Output Regulation Theory Research Articles

Event‐triggered output synchronization for nonhomogeneous agent systems with periodic denial‐of‐service attacks

SummaryThis article presents a two‐layered framework to investigate the output synchronization problem in nonhomogeneous agent systems in the presence of periodic energy‐limited denial‐of‐service (DoS) attacks with an event‐triggered control strategy. Under the developed framework, the proposed controller for different agents is composed of a dynamic compensator and a regulator, where the dynamic compensator on the first layer can copy the dynamics of the leader node. DoS attacks with a periodic (partially known) attack strategy are based on a time sequence and interrupt the data exchange over a shard network consisting of the leader node and dynamic compensators in the first layer. An event‐triggered control protocol is proposed to reduce the update frequency of the controller, and it also ensures that the output of every dynamic compensator can track the output of the leader node without occurring “Zeno phenomenon.” Based on the output regulator theory, the regulator for every agent can guarantee that all nonhomogeneous agents can converge to the trajectory of every dynamic compensator in the bottom layer. Finally, a simulation example is demonstrated to verify the new design method developed.

Output Homogenization and Synchronization of Heterogeneous Nonlinear Multiagent Networks

In this article, we are concerned with the output synchronization of a group of heterogeneous agents with nonlinear dynamics. It is shown that via dynamic coupling, the output synchronization problem is transformed into a family of output homogenization and internal-model-based synchronization problems. In contrast to conventional approaches, the adopted approach does not rely on the generation of a specific reference trajectory, to be tracked by all agents. Based on this premise, we propose a distributed state-feedback protocol driving all the heterogeneous multiagent individual systems onto a copy of a virtual reference signal. Invoking the results from the theory of output regulation and cooperative control, the state-feedback controller synthesis is conducted to achieve the output synchronization of heterogeneous multiagent networks. Immediate extensions of the obtained results to observer-based control are also discussed. The effectiveness of the proposed output synchronization algorithm is verified through theoretical analysis and case studies.

Cooperative adaptive optimal output regulation of nonlinear discrete-time multi-agent systems

This paper studies a cooperative adaptive optimal output regulation problem for a class of strict-feedback nonlinear discrete-time (DT) multi-agent systems (MASs) with partially unknown dynamics. Adaptive distributed observer, reinforcement learning (RL) and output regulation techniques are integrated to compute an adaptive near-optimal tracker for each follower. First, under the output regulation theory, the cooperative adaptive optimal output regulation problem is decomposed into a feedforward control design problem which can be addressed by solving nonlinear regulator equations, and an adaptive optimal feedback control problem. Different from general adaptive optimal stabilization problem of nonlinear DT systems, the value function of the optimal output regulation problem is positive semidefinite. This paper analyzes the stability of the closed-loop system without relying on the Lyapunov stability theory and also proposes a policy iteration (PI) approach to approximate the value function with the convergence proof. Then, an adaptive distributed observer is designed for each follower so that they can estimate the state of the leader. A model-state-input structure is developed to find the solutions to regulator equations for each follower and a critic–actor structure is employed to solve the optimal feedback control problem using the measured data based on the neural network (NN) and RL. It is shown that using the estimate values, the tracking errors are uniformly ultimately bounded. A simulation example is given to show the effectiveness of the proposed method.

Voltage Regulation of DC-Microgrid With PV and Battery

This paper studies voltage regulation and maximum power point tracking (MPPT) control for a DC-microgrid that includes a photovoltaic (PV) panel, battery, constant resistance and constant power loads. A dynamic model of the DC-microgrid system described by a multi-input and multi-output nonlinear system with non-affine inputs is derived. Based on this nonlinear dynamic model, we use output regulation theory to design a local state feedback controller that regulates voltages to prescribe set points and maximizes PV power output. Global set point regulation is also studied using passive system theory for non-affine systems and Lyapunov stability theory. The effectiveness of the proposed control schemes is investigated using simulations when changes in both illumination and load occur.

