Global Robust Output Regulation Problem Research Articles

Practical output regulation for nonlinear multiagent systems with event‐triggered control protocol under directed switching networks

SummaryIn this paper, the event‐triggered‐based cooperative global robust practical output regulation problem is studied for nonlinear multiagent systems with directed switching networks. Firstly, the considered problem can be resolved with a prerequisite where the problem is solvable by an input‐to‐state stabilizing controller with measurement feedback. Specifically, the considered problem can be converted into a stabilization one for the so‐called augmented system through the canonical internal model construction. Then by combining the multiple Lyapunov functions (MLF) with the average dwell time (ADT) method, it is demonstrated that this stabilization problem can be solved by output feedback with measurement disturbances, which indicates a solution to the initial problem. At last, a suitable event‐triggering mechanism is proposed to save communication resources and reduce computational burden among all the agents. Finally, a group of FitzHugh‐Nagumo multiagent systems is provided to verify our theoretical results.

Global position tracking control of PMSM servo system via internal model approach and experimental validations

SummaryIn practical engineering, load torque disturbance and parameter uncertainties are two important factors, which may deteriorate the tracking accuracy of permanent magnet synchronous motor (PMSM) servo system. Therefore, its global position tracking control problem is a challenging task when the load torque disturbance is time‐varying and the motor parameters are unknown. In this article, an internal model controller based on global robust output regulation (GROR) theory is proposed to achieve this control objective. In particular, we first formulate the global position tracking control problem as a GROR problem. Then, the GROR problem is converted into a global robust stabilization problem of an augmented system by constructing an appropriate internal model. Finally, we can stabilize the augmented system by a global stabilization controller instead of local stabilization controller used in the recent work, which guarantees global position tracking and disturbance rejection of PMSM servo system. The excellent position tracking performance of our design is demonstrated by both simulation and experimental results.

Nonlinear speed tracking control of PMSM servo system: A global robust output regulation approach

It is well known that load torque disturbance and parametric uncertainties commonly exist in permanent magnet synchronous motor (PMSM) and may reduce the tracking accuracy especially when the reference trajectory is time-varying. Thus it is challenging to achieve precise speed tracking control with both load torque disturbance and parametric uncertainties being taken into account. This task can be formulated as a global robust output regulation problem (GRORP) of multi-input, multi-output nonlinear system. In this paper, a systematic internal model control (IMC) method is proposed to solve the GRORP. By constructing a suitable internal model, we convert the GRORP into a global stabilization problem of an augmented system, and then design a stabilization controller to globally stabilize the augmented system. To validate the advantages of the proposed IMC method, comparative studies with conventional proportional–integral speed control method and linear active disturbance rejection control method are conducted via simulations and experiments. It is worthy of mentioning that our method can not only achieve high precision speed tracking performance under time-varying reference speed and/or load torque disturbance, but also allow all the motor parameters to be uncertain.

Global robust output regulation of a class of MIMO nonlinear systems by nonlinear internal model control

AbstractRecently, the global robust output regulation problem for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems which may not have well‐defined relative degree and are subject to a nonlinear exosystem has been studied based on a constructive nonlinear internal model. However, the proposed nonlinear internal model‐based control law is applicable to the case where the exogenous signals are reference input and/or measurable disturbance rather than unmeasurable disturbance. For this reason, this paper further studies the same control problem based on a general nonlinear internal model independent of the exogenous signal. It is shown that this control problem can be converted into a global robust stabilization problem of a more complicated MIMO nonlinear system with various uncertainties and well solved by a recursive state feedback controller design. Thus our approach applies to a broader class of output regulation problem of MIMO nonlinear systems.

Event-Triggered Adaptive Output Regulation for a Class of Nonlinear Systems With Unknown Control Direction

In this paper, the global robust output regulation problem of a class of uncertain nonlinear systems is investigated by the event-triggered adaptive control law for the case of unknown control direction. The Nussbaum-type function-based technique is proposed to tackle the presence of unknown control direction. Then, by applying the adaptive control technique and the internal model principle, a new event-triggered adaptive control method is proposed. With the proposed corresponding event-triggered mechanism, the output regulation of the nonlinear systems can be realized regardless of the unknown control direction, meanwhile the Zeno behavior can be excluded. Finally, a numerical example is presented to verify the effectiveness of the proposed control law.

