Output Regulation Theory Research Articles

A Coordinated Emergency Frequency Control Strategy Based on Output Regulation Approach for an Isolated Industrial Microgrid

Constructing isolated industrial microgrids with wind power is beneficial for improving the economic benefits of high-energy-consuming production, such as the electrolytic aluminum industry. Due to the specialized structure of industrial microgrids and the unique characteristics of the electrolytic aluminum load (EAL), the common emergency frequency control methods do not apply to the specific operational requirements of isolated industrial microgrids. Since EALs have huge regulating capacities and fast responses, this paper proposes a coordinated emergency frequency control scheme to deal with power disturbances in isolated industrial microgrids. The coordinated frequency control model of an industrial microgrid considering demand-side participation is derived. With the help of output regulation theory, a practical, feasible coordinated frequency controller is designed by introducing frequency deviation and power disturbance as feedback control signals. The proposed control scheme achieves reserve power distribution between the generation and demand sides. The microgrid frequency can be maintained within a permitted range in the presence of large power imbalances. The simulation results conducted in an actual isolated industrial microgrid validate the effectiveness and dynamic performance of the proposed control scheme.

Theory and experiment on distributed output formation tracking of unmanned aerial and ground vehicle swarm systems over jointly connected digraphs

This paper studies the distributed output formation tracking control problem of the unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) swarm systems, where the UAV swarm cooperatively tracks the output trajectory of the UGV in a formation under directed jointly connected communication networks. A three-layer formation tracking protocol is proposed. Firstly, a novel distributed observer using neighbor interactions is designed for each UAV to estimate the states of the UGV with parameterized inputs over periodic jointly connected digraphs. Next, based on the observation result and output regulation theory, a virtual reference system that tracks the trajectory of the UGV in the desired formation is constructed to generate reference states for each UAV. Then based on the differential flatness of UAVs, a geometric controller is utilized for UAVs to track the reference states and form the formation. An algorithm to determine the gain matrices of the protocol is also presented while the convergence of the system is analyzed. Finally, an experiment platform with three quadrotor UAVs and one UGV is built. The effectiveness of the proposed protocol is validated both by the simulation and experiment.

Time‐varying output group formation‐containment tracking control for heterogeneous multi‐agent system

AbstractThe time‐varying output group formation‐containment tracking (TVOGFCT) problem of discrete‐time heterogeneous multi‐agent system (MAS) is investigated in this paper. Assuming the MAS consists of multiple tracking leaders, formation leaders, and followers, and all the agents are divided into several groups. Firstly, to estimate the convex combination of tracking leaders in the same group, the distributed observers are designed for the formation leaders, and the observer‐based formation tracking protocols are also presented to make formation leaders realize the desired time‐varying group formation while tracking the convex combination of tracking leaders. Then, two types of observers are proposed to estimate the convex combination of tracking information and formation functions, based on which the containment tracking protocols are designed for the followers of each group. By using output regulation theory and Lyapunov theory, it is illustrated that the designed protocols can make the MAS realize TVOGFCT. Finally, the simulation results prove the correctness of the theoretical analysis.

Semiglobal Suboptimal Output Regulation for Heterogeneous Multi-Agent Systems With Input Saturation via Adaptive Dynamic Programming.

This article considers the semiglobal cooperative suboptimal output regulation problem of heterogeneous multi-agent systems with unknown agent dynamics in the presence of input saturation. To solve the problem, we develop distributed suboptimal control strategies from two perspectives, namely, model-based and data-driven. For the model-based case, we design a suboptimal control strategy by using the low-gain technique and output regulation theory. Moreover, when the agents' dynamics are unknown, we design a data-driven algorithm to solve the problem. We show that proposed control strategies ensure each agent's output gradually follows the reference signal and achieves interference suppression while guaranteeing closed-loop stability. The theoretical results are illustrated by a numerical simulation example.

Data-Based Collaborative Learning for Multiagent Systems Under Distributed Denial-of-Service Attacks

This paper employs a reinforcement learning (RL) technique to investigate the distributed output tracking control of heterogeneous multiagent systems (MASs) under multiple denial-of-service (DoS) attacks. Different from existing results where the dynamic of the leader is known for partial or all agents, the leader’s system matrix is completely unknown for each follower in this paper. To learn the leader system matrix, a data-based learning mechanism is first proposed using the idea of the data-driven method. Then, under the data-based learning mechanism, a resilient predictor subject to multiple DoS attacks is exploited to provide the estimation of the leader’s state for each agent, where adversaries attack different communication links independently. Moreover, a resilient dynamic output feedback controller is proposed to solve the output tracking control problem based on the output regulation theory. To consider the transient responses of agents, a RL-based dynamic output feedback controller is developed to realize the optimal output tracking control by solving discounted algebraic Riccati equations (AREs) in both offline and online ways. Theoretical analysis shows that the secure output tracking control of MASs can be achieved under the proposed data-based resilient learning control algorithm. Finally, a numerical example is provided to verify the effectiveness of theoretical analysis.

Accurate voltage regulation for a DC microgrid using nonlinear state feedback controller

AbstractThe high penetration of distributed generation systems poses challenges in effectively managing both DC bus voltage and power‐sharing in DC microgrids (MGs). To ensure precise voltage regulation across various distributed generation systems and maintain overall system stability, this paper studies the modelling and control of an islanded DC MG described by a set of nonlinear‐nonaffine differential equations. In the proposed DC MG, a battery storage, a photovoltaic (PV) power plant, and a back‐end power converter with DC loads have been connected to a common DC bus. First, a dynamic model of a DC MG was developed. Then, to find the maximum power point of solar PV, a straightforward method based on an artificial neural net is employed. Afterward, a nonlinear local state feedback controller through output regulation theory is applied to achieve voltage stability, overcoming the drawbacks of droop‐based techniques. Moreover, partial state feedback capability simplifies controller design. To verify the effectiveness of the proposed approach, various scenarios, including sudden load variation, illumination change, and changes in the MG configuration, have been examined. Finally, numerical studies were carried out in a simulation environment to demonstrate the superiority of the proposed nonlinear control scheme over constant feedback control.