Output Consensus of Heterogeneous Multiagent Systems: A Distributed Observer-Based Approach

As the control tasks become complex, fulfilling such tasks cooperatively is the first choice in practice. In this article, the output consensus problem of heterogeneous multiagent systems is studied by deploying distributed observers in follower agents. Each observer in the follower only measures part of the leader’s output, which relieves the burden of a simple agent when the leader’s output is of large-scale dimensions. Then, all followers in the system work cooperatively to estimate the full state of the leader. By using parameterized Riccati equation and output regulation theory, sufficient conditions are given to design the distributed observers and the output consensus protocol. Finally, a numerical example is conducted to verify the obtained result.

Position control of spherical inverted pendulum via improved discrete-time neural network approach

Much recently, a discrete-time neural network (NN) approach from the output regulation theory was adopted to solve the position tracking problem of the spherical inverted pendulum (SIP) system. The key of this approach is to find the approximate solution of the corresponding discrete regulator equations (DREs) of the SIP system, which are composed of 10 nonlinear algebraic functional equations. However, the procedure for calculating the approximate solution of the DREs is quite tedious and is dependent on the system parameters. In this paper, an improved discrete-time NN control algorithm is proposed, which relies on the NN approximation of the feedforward function. Since the feedforward function is two-dimensional, the improved NN approach is much simpler compared with the existing NN approach. Moreover, a distinct advantage of our approach is that it allows certain robustness to the system parameters when every state is available. Simulation results demonstrate that our approach leads to much smaller tracking errors than the existing NN approach.

Supervised Output Regulation via Iterative Learning Control for Rejecting Unknown Periodic Disturbances

The internal model principle (IMC) in linear robust output regulation theory states that a dynamical controller needs to incorporate a copy of the model generating the periodic signals in order to achieve perfect rejection/tracking, robustly with respect to plant’s parameters. On the other hand Iterative Learning Control (ILC) is a data-based approach which not requires any a priori knowledge, and can be used to find the required control action for attenuating periodic disturbances or tracking periodic references. The control signal generated by ILC includes the frequency and amplitude information of the disturbance and can be used to build the internal model needed for a linear output regulator problem. The objective of this work is therefore that of trying to combine the two approaches, that is IMC and ILC, in order to retain the advantages of each methodology. The proposed methodology, denoted as Supervised Output Regulation via Iterative Learning Control (SOR-ILC), allows to address the problem of output regulation in presence of unknown frequencies. The performances of SOR-ILC are validated through numerical simulations in case of complex periodic disturbances and parameter uncertainties.

Event-triggered Control for Heterogeneous Discrete-time Multi-agent Systems Subject to Uncertainties and Noises

This paper investigates the event-triggered control problem of heterogeneous discrete-time multi-agent systems (MASs) subject to uncertainties and noises. Based upon the output regulation theory, a new distributed event-triggered control scheme is proposed to reduce communication burden and attenuate effects of stochastic noises. Two types of event-triggered control laws based on dynamic state feedback and dynamic output feedback are designed, respectively. Moreover, to compensate parameter uncertainties, a p-copy internal model is synthesized into the designed controllers. It is shown that all tracking errors are exponentially ultimately bounded in the mean square sense regardless of uncertainties and noises. Several examples are finally given to demonstrate the validity of main results.

Moments of Random Variables: A Systems-Theoretic Interpretation

Moments of continuous random variables admitting a probability density function are studied. We show that, under certain assumptions, the moments of a random variable can be characterized in terms of a Sylvester equation and of the steady-state output response of a specific interconnected system. This allows to interpret well-known notions and results of probability theory and statistics in the language of systems theory, including the sum of independent random variables, the notion of mixture distribution and results from renewal theory. The theory developed is based on tools from center manifold theory, the theory of the steady-state response of nonlinear systems, and the theory of output regulation. Our formalism is illustrated by means of several examples and can be easily adapted to the case of discrete and multivariate random variables.

Robust output regulation for state feedback descriptor systems with nonovershooting behavior

In this paper, the design of robust non-overshooting (NO) controllers for output regulation is presented for a continuous linear time-invariant (LTI), multi-input multi-output (MIMO) state feedback based descriptor system. In this method of controller design for descriptor system, the integral sliding mode (ISM) technique along with generalised Moore’s eigen structure assignment method and output regulation theory for descriptor system is invoked to ensure robust output regulation with NO behavior. The efficiency of the proposed controller is also demonstrated with the help of a numerical example and simulation results presented at the end.

