Semi-global Output Regulation Research Articles

Semiglobal Periodic Event-Triggered Output Regulation for Nonlinear Multiagent Systems

This study focuses on periodic event-triggered (PET) cooperative output regulation problem for a class of nonlinear multiagent systems. The key feature of PET mechanism is that event-triggered conditions are required to be monitored only periodically. This approach is beneficial for Zeno behavior exclusion and saving of battery energy of onboard sensors. At first, new PET distributed observers are proposed to estimate the leader information. We show that the estimation error converges to zero exponentially with a known convergence rate under asynchronous PET communication. Second, a novel PET output feedback controller is designed for the underlying strict feedback nonlinear multiagent systems. Based on a state transformation technique and a local PET state observer, the cooperative semiglobal output regulation problem can be solved by the proposed new control design technique. Simulation results of multiple Lorenz systems illustrate that the developed control scheme is effective.

Cooperative Semiglobal Robust Output Regulation of Non-Introspective Nonlinear Agents With Partial Normal Form and State-Dependent High-Frequency Gain

This paper investigates cooperative semig-lobal robust output regulation problem for a class of non-introspective nonlinear multiagent systems. Each agent of this class is allowed to have a partial normal form , instead of only the conventional normal form, with a state-dependent high-frequency gain. Besides, all agents are unaccessible to the controller states of their neighbors. In this setting, if the uniform detectability assumption in the sense of [25] is satisfied, then a robust distributed regulator can be designed with the employment of a distributed nonlinear internal model and a novel distributed extended lower-power high-gain observer, such that the numerical implementation problem is solved and the regulated output of each agent asymptotically converges to the desired reference input robustly with guaranteed domain attraction.

Semi-global output feedback cooperative control for nonlinear multi-agent systems via internal model approach

In this paper, we present an internal model based output feedback control for the cooperative semi-global output regulation of nonlinear strict-feedback multi-agent systems with arbitrary non-identical relative degrees and switching network topologies. The problem is first converted into a cooperative semi-global stabilization problem by introducing a distributed internal model. We then propose a distributed output feedback stabilizer that is determined by a novel distributed observer composed of a distributed dynamic compensator and a modified reduced order high gain observer. It is shown that this novel observer is capable of estimating the states of nonlinear subsystems with arbitrary non-identical relative degrees. A semi-global common Lyapunov function is then developed for conducting the stability analysis of nonlinear switched closed-loop system. The benefit of our design also lies in that it has removed the average dwell time assumption in some existing literatures.

An Internal Model Based Semi-global Output Feedback Control for Nonlinear Multi-agent Systems

In this paper, we present an internal model based output feedback control for the cooperative semi-global output regulation of nonlinear strict-feedback multi-agent systems with arbitrary non-identical relative degrees. The problem is first converted into a cooperative semi-global stabilization problem by introducing a distributed internal model. We then propose a distributed output feedback stabilizer that is determined by a distributed high-gain observer. It is shown that this novel observer is capable of estimating the states of nonlinear subsystems with arbitrary non-identical relative degrees.

Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

ABSTRACTMost of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.

Semi-global output regulation for discrete-time singular linear systems with input saturation via composite nonlinear feedback control

The semi-global output regulation problem of multi-variable discrete-time singular linear systems with input saturation is investigated in this paper. A composite nonlinear feedback control law is constructed by using a low gain feedback technique for semi-global stabilisation of discrete-time singular linear systems with input saturation. The sufficient solvability conditions of the semi-global output regulation problem by composite nonlinear feedback control are established. When the composite nonlinear feedback control law is reduced to a linear control law, the solvability conditions are an exact discrete-time counterpart of the semi-global output regulation problem of continuous-time singular linear systems. With the extra control freedom of the nonlinear part in the composite nonlinear feedback control law, the transient performance of the closed-loop system can be improved by carefully choosing the linear feedback gain and the nonlinear feedback gain. The design procedure of the composite nonlinear feedback control law and the improvement of the transient performance are illustrated by a numerical example.

Semi-global output regulation problem of switched linear multi-agent systems subject to input saturation

This paper addresses the distributed output regulation problem of switched multi-agent systems subject to input saturation. Two types of independent switching signals are considered in this work. Each agent is described by a switched linear system with an average dwell time and input saturation. The interconnection topologies are also switched subject to dwell time. Since not every agent can obtain the information of the exosystem, the distributed feedback controller is designed. An agent-dependent average dwell time method with an adjustable parameter based on algebraic Riccati equations is proposed to solve the output regulation problem. Finally, two examples are provided to illustrate the electiveness of our results.

Cooperative Semi-Global Output Regulation of Nonlinear Strict-Feedback Multi-Agent Systems With Nonidentical Relative Degrees.

In this paper, we study the cooperative semi-global output regulation problem for a class of nonlinear strict-feedback multi-agent systems, where the subsystems are assumed to have nonidentical relative degrees. We first introduce the so-called distributed internal model that converts our problem into the cooperative semi-global stabilization problem of the corresponding augmented system composed of the original multi-agent system and the internal model. We then put this augmented system into the general block lower triangular form, and develop the block semi-global backstepping technique to stabilize it. Comparing with some existing literatures, our design has removed the identical relative degree assumption, and hence applies to a much larger group of nonlinear multi-agent systems.

