Systems In Output Feedback Form Research Articles

Globally Adaptive Neural Network Tracking for Uncertain Output-Feedback Systems.

This article investigates the problem of global neural network (NN) tracking control for uncertain nonlinear systems in output feedback form under disturbances with unknown bounds. Compared with the existing NN control method, the differences of the proposed scheme are as follows. The designed actual controller consists of an NN controller working in the approximate domain and a robust controller working outside the approximate domain, in addition, a new smooth switching function is designed to achieve the smooth switching between the two controllers, in order to ensure the globally uniformly ultimately bounded of all closed-loop signals. The Lyapunov analysis method is used to strictly prove the global stability under the combined action of unmeasured states and system uncertainties, and the output tracking error is guaranteed to converge to an arbitrarily small neighborhood through a reasonable selection of design parameters. A numerical example and a practical example were put forward to verify the effectiveness of the control strategy.

Virtual control strategy and conditioning technique for tracking and learning controls under input restrictions

The virtual control strategy for mechanical systems has been recently proposed (Gnucci and Marino, 2021) in the context of under-actuated mechanical systems. Such a strategy views and represents an under-actuated mechanical system as a fully actuated system with virtually added inputs and outputs having to satisfy, through a suitable choice of the virtual output reference signals, the virtual input zero-equality constraint: the related adaptive tracking control problem is then solved through standard design techniques. This paper exhibits a twofold aim. The first one is: to enlarge the concept of zero-input constraint and thus naturally adapt the virtual control approach to the case in which an actuator fault can occur. The second aim is: to show how the application and transposition of such an adaptation to two well-known classes of nonlinear systems (special systems in multi-variable tracking form with two inputs and outputs under actuator faults; one-relative-degree, single-input, single-output systems in output feedback form under input saturation) not only own strong connections with the conditioning technique, originally conceived in the context of anti-windup problems under input constraints, but they also gain original results.

Adaptive output regulation of a class of nonlinear output feedback systems with unknown high frequency gain

This paper presents an output feedback design approach based on the adaptive control scheme developed for nonlinearly parameterized systems, to achieve global output regulation for a class of nonlinear systems in output feedback form. We solve the output regulation problem without the knowledge of the sign and the value of the high frequency gain a priori. It is not necessary to have both the limiting assumptions that the exogenous signal w and the unknown parameter μ belong to a prior known compact set and the high frequency gain has a determinate lower and upper bounds. The effectiveness of the proposed algorithm is shown with the help of an example.

Global robust practical output regulation for nonlinear systems in output feedback form by output‐based event‐triggered control

SummaryIn this paper, we study the event‐triggered global robust practical output regulation problem for a class of nonlinear systems in output feedback form with any relative degree. Our approach consists of the following three steps. First, we design an internal model and an observer to form the so‐called extended augmented system. Second, we convert the original problem into the event‐triggered global robust practical stabilization problem of the extended augmented system. Third, we design an output‐based event‐triggered control law and a Zeno‐free output‐based event‐triggered mechanism to solve the stabilization problem, which, in turn, leads to the solvability of the original problem. Finally, we apply our result to the controlled hyperchaotic Lorenz systems.

Adaptive cooperative output regulation of nonlinear multiagent systems with arbitrarily large parametric uncertainties and an uncertain leader

SummaryThis paper extends the result for cooperative output regulation problem for uncertain nonlinear multiagent systems in output feedback form in the sense that the exosystem generating leader's signal and disturbance is allowed to contain unknown parameter, and all parameters in the whole multiagent system can be arbitrarily large. Since only the information of itself and its neighbors is available, constructing a distributed control law is necessary for the asymptotic tracking of the uncertain leader's signal and the rejection of unknown external disturbances, which is also the main challenge here. A series of simulations are conducted to illustrate the efficiency and advantage of our designs together with the comparison of the design in the existing work.

