Global Robust Output Regulation Problem Research Articles

Parameter convergence and minimal internal model with an adaptive output regulation problem

The parameter convergence of nonlinear adaptive control systems is an important yet not well addressed issue. In this paper, using the global robust output regulation problem of output feedback systems with unknown exosystems as a platform, we will show that the well known persistency of excitation (PE) condition still guarantees the convergence of the estimated parameter vector to the true parameter vector. Moreover, the PE condition will be satisfied if the internal model is minimal in certain sense.

An Asymptotic Tracking Problem and Its Application

This paper deals with an asymptotic tracking problem for the Chua's circuit. We first show that the control problem for the Chua's circuit can be formulated as the global robust output regulation problem for nonlinear systems in output feedback form. Then we show that the solvability conditions for the output regulation problem for the Chua's circuit are all satisfied. Finally, an output feedback control law is designed for the Chua's circuit. The control law enables, in the presence of large parameter variations, the output of the circuit to track a class of sinusoidal signals with arbitrary amplitudes and initial phases while maintaining the global stability of the closed-loop system.

Asymptotic Disturbance Rejection of the Duffing's System by Adaptive Output Feedback Control

This paper studies the output feedback disturbance rejection problem of the uncertain Duffing's system subject to a sinusoidal external disturbance with unknown frequency and amplitude. We first formulate the problem as a global robust output regulation problem subject to an uncertain exosystem which models the sinusoidal disturbance. Then, we apply the adaptive output regulation technique to construct an output feedback control law to solve the problem. Our adaptive control law contains a parameter update law for estimating the unknown frequency of the disturbance, and we will show that the estimated frequency converges to its real value.

Global robust output regulation of lower triangular systems with unknown control direction

This paper presents the solvability conditions for the global robust output regulation problem for lower triangular nonlinear systems assuming the control direction is unknown. The approach used is an integration of the robust stabilization technique and Nussbaum gain technique.

An Alternative Approach to Global Robust Output Regulation of Output Feedback Systems

The global robust output regulation problem of the output feedback systems has been extensively studied under various assumptions of the complexity and uncertainty. All these approaches boil down to a stabilization problem of a so-called augmented extended system. This paper will describe an alternative approach which converts the original problem into a stabilization problem of a so-called extended augmented system. As the extended augmented system is somewhat simpler than the augmented extended system, this alternative approach is also simpler than the first approach.

Global Robust Output Regulation of Output Feedback Systems With Unknown High-Frequency Gain Sign

The global robust output regulation problem for nonlinear systems in output feedback form has been solved under a key assumption that the high-frequency gain sign is known. This note shows that this assumption can be removed by incorporating the Nussbaum gain technique into the existing framework for handling the robust output regulation problem.

A general formulation and solvability of the global robust output regulation problem

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 for output feedback systems

The global robust output regulation problem for the class of nonlinear systems in output feedback form has been studied under the assumption that the solution of the regulator equations is polynomial. This assumption essentially requires these systems contain only polynomial nonlinearity and is due to the failure of finding a nonlinear internal model to account for more complex nonlinearities than polynomials. Recently, it was found that a nonlinear internal model can be constructed under some assumption much milder than the polynomial assumption. In this note, we will apply this type of internal model to solve the global robust output regulation problem for the class of nonlinear systems in output feedback form.

A General Framework for Tackling the Output Regulation Problem

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.

Global adaptive robust servomechanism of lower triangular systems via nonlinear internal model

The global robust servomechanism problem (alternatively, global robust output regulation problem) for lower triangular systems has been studied for two special cases. The first case assumes that the systems only contain polynomial nonlinearities, and the second case limits the exogenous signals and the unknown parameters to be within a known bounded set. This paper presents the solvability conditions of the global robust servomechanism problem for the lower triangular systems for the most general case where neither of the above two assumptions is needed.

Global robust servomechanism problem of lower triangular systems in the general case

The global robust servomechanism problem (alternatively, global robust output regulation problem) for lower triangular systems has been studied for two special cases. The first case assumes that the systems only contain polynomial nonlinearities, and the second case limits the exogenous signals and the unknown parameters to be within a known bounded set. This paper presents the solvability conditions of the global robust servomechanism problem for the lower triangular systems for the most general case where neither of the above two assumptions is needed. Our approach consists of two steps. In the first step, we convert the problem into a global adaptive regulation problem for lower triangular systems subject to both dynamic and static uncertainties. In the second step, we derive the solvability conditions of the problem by appealing to the recent result on the solvability of the global adaptive regulation problem for lower triangular systems with both dynamic and static uncertainties.