement output. Conditions for solvability of the problem are given and two algorithms are presented for designing controllers that achieve robust output regulation; each of them consists of a proportional plus integral regulator and a proportional plus integral observer. It turned out that the regulator is a state feedback controller that achieves output regulation and the observer is an unknown input observer for a system with either fictitious exogenous input or fictitious controlled output.

Output regulation aims to achieve, in addition to closed-loop stability, asymptotic tracking and disturbance rejection for a class of reference inputs and disturbances. Thus, it poses a more challenging problem than stabilization. For over a decade, the nonlinear output regulation problem has been one of the focuses in nonlinear control research, and active research on this problem has generated many fruitful results. Nevertheless, there are two hurdles that impede the further progress of the research on the output regulation problem. The first one is the assumption that the solution or the partial solution of the regulator equations is polynomial. The second one is the lack of a systematic mechanism to handle the global robust output regulation problem. We establish a general framework that systematically converts the robust output regulation problem for a general nonlinear system into a robust stabilization problem for an appropriately augmented system. This general framework, on one hand, relaxes the polynomial assumption, and on the other hand, offers a greater flexibility to incorporate recent new stabilization techniques, thus setting a stage for systematically tackling the robust output regulation with global stability.

In this paper, we extend to the case of higher relative degree and uncertain high-frequency gain a recently proposed method for the solution of problems of output regulation for nonlinear systems. The method is applicable to systems with possibly unstable zero dynamics, in which case the problem at issue is addressed by rendering an appropriate auxiliary system stable, with a constrain on the gain. The dynamics of this auxiliary system only depend on the zero dynamics of the controlled plant, while the constraint on the gain only depends on some parameters of the exogenous input which have to be tracked.

This paper investigates the problem of output regulation of the Arneodo-Coullet chaotic system, which is one of the paradigms of the chaotic systems proposed by A. Arneodo, P. Coullet and C. Tresser (1981). Explicitly, state feedback control laws to regulate the output of the Arneodo-Coullet chaotic system have been derived so as to track the constant reference signals as well as to track periodic reference signals. The control laws are derived using the regulator equations of C.I. Byrnes and A. Isidori (1990), who solved the problem of output regulation of nonlinear systems involving neutrally stable exosystem dynamics. The output regulation of the Coullet chaotic system has important applications in Electrical and Communication Engineering. Numerical simulations are shown to verify the results.

This paper deals with the problem of robust tracking and disturbance rejection for a linear time-invariant system where the uncertainty of the system is represented in a structured form and the output to be controlled may be different from the measurement output. First, the problem is considered in a rather classical setting in that the required property of tracking and disturbance rejection can be attained as long as the resulting closed-loop system remains stable. Conditions for solvability of the problem are given and two algorithms are presented for designing controllers having the robust tracking and disturbance rejection property. Second, the problem of robust output regulation with robust stability is formulated as one of finding a controller such that the resulting closed-loop system satisfies an additional requirement of robust stability and thus the output regulation property can be maintained for all perturbations of uncertain parameters within a prescribed set. A procedure based on a high gain observer approach is proposed to solve this problem.

In this paper the robust cooperative output regulation problem for multi-agent systems (MAS) with general heterodirectional hyperbolic PIDE-ODE agents is considered. This setup also covers networks of ODEs with arbitrarily long input and output delays. The output of the agents can be defined at all boundaries, in-domain and may depend on the ODE state, while disturbances act on the agents in-domain, at the boundaries, the output and the ODE. The communication network is described by a constant digraph and if its Laplacian is reducible, then heterogeneous agents are permitted also in the nominal case. The solution is based on the cooperative internal model principle, which requires to include a diffusively driven internal model in the controller. The corresponding state feedback regulator design starts with a local backstepping stabilization of the coupled hyperbolic PIDE-ODE systems. It is shown that the remaining simultaneous stabilization of the MAS can be traced back to the simultaneous stabilization of the finite-dimensional cooperative internal model. Solvability conditions in terms of the network topology and the agents transfer behavior are presented. The new design method is applied to the formation control of a platoon of uncertain heavy ropes carrying loads to verify its applicability. Simulations confirm the synchronization performance achieved by the resulting networked controller.

Formation control for nonlinear multi-agent systems by robust output regulation