MIMO regulation control design for magnetic steering of a ferromagnetic particle inside a fluidic environment

As an important development of medical instrumentation, minimally invasive therapeutic operations have been recently introduced. The foremost element of minimally invasive techniques is navigating a micro-device through human body, especially inside blood vessels. A remote actuation over the micro-device is normally provided by electromagnetic actuators. In most applications, a control scheme is also required to initiate the actuation force, the magnetic propulsion, such that at every time step, the micro-device moves towards or along a given path.This paper contributes in development of the electromagnetic system model mostly used in magnetic navigation systems to be representable in control affine form. Next, a multi-input multi-output (MIMO) trajectory tracking controller is designed to conduct the auto-navigation of the device along a given path. This method is a generalised version of a ‘semi-global nonlinear output regulation’ introduced for single-input single-output (SISO) systems. Finally, the proposed scheme is examined for an iron particle moving in a fluidic environment. The simulation results show fast decay in deviation of the particle position from the reference path under some assumptions. This shows that the proposed scheme can be offered for medical applications.

Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control

To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.

Global stabilisation of large‐scale hydraulic networks with quantised and positive proportional controls

The problem considered here is output regulation of a large-scale hydraulic network where the structure of the network is subject to change and where the actuation is subject to a non-negativity constraint. Previous results have shown that semi-global practical output regulation is achievable using a set of decentralised, logarithmic quantised and constrained control actions with properly designed quantisation parameters. That is, an attractor set with a compact basin of attraction exists. Subsequently, the basin can be increased by increasing the control gains. In our work, this result is extended by showing that an attractor set with a global basin of attraction exists for arbitrary values of positive control gains, given that the upper level of the quantiser is properly designed. Furthermore, the proof is given for general monotone quantisation maps. Since the basin of attraction is global and the result is independent on the size of the network, this shows that structural changes can be implemented without destabilising the closed-loop system.

Robust design of nonlinear internal models without adaptation

We propose a solution to the problem of semiglobal output regulation for nonlinear minimum-phase systems driven by uncertain exosystems that does not rely upon conventional adaptation schemes to estimate the frequency of the exogenous signals. Rather, the proposed approach relies upon regression-like arguments used to derive a nonlinear internal model able to offset the presence of an unknown number of harmonic exogenous inputs of uncertain amplitude, phase and frequency. The design methodology guarantees asymptotic regulation if the dimension of the regulator exceeds a lower bound determined by the actual number of harmonic components of the exogenous input. If this is not the case, a bounded steady-state regulation error is ensured whose amplitude, though, can be arbitrarily decreased by acting on a design parameter of the regulator.

On the Transient Response of a Nonlinear Output Regulator

In, Serrani, Isidori, and Marconi design an output feedback controller that achieves semiglobal output regulation for a class of minimum phase nonlinear systems. The controller has three components: an internal model to ensure asymptotic regulation, a high-gain partial state feedback controller to stabilize the augmented system of the plant and internal model, and a high-gain observer to implement the partial state feedback. In this note we show a property of the transient response of this controller. We consider an alternate controller that shares with the controller of the structure of high-gain partial state feedback and high-gain observer, but without internal model. Such controller can only achieve practical regulation. We show that when the controller and observer gains are large enough, the trajectories under the two controllers will be close to each other. Hence, the transient response of the controller of is not degraded by the inclusion of internal model. A similar transient response property is shown by Seshagiri and Khalil for the conditional servocompensator. Similarities and differences between the two designs are pointed out.

Certainty Equivalence in Nonlinear Output Regulation with Unmeasurable Regulated Error

In the present paper we consider a general nonlinear output regulation problem in which the regulated error is unmeasurable. It is assumed that the interconnection of the controlled plant with the exosystem observed through the measured output satisfies some appropriate observability conditions that allow the design of an asymptotic observer. Then, the contribution of this paper consists in showing that in the latter scenario, a design based on certainty equivalence is effective for determining a controller that achieves semiglobal output regulation.

Semi-global stabilization and output regulation of constrained linear plants via measurement feedback

Semi-global stabilization and output regulation of linear systems subject to state and/or input constraints have been studied in our earlier work by using state feedback. For the same problems, observer based measurement feedback control designs are the topics of this paper. High-gain observers are used in the feedback design in order to obtain accurate estimates of the state so that the constraint violation can be avoided. Due to the peaking phenomenon associated with a high-gain observer, a special saturation protection is built in the control laws to avoid possible constraint violation. The results in this paper show that the semi-global stabilization and semi-global output regulation problems for constrained linear systems are solvable via measurement feedback under solvability conditions similar to those in the state feedback.

Semiglobal robust output regulation of minimum‐phase nonlinear systems

Semiglobal robust output regulation of minimum‐phase nonlinear systems

An improvement to the low gain design for discrete-time linear systems in the presence of actuator saturation nonlinearity

A low-gain design for linear discrete-time systems subject to input saturation was recently developed to solve both semi-global stabilization and semi-global output regulation problems. This paper proposes an improvement to the low-gain design and determines controllers with the new design that achieve semi-global output regulation. The improvement is reflected in better utilization of available control capacity and consequently better closed-loop performance. Copyright © 2000 John Wiley & Sons, Ltd.

An Improvement to the Low Gain Design for Discrete-Time Linear Systems Subject to Input Saturation - Solution of Semi-Global Output Regulation Problems

A low gain design for linear discrete-time systems subject to input saturation was recently developed in (Lin and Saberi 1995a, Lin et al. 1995a, Mantri et al. 1995) to solve both semi-global stabilization and semi-global output regulation problems. This paper proposes an improvement to the low gain design and determines controllers with the new design that achieve semi-global output regulation. The improvement is reflected in better utilization of available control capacity and consequently better closed-loop performance.