Robust State Feedback Regulator Design for General Linear Heterodirectional Hyperbolic Systems

This paper considers the minimum time output regulation problem for general linear heterodirectional hyperbolic systems with spatially-varying coefficients. For this, a state feedback regulator achieving output regulation in minimum time is determined. In order to obtain an output feedback regulator, finite-time reference and disturbance observers are designed. The latter observer achieves the estimation of the disturbance model and plant states in minimum time. For this, only an additional ODE has to be added to the usual asymptotic-time disturbance observer. The combination of the state feedback regulator with these observers results in an output feedback regulator, for which minimum time output regulation is verified. The output regulation approach is formulated for general signal models, that need not be diagonalisable, and is applied to an unstable hyperbolic system. The comparison of the obtained results with an asymptotic-time design confirms the performance increase gained by the solution of the minimum time output regulation problem.

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.

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.

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 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.

This technical note deals with the robust output regulation problem for boundary controlled linear 2 × 2 hyperbolic systems. Thereby, the output to be controlled can be located at one of the boundaries or is a pointwise in-domain output. By utilizing the internal model principle, a state feedback regulator is determined for a finite-dimensional signal model describing the exogenous signals. This amounts to stabilizing a hyperbolic PDE-ODE cascade coupled at an intermediate point. For this, a systematic backstepping method is developed to determine the stabilizing state feedback controller. The solvability of the considered output regulation problem can easily be verified on the basis of the nominal plant transfer behaviour. For non-destabilizing model uncertainties the robustness of the achieved output regulation is verified. An uncertain hyperbolic system with an in-domain output illustrates the results of the technical note.

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.

This paper deals with the problem of robust output regulation of planar two degrees of freedom robotic manipulators. An internal model controller is synthesized by a systematic framework that considers polynomial mappings of the steady-state trajectory. The closed- loop stabilization is guaranteed by using a descriptor differential-algebraic representation of the system. This methodology allows the controller design problem to be cast as a convex optimization problem subject to linear matrix inequalities.

In this paper, robust output regulation problems of singular linear systems are studied. Under appropriate assumptions, it is given that the solvability of robust output regulation problems equals to a specifically row full rank matrix. Moreover, the methods for constructing the feedback regulator are discussed.

Robust output regulation of discrete-time linear systems by quantized output feedback control

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.

While the output regulation problem for linear systems accommodates both bounded and unbounded exogenous signals, the existing formulation of the output regulation problem for nonlinear systems only allows bounded exogenous signals produced by an exosystem with a neutrally stable equilibrium. In particular, when it comes to the robust output regulation problem, the only admissible exogenous signal is a finite combination of step and sinusoidal functions. In this paper, we give a general formulation of the robust output regulation problem that admits unbounded exogenous signals, and contains the previous formulations as special cases when the system is linear or when the exogenous signals are bounded. Then, we give conditions under which the problem can be solved by solving a robust stabilization problem of an augmented system. Finally, we apply our general result to obtain the solvability conditions of the general robust output regulation problem for the class of lower triangular nonlinear systems.

Global robust output regulation of nonlinear strict feedforward systems

The semi-global stabilization problem and output regulation problem of singular linear systems subject to input saturation are addressed. A reduced-order normal system is obtained by a standard coordinate transformation. It is further shown that the controller that solves the stabilization (output regulation) problem of the reduced-order normal systems also solves the stabilization (output regulation) problem of the original singular systems.

Robust regulation for a 3-DOF helicopter via sliding-mode observation and identification