Internal Model Control of PMSM Position Servo System: Theory and Experimental Results

Much recently, an internal model approach from output regulation theory has been adopted to solve the speed tracking control problem of the permanent magnet synchronous motor (PMSM) system on simulation level. A striking advantage of this approach is that it can achieve multiple goals including trajectory tracking, disturbance rejection, and robustness simultaneously. This article further studies a position tracking control problem of the PMSM system under nonlinear load torque disturbance. A nonlinear internal model based output feedback controller is proposed, which can achieve exact position tracking and allow certain parameter uncertainties. Besides simulation results, a real-time experimental setup is built and experimental results are provided to illustrate the effectiveness of the proposed controller. It is worth mentioning that the proposed controller can lead to a high precision position tracking performance under nonlinear load torque disturbance.

Output Regulation Control for Satellite Formation Flying Using Differential Drag

This paper proposes a new approach of using differentials in aerodynamic drag in combination with thrusters to control satellite formation flying in low Earth orbits. Parameterized output regulation theory for formation-flying missions with combined control action is developed based on the Schweighart–Sedwick relative dynamics equations. The theory is implemented to precisely track the different trajectories of reference relative motion and eliminates the effects of the perturbations. The parametric Lyapunov algebraic equation is proposed to ensure the stability of the linear relative model subject to saturated inputs. The main goal of this study is to approve the viability of using the differentials in aerodynamic drag to precisely control different formation-flying missions. Numerical simulations using a high-fidelity relative dynamics model and a high-precision orbit propagator are implemented to validate and analyze the performance of the proposed control algorithm in comparison with the linear quadratic regulator algorithm based on actual satellite models.

Optimal Tracking With Disturbance Rejection of Voltage Source Inverters

This paper presents a novel voltage regulator design methodology for a three-phase voltage source inverter with uncertain load dynamics. Different from existing literature, the load is treated as a dynamic uncertainty and a robust optimal state-feedback controller is proposed through the integration of optimal output regulation theory and backstepping method. To avoid sensing the inductor current, an output-feedback control scheme is developed as well. Stability of the inverter–load system is rigorously analyzed via the small-gain techniques. It is ensured that the tracking error asymptotically converges to zero through both the proposed state-feedback and output-feedback controllers. A standard proportional resonant controller is also designed for the purpose of comparison. It is shown that the proposed controller has inherent robustness and does not require retuning with different applications. The controller design method is generalized for grid-tie applications, since the grid can be regarded as a stable load system. Simulations and experimental results show the effectiveness of the control approaches.

Sliding Mode Output Regulation for a Boost Power Converter

This work deals with the novel application of the sliding mode (discontinuous) output regulation theory to a nonlinear electrical circuit, the so-called boost power converter. This theory has excelled due to the fact that trajectory tracking plays a central role. The control of a boost power converter for the output tracking of a DC biased sinusoidal signal is a challenging problem for control engineers. The main difficulties are the computation of a proper reference signal for the inductor current, and the stabilization of the inductor current dynamics or to guarantee the correct output tracking of the capacitor voltage. With the application of the discontinuous output regulation these problems are solved in this work. Simulations and real time experiments were carried out with an unknown variation of the DC input voltage, where the good output tracking of the capacitor voltage was verified along with the stabilization of the inductor current. The discontinuous output regulation theory has proven to be a suitable tool in the output tracking for the boost power converter.

Cluster output regulation of heterogeneous multi-agent systems

This paper studies the cluster output regulation problem of heterogeneous linear multi-agent systems under fixed directed topology, where dynamics of all agents are allowed to be different. Compared with the standard consensus problem, the interactions among clusters, which can be negatively weighted, impose a challenge on dealing with the issue. Based on the output regulation theory and the small-gain theorem, distributed state feedback and output feedback controllers are proposed to solve the problem. In each case, a small-gain criterion is given to guarantee cluster output regulation. Furthermore, a unified design procedure is given for both cases. Our results provide a new way to understand the relationship between the standard consensus problem and the cluster consensus problem. Numerical simulations are provided to verify the effectiveness of theoretical results.