Data-driven global robust optimal output regulation of uncertain partially linear systems

In this paper, a data-driven control approach is developed by reinforcement learning ( RL ) to solve the global robust optimal output regulation problem ( GROORP ) of partially linear systems with both static uncertainties and nonlinear dynamic uncertainties. By developing a proper feedforward controller, the GROORP is converted into a global robust optimal stabilization problem. A robust optimal feedback controller is designed which is able to stabilize the system in the presence of dynamic uncertainties. The closed-loop system is assured to be input-to-output stable regarding the static uncertainty as the external input. This robust optimal controller is numerically approximated via RL. Nonlinear small-gain theory is applied to show the input-to-output stability for the closed-loop system and thus solves the original GROORP. Simulation results validates the efficacy of the proposed methodology.

Cooperative Adaptive Output Regulation for Lower Triangular Nonlinear Multi-Agent Systems Subject to Jointly Connected Switching Networks.

The cooperative global robust output regulation problem for multi-agent systems is a generalization of the leader-following consensus problem. The problem has been studied for various multi-agent systems over connected static networks and for some special classes of nonlinear multi-agent systems over jointly connected switching networks. In this paper, we further consider the same problem for a class of heterogeneous lower triangular nonlinear multi-agent systems over jointly connected switching networks. This class of systems is quite general in that it contains inverse dynamics, is of any order, and its subsystems can have different relative degrees. We will integrate the adaptive distributed observer and the distributed internal model approach to come up with a recursive approach to deal with our problem. We will also apply our approach to a leader-following consensus problem for a group of hyperchaotic Lorenz systems.

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.

Constructive Nonlinear Internal Models for Global Robust Output Regulation and Application

This technical note focuses on an internal model construction approach. Several novel types of parameterized nonlinear internal models with certain output are proposed to be useful for achieving nonadaptive control based global robust output regulation with uncertain exosystems. That is, the globally stabilizing control for the augmented system can be done independent of adaptive stabilization control law. We also solve a cooperative global robust output regulation problem as an interesting application of the proposed internal models. In this way, we note that the hurdles can be circumvented arising in the same problem if the canonical linear internal model were used.

Cooperative global robust output regulation for a class of nonlinear multi-agent systems by distributed event-triggered control

This paper studies the event-triggered cooperative global robust output regulation problem for a class of nonlinear multi-agent systems via a distributed internal model design. We show that our problem can be solved practically in the sense that the ultimate bound of the tracking error can be made arbitrarily small by adjusting a design parameter in the proposed event-triggered mechanism. Our result offers a few new features. First, our control law is robust against both external disturbances and parameter uncertainties, which are allowed to belong to some arbitrarily large prescribed compact sets. Second, the nonlinear functions in our system do not need to satisfy the global Lipschitz condition. Thus our systems are general enough to include some benchmark nonlinear systems that cannot be handled by existing approaches. Finally, our control law is a specific distributed output-based event-triggered control law, which lends itself to a direct digital implementation.

Event-Triggered Cooperative Global Robust Practical Output Regulation for Second-Order Uncertain Nonlinear Multiagent Systems.

In this paper, we study the cooperative global robust practical output regulation problem for a class of second-order uncertain nonlinear multiagent systems via a distributed event-triggered state feedback control strategy. Compared with the existing work, one of the main challenges is that we need to design two distributed internal models to learn both the desired steady-state state and steady-state input for each agent. Moreover, to obtain a directly implementable digital control law, the two distributed internal models of each agent only depend on the sampled states of the neighboring agents and itself. As a result, the resulting augmented system is more complicated, and the control law needs to be recursively designed. To overcome the difficulty, we propose a novel distributed event-triggered control law and a novel distributed event-triggered mechanism to deal with our problem. By adjusting a design parameter in the proposed event-triggered mechanism, we show that the Zeno behavior does not happen and the ultimate bound of the tracking error can be made arbitrarily small. Our design will be illustrated by two examples.