Single-Loop Robust Model Predictive Speed Regulation of PMSM Based on Exogenous Signal Preview

Speed regulation problem of permanent magnet synchronous motor (PMSM) with overcurrent protection is addressed in this paper by using a single-loop robust model predictive control (MPC) approach. The unique feature of this new disturbance rejection MPC method is the utilization of the preview information of lumped exogenous signal. Different from most of the existing disturbance observer-based MPC approaches, the reference inputs, the lumped disturbances in PMSM, and their higher-order differences are explicitly considered as a part of this new concept of lumped exogenous signal by exploiting output regulation theory. Preview of the possible future behaviors of this exogenous signal is conducted based upon the development of two generalized proportional integral observers (GPIOs). An accuracy enhanced prediction model is obtained by exploiting the estimation and preview of the exogenous signal during the prediction horizon. Speed regulation problem of the PMSM is transformed into an error stabilization problem by means of regulator equations and preview information where the faster time-varying exogenous signal is considered. The overcurrent protection problem is also taken into account throughout the receding horizon optimization process. Experimental studies show that the proposed method achieves effective functionality in overcurrent protection, and much better dynamic performance against time-varying exogenous inputs.

Data-Driven Practical Cooperative Output Regulation Under Actuator Faults and DoS Attacks.

This article addresses the resilient practical cooperative output regulation problem (RPCORP) for multiagent systems subjected to both denial-of-service (DoS) attacks and actuator faults. Fundamentally different from the existing solutions to RPCORPs, the system parameters considered in this article are unknown to each agent, and a novel data-driven control approach is introduced to handle such an issue. The solution starts with developing resilient distributed observers for each follower in the presence of DoS attacks. Then, a resilient communication mechanism and a time-varying sampling period are introduced to, respectively, ensure the neighbor state is available as soon as attacks disappear and to avoid targeted attacks launched by intelligent attackers. Furthermore, a model-based fault-tolerant and resilient controller is designed based on the Lyapunov approach and the output regulation theory. In order to remove the reliance on system parameters, we leverage a new data-driven algorithm to learn controller parameters via the collected data. Rigorous analysis shows that the closed-loop system can resiliently achieve practical cooperative output regulation. Finally, a simulation example is given to illustrate the effectiveness of the achieved results.

Switched Energy and Neural Network-Based Approach for Swing-Up and Tracking Control of Double Inverted Pendulum

The double inverted pendulum (DIP) system is a benchmark underactuated mechanical system. The control problem of the DIP system is challenging since it not only has high nonlinearity, but also has underactuation degree equal to two. In this article, a switched energy-based swing-up and neural network (NN) controller is proposed to solve the swing-up and tracking control problem of the DIP system when the desired position is time varying. The implementation of the proposed controller can be divided into three steps. In step one, the energy-based control method is adopted to drive the first pendulum from the downward position to the neighborhood of the upright position. In step two, the sliding mode control method is adopted to stabilize the first pendulum. Meanwhile, a method combining energy-based control and “equivalent cart” is adopted to swing up the second pendulum. In step three, on the basis of approximate nonlinear output regulation theory, the NN controller is used for achieving satisfactory position tracking performance. Finally, the effectiveness of our design is verified by experimental results.

Fully distributed bipartite output formation tracking for heterogeneous singular multiagent systems on signed digraphs

AbstractThis article investigates the bipartite output formation tracking problem of heterogeneous singular multiagent systems (MASs) over a signed digraph on which two types of cases without and with input saturation are considered, respectively. First, a novel formation tracking protocol is presented for heterogeneous singular MASs in the absence of input saturation constraints. In the proposed protocol, a distributed observer with adaptive updating mechanism is constructed for each follower, which does not involve global information of communication graph. Based on the observer, the designed controller addresses bipartite output formation tracking of heterogeneous singular MASs in a fully distributed fashion. Then, by the output regulation theory and low‐gain feedback technique, a low‐gain formation tracking protocol is proposed to achieve semi‐global bipartite output formation tracking for heterogeneous singular MASs subject to input saturation constraints. Finally, two simulation examples are given to illustrate the feasibility of theoretical results.

Cooperative output feedback tracking control of stochastic nonlinear heterogeneous multi‐agent systems

SummaryWe study cooperative output feedback tracking control of stochastic nonlinear heterogeneous leader‐following multi‐agent systems. Each agent has a continuous‐time stochastic nonlinear heterogeneous dynamics with an unmeasurable state, and there are additive and multiplicative noises along with information exchange among agents. We propose admissible distributed observation strategies for estimating the leader's and the followers' states, and admissible cooperative output feedback control strategies based on the certainty equivalence principle. By output regulation theory and stochastic analysis, we show if the dynamics of each agent satisfies the Lipschitz condition, and the product of the leader's Lipschitz coefficient, the intensity of multiplicative measurement noises, and the constant related to the leader's Lipschitz coefficient and dimension is less than the minimum nonzero eigenvalue of graph Laplacian, then there exist admissible distributed observation and cooperative control strategies to ensure mean square bounded output tracking. Finally, the effectiveness of our control strategies is demonstrated by a numerical simulation.

Robust Output Regulation and Reinforcement Learning-Based Output Tracking Design for