Cooperative Global Robust Output Regulation for Nonlinear Output Feedback Multiagent Systems Under Directed Switching Networks

In this paper, we study the cooperative global robust output regulation problem for nonlinear multiagent systems in output feedback form with any relative degree subject to directed switching networks. Through the augmentation by a distributed internal model and a distributed observer of the given system, we first convert the original problem into the global robust stabilization problem of the so-called extended augmented system, which is a multi-input-coupled switched system. Then, we establish a few technical lemmas to lay the foundation for constructing a switching control law and the corresponding multiple Lyapunov functions for the switched system. Then, we present the solvability conditions of our problem via the multiple Lyapunov functions and average dwell time method. The main result will be applied to the leader-following synchronization problem for a group of hyperchaotic Lorenz multiagent systems with a directed switching network.

Global Robust Output Regulation for a Class of Nonlinear Systems via Event-Triggered Control * *This work has been supported by the Research Grants Council of the Hong Kong Special Administration Region under grant No. 14200515.

Abstract In this paper, we study the event-triggered global robust output regulation problem for a class of nonlinear systems in output feedback form with unity relative degree. We first convert the problem into the event-triggered global robust stabilization problem of a well defined augmented system by the internal model approach. Then, we solve the stabilization problem by an output-based event-triggered control law together with an output-based event-triggered mechanism. Finally, the theoretical result is applied to the Lorenz systems.

A larger family of nonlinear systems for the repetitive learning control

A generalization of the PIDρ−1 control has been recently presented in Marino et al. (2012), which guarantees the output tracking of smooth periodic reference signals (with known period) for uncertain minimum phase nonlinear systems in output feedback form with any relative degree ρ≥1. In this note, we show that the repetitive learning control proposed in Marino et al. (2012) also solves the same output tracking problem for a larger class of uncertain nonlinear systems in normal form, provided that the inverse system dynamics satisfy the Demidovich condition on suitable compact sets.

Cooperative output regulation for a class of nonlinear multi-agent systems with arbitrarily large uncertainty

This paper studies the cooperative global robust output regulation problem for the nonlinear multi-agent systems in output feedback form with relative degree $r=2$ subject to arbitrarily large uncertainty. The robust control method alone cannot handle arbitrarily large uncertainty. By combining the robust and adaptive high gain technique, we develop a recursive procedure to construct a distributed output feedback control law to deal with the problem. The theoretical result of this paper is applied to the leader-following consensus problem of a family of hyper-chaotic Lorenz systems.

Output feedback adaptive control of a class of nonlinear discrete-time systems with unknown control directions and preceded by hysteresis

This paper considers the output feedback adaptive controller design problem for a class of discrete-time nonlinear systems in output feedback form with unknown control directions and preceded by unknown hysteresis. The problem of lacking in a-priori knowledge on the control directions and unknown hysteresis are solved by using the discrete Nussbaum gain and Prandtl–Ishlinskii model, respectively. The system is transformed into the form of a nonlinear auto regressive moving average (NARMA) model to construct an output feedback control. To overcome the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead-zone technique are constructed on the basis of the NARMA model. The proposed control algorithm guarantees that all the signals in the controlled system are bound and the output tracking error is made to be neighbourhood around zero, ultimately. Finally, simulations are performed on a nonlinear system to show the effectiveness of the proposed method

Cooperative Global Output Regulation for a Class of Nonlinear Multi-Agent Systems

In this technical note, we consider the cooperative global robust output regulation problem for nonlinear multi-agent systems in output feedback form by distributed output feedback control. The main result can be summarized as follows: if the information of the leader can reach every follower through a path and the communication flows among the followers are bidirectional, then the problem can be solved by a distributed output feedback control law if the global robust output regulation problem for each subsystem can be solved by an output feedback control law.

A class of nonlinear internal models for global robust output regulation problem

SummaryThe global robust output regulation problem of nonlinear systems in output feedback form has been studied via a linear internal model. In this paper, we study the same problem using a class of nonlinear internal models. An advantage of nonlinear internal models is that it exists even when the system contains nonpolynomial nonlinearity and the exosystem is nonlinear. Thus, the result of this paper applies to a larger class of nonlinear systems and a larger class of exosystems. Copyright © 2014 John Wiley & Sons, Ltd.