Output Regulation for a Class of MIMO Uncertain Stochastic Nonlinear Systems by Active Disturbance Rejection Control Approach

In this paper, the active disturbance rejection control (ADRC) approach is applied to a class of multi-input multioutput (MIMO) uncertain stochastic nonlinear systems. An extended state observer (ESO) is first designed for estimation of both unmeasured states and stochastic total disturbance of each subsystem which represents the total effects of internal unmodeled stochastic dynamics and external stochastic disturbance with unknown statistical property. The ADRC controller based on the states of ESO is further designed to achieve the closed-loop system’s output regulation performance including practical mean square reference signals tracking, disturbance attenuation, and practical mean square stability when the reference signals are zero avoiding solving any partial differential equations in the conventional output regulation theory. Some numerical simulations are presented to demonstrate the effectiveness of the proposed ADRC approach.

Fault-Tolerant Containment Control for Linear Multi-Agent Systems: An Adaptive Output Regulation Approach

This paper addresses the problem of fault-tolerant containment control (FTCC) for linear multi-agent systems (MASs) with process faults. First, distributed observers for followers are designed by utilizing their relative output estimation errors. Then, a new distributed adaptive FTCC law based upon the output regulation theory is proposed, where a distributed adaptive observer is implemented to estimate the synthesized information for leaders. It is shown that no matter whether there exist faults or not, all the followers can asymptotically move into a convex hull formed by the leaders. Finally, an example is given to illustrate the effectiveness of the designed distributed control law.

Discrete-Time Neural Network Approach for Tracking Control of Spherical Inverted Pendulum

In recent years, the tracking problem of spherical inverted pendulum (SIP) system with multi-input, multi-output nature and unstable zero dynamics has been well addressed based on continuous-time nonlinear output regulation (NOR) theory. For the convenience of digital implementation, this paper further investigates the approximate NOR problem of the SIP system in discrete-time framework. The key for solving the discrete-time NOR problem lies in how to solve a set of algebraic functional equations known as discrete regulator equations (DRE). Since the equations are very complicated, the accurate solution of the DRE can not be obtained. In this paper, we first show that the DRE associated with the SIP system are solvable by center manifold theorem and then use neural network approach to tackle with the tracking problem. Finally, we compare our method with polynomial approximation method.

Voltage and Frequency Regulation of Microgrid With Battery Energy Storage Systems

This paper presents a novel primary control strategy based on output regulation theory for voltage and frequency regulations in microgrid systems with fast-response battery energy storage systems (BESS). The proposed control strategy can accurately track voltage and frequency set points while mitigating system transients in the presence of disturbance events. Therefore, it overcomes the key weaknesses of droop-based control methods such as large steady-state voltage and frequency deviations and poor transient performance. Throughout this paper, four control schemes are derived with tradeoffs between communication requirement and system dynamic performance. Their effectiveness is validated through MATLAB Simulink simulation studies involving a medium-voltage microgrid with both synchronous generation resources and BESS. Although the proposed control schemes are centralized, practical implementation is possible with available communication links in microgrids and embedded hardware technologies.

Semi‐global leader‐following output consensus of heterogeneous multi‐agent systems with input saturation

SummaryIn this paper, we consider the semi‐global leader‐following output consensus problem for a heterogeneous multi‐agent system with input saturation over a directed network on which the leader agent is globally reachable. By using the low gain feedback technique and the output regulation theory, we construct two consensus protocols, of the state feedback type and the output feedback type. In the state feedback case, a distributed leader state observer is constructed to estimate the leader state for each follower agent. In the output feedback case, follower agents are divided into two groups, namely, the informed follower agents that have access to the information of the leader agent and the uninformed follower agents that have not. Besides a distributed leader state observer that is designed for the uninformed agents, state observers are constructed for each follower agents. Based on these observers, the consensus protocols can solve the semi‐global leader‐following output consensus problem. Simulation results illustrate the effectiveness of our proposed approaches.