Uncertain Exosystem Research Articles

Robust internal model‐based control for linear‐time‐invariant systems

AbstractThis article addresses robust output regulation for systems affected by disturbances generated by an uncertain exosystem as well as matched external disturbances. The robustness of the feedback loop is achieved by combining internal model based control with sliding mode control, resulting in a structurally simple controller. The design of the proposed controller is presented first for the full information problem, that is, the disturbances generated by the exosystem and the state‐information is available for the control algorithm. This requirement is relaxed in the second step of the controller design, where the observer‐based robust output feedback‐loop structure is developed. Results from a comparative simulation study are presented to illustrate the advantages and the effectiveness of the proposed controller concept.

Distributed Nash Equilibrium Seeking With Dynamics Subject to Disturbance of Unknown Frequencies Over Jointly Strongly Connected Switching Networks

In this paper, we study the problem of distributed Nash equilibrium seeking of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -player games with single integrator dynamics subject to disturbances generated by an uncertain exosystem. Similar problems have been studied for games with single integrator dynamics subject to disturbances generated by a known exosystem. In addition, this paper offers some other new features. First, the existing results only apply to static, connected, and undirected graphs while the result of this paper applies to jointly strongly connected switching graphs, which can be disconnected at every time instant. Second, the existing results are asymptotic or ultimately uniformly bounded, while our result guarantees the exponential convergence when the exosystem is known. Third, the validity of existing results relies on an inequality involving some Lipschitz constant and the smallest nonzero eigenvalue of the Laplacian of the network graph. In contrast, the result of this paper is unconditional other than satisfying the same assumptions on the cost functions as those in the literature. Our design is illustrated by an application to velocity-actuated robots in sensor networks.

The regulation controller design for linear random systems with an uncertain exosystem

A new controller with an internal model architecture for the random systems is proposed in this paper. The conventional internal model principle as an effective control method depending on the structural knowledge of the external stimuli is applied to cancel the external inputs to achieve the trajectory tracking. However, it is known that there always exist uncertain random disturbances in systems, especially in a physical model working. For this situation, this paper constructs a new controller with the internal model form, such that the closed-loop system to be noise-to-state stable in the mean square (NSS-2-M). As a natural extension, considering the uncertainties of the exosystem, an adaptive internal control law is proposed in this paper and the noise-to-state practically stable in the mean square (NSpS-2-M) of the closed-loop system is also presented. The simulation results illustrate that all the signals of the closed-loop system are bounded, and the tracking error tends to an arbitrarily small neighborhood of the origin by turning the designed parameters.

Innovation Feedback Kalman Filter

The conventional Kalman filter demands complete knowledge of the actual filter model, which is usually inaccessible in practical problems. When dealing with the filtering problem with uncertainty, any improper prediction of the uncertainty may degrade the filtering performance and even lead to divergence phenomenon. In this paper, the innovation feedback Kalman filter, which introduces the innovation feedback controller to the Kalman filter equations, is newly proposed on the basis of automatic control theory to address the filtering problem with uncertainty and is different from other filtering methods. By studying the estimate error equations, the estimate bias is extracted and its propagation mechanism is formulated. The estimate bias propagation equations reveal that eliminating the estimate bias essentially equivalents to an output regulation problem with uncertain exosystem. And a concise yet effective innovation feedback controller is subsequently given as an example. The proposed method is applied to one-dimension target tracking scenario and its high estimation accuracy performance and good stability are simulated through a comparative analysis with the ideal filtering results.

Global disturbance rejection for nonlinear lower triangular systems with iISS inverse dynamics and uncertain exosystem

SummaryThis paper concerns about the global disturbance rejection problem for uncertain nonlinear lower triangular systems with integral input‐to‐state stable (iISS) inverse dynamics and an uncertain exosystem. The main challenges addressed in this paper include uncertain exosystem, unknown control direction, iISS inverse dynamics, and complex structure of lower triangular systems. Because of the presence of both uncertain exosystem and unknown control direction, simply combining the existing techniques for each of these challenges cannot solve the proposed problem. In fact, to handle the current case, appropriate new update laws for the estimators of the uncertain parameters are required, such that the estimators can be successfully integrated with the internal model principle. Furthermore, the changing supply function technique for iISS systems is utilized to deal with the iISS inverse dynamics. With the proposed controller, the closed‐loop system is globally asymptotically stable, and the disturbance is globally rejected. Two simulation examples are finally presented to show the effectiveness of the proposed control scheme and the practical relevance of our work. Copyright © 2016 John Wiley &amp; Sons, Ltd.

An adaptive regulation problem and its application

This paper studies an adaptive regulation problem for the modified FitzHugh-Nagumo neuron model under external electrical stimulation. We first present the solution of the global robust output regulation problem for output feedback system with an uncertain exosystem which models the external electrical stimulation with unknown frequency and amplitude. Then, we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output regulation problem for the modified FitzHugh-Nagumo neuron model are all satisfied. Then, we apply the obtained output regulation result to constructing an output feedback control law for the modified FitzHugh-Nagumo neuron model to achieve global stability of the closed-loop system in the presence of uncertain parameters and external stimulus. An example is given to show that the proposed algorithm can completely reject the external electrical stimulation.

Output regulation problem for a class of SISO infinite dimensional systems via a finite dimensional dynamic control

This paper deals with the output regulation problem for a class of SISO infinite dimensional systems with an uncertain exosystem. For these systems, a concept of relative degree is firstly introduced and used to construct a transformation which leads to the canonical form of output feedback systems. Then, based on this canonical form, by means of an internal model and a recursive adaptive control, the authors obtain an adaptive regulator which solves the problem. It should be pointed out that the proposed regulator is finite dimensional while it is usually infinite dimensional in existing literatures.

Global output regulation for output feedback systems with an uncertain exosystem and its application

AbstractThis paper presents the solvability conditions for the global robust output regulation problem for a class of output feedback systems with an uncertain exosystem by using output feedback control. An adaptive control technique is used to handle the unknown parameter vector in the exosystem. It is shown that this unknown parameter vector can be exactly estimated asymptotically if a controller containing a minimal internal model is employed. The effectiveness of our approach has been illustrated by an asymptotic tracking problem of a generalized fourth‐order Lorenz system. Copyright © 2009 John Wiley &amp; Sons, Ltd.

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.

Decentralized adaptive output regulation for a class of large-scale nonlinear systems

We address the output regulation problem for a class of large-scale nonlinear systems with a neutrally stable uncertain exosystem via a decentralized error feedback adaptive control strategy.