Cooperative global robust group output regulation for multi-agent systems with heterogeneous uncertain second-order nonlinear dynamics

In this paper, we study the global robust group output regulation problem for multi-agent systems with heterogeneous uncertain second-order nonlinear dynamics. The intelligence factor is introduced to construct a designed graph matrix which overcomes the communication influence between multiple coupled subnetworks with different exosystems. In terms of internal model principle, the global robust group output regulation problem is converted into the global robust dynamic stability problem of the so-called augmented multi-agent system. Further, the augmented multi-agent system is globally stabilized via a distributed state feedback control law. A special case of the main result of this paper leads to the solution of the global robust multi-tracking control problem for nonlinear multi-agent networks. A simulation is performed to illustrate the effectiveness of the theoretical results.

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.

Event-Triggered Global Robust Output Regulation for a Class of Nonlinear Systems

This note studies the global robust output regulation problem for a class of nonlinear systems by an output-based event-triggered control law. First, we convert the problem into the event-triggered global robust stabilization problem of a well-defined augmented system based on the internal model approach. Then, we design an output-based event-triggered control law together with an output-based event-triggered mechanism to solve the stabilization problem, which in turn leads to the solution to the original problem by an output-based event-triggered control law. Finally, we illustrate our approach by an example.

Global Robust Output Regulation for a Class of Nonlinear Systems via Event-Triggered Control

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.

Cooperative Adaptive Output Regulation for Second-Order Nonlinear Multiagent Systems With Jointly Connected Switching Networks.

This paper studies the cooperative global robust output regulation problem for a class of heterogeneous second-order nonlinear uncertain multiagent systems with jointly connected switching networks. The main contributions consist of the following three aspects. First, we generalize the result of the adaptive distributed observer from undirected jointly connected switching networks to directed jointly connected switching networks. Second, by performing a new coordinate and input transformation, we convert our problem into the cooperative global robust stabilization problem of a more complex augmented system via the distributed internal model principle. Third, we solve the stabilization problem by a distributed state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of Van der Pol oscillators.

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

In this technical note, we study the cooperative global robust output regulation problem for the unity relative degree nonlinear multi-agent system in normal form with a nonlinear leader system. The same problem was studied recently under the assumptions that the system contains only polynomial nonlinearities, the leader system is linear and the communication network is undirected. By employing a distributed nonlinear internal model, we will construct a control law that accommodates non-polynomial nonlinearities, nonlinear leader systems, and directed communication networks. Our result will be illustrated by an example with the well known Van der Pol oscillator as the leader system.

Output regulation of output feedback systems with unknown exosystem and unknown high-frequency gain sign

This paper discusses the global robust output regulation problem for a class of nonlinear output feedback systems. It is assumed that the exosystem and the high-frequency gain sign are unknown and that the unknown parameters can be arbitrarily large. To solve this problem, two major challenges are to be overcome. First, the concurrence of the unknown exosystem and the unknown high-frequency gain sign cannot be handled merely by designing estimators for the two unknown parameters respectively. Second, the conventional extended matching design approach cannot be directly implemented, owing to the arbitrarily large unknown parameters. To cope with these difficulties, a new estimator is developed, and the extended matching design approach is modified to obtain a suitable update law for the estimator. The effectiveness of the proposed adaptive controller is illustrated by an example.

Global robust output regulation of multivariable systems with nonlinear exosystem

Summary It is well known that multi-input, multi-output nature of nonlinear system and generalized exosystem have posed some challenges to output regulation theory. Recently, the global robust output regulation problem for a class of multivariable nonlinear system subject to a linear neutrally stable exosystem has been studied. It has been shown that a linear internal model-based state feedback control law can lead to the solution of previous problem. In this paper, we will further study the global robust output regulation problem of the system subject to a nonlinear exosystem. By utilizing nonlinear internal model design and decomposing the multi-input control problem into several single-input control problems, we will solve the problem by recursive control law design. The theoretical result is applied to the non-harmonic load torque disturbance rejection problem of a surface-mounted permanent magnet synchronous motor. Copyright © 2016 John Wiley & 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.