Global Adaptive Regulation of Uncertain Nonlinear Systems in Output Feedback Form

Minimum phase uncertain nonlinear systems in output feedback form are considered: they are subject to disturbances and/or uncertainties and are required to track reference signals. Both disturbances and references are generated by an exosystem whose model and order are uncertain. Assuming that the regulator problem has a solution, but with no a priori assumption on the required control input (e.g. no `immersion' assumption), a global robust error feedback regulator is explicitly computed which includes an adaptive internal model and a nonlinear stabilizing control, on the basis of known bounding functions for the uncertain system nonlinearities. The regulation error tends to a residual set which decreases as the reference input modeling error due to the internal model choice decreases. If the adaptive internal model can generate the required unknown control input, global asymptotic regulation is achieved.

Distributed Output Regulation for Multi-Agent Systems in Output Feedback Form with Parametric-Uncertain Leaders

In this paper, the distributed output regulation problem for a class of nonlinear multi-agent systems in output feedback form is considered. Here, the leader in the multi-agent system contains parametric uncertainties and the interconnection topology is described by a chain digraph. With regarding the leader as an exosystem, a distributed regulator is constructed by combining a distributed internal model and a distributed dynamic output feedback control.

Learning control for nonlinear systems in output feedback form

The class of single-input, single-output, minimum phase, nonlinear, time-invariant systems with unknown output-dependent nonlinearities, unknown parameters and known relative degree ρ is considered. The output regulation problem is addressed and solved in the presence of unknown periodic reference and/or disturbance signals of known common period. A simple learning control algorithm is designed which guarantees asymptotic output tracking for any initial condition belonging to any given connected compact set. It can be interpreted as a generalization of the classical PIDρ−1 control which solves the regulator problem when reference and disturbance signals are constant. As far as linear systems are concerned, global results are achieved.

Robust Adaptive Regulation by Output Error Feedback for Uncertain Nonlinear Systems

AbstractMinimum phase uncertain nonlinear systems in output feedback form are considered: they are subject to disturbances and/or uncertainties and are required to track reference signals. Both disturbances and references are generated by an exosystem whose parameters are uncertain. Under the assumption that the regulator problem has a solution, but with no a priori assumption on the required control input (e.g. no ‘immersion’ assumption), a global robust error feedback regulator is designed. If its adaptive internal model can generate the required control input global asymptotic regulation is achieved, otherwise the regulation error tends to a residual set which decreases as the reference input modeling error decreases.

Asymptotic stabilisation of a class of nonlinear systems via sampled-data output feedback control

This article considers sampled-data output feedback control of a class of nonlinear systems in output feedback form. The underlying continuous-time controller is designed based on backstepping technique, employing a linear dynamic filter, and globally asymptotically stabilises the system. Rigorous analysis shows that when implemented with a sampling and zero-order hold device, the sampled-data version of the continuous-time controller semi-globally asymptotically stabilises the original system, given that the sampling period is smaller than a specific value, which depends on the initial values and nonlinearity of the system. Simulation results of a physical system are included in the end.

Output feedback adaptive control of a class of nonlinear discrete-time systems with unknown control directions

In this paper, output feedback adaptive control is investigated for a class of nonlinear systems in output-feedback form with unknown control gains. To construct output feedback control, the system is transformed into the form of the NARMA (nonlinear-auto-regressive-moving-average) model, based on which future output prediction is carried out. With employment of the predicted future output, a constructive output feedback adaptive control is given with the discrete Nussbaum gain exploited to overcome the difficulty due to unknown control directions. Under the global Lipschitz condition of the system functions, the boundedness of all the closed-loop signals and asymptotical output tracking are achieved by the proposed control. Simulation results are presented to show the effectiveness of the proposed approach.

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.

A Sampled-Data Scheme for Disturbance Rejection of Nonlinear Systems in Output Feedback Form

This paper presents a sampled-data control scheme for disturbance rejection of nonlinear systems in output feedback form. The continuous-time controller is designed first using a filtered transformation and the internal model technique. Obtained on an emulation-based approach, the proposed sampled-data control uses the sampled output and a discrete-time implementation of the filter and the internal model is involved. The proposed control is shown to render the overall system stable in a spirit of fast sampling. Specifically, the ultimate bound of the output is allowed to be arbitrarily small by choosing appropriate gain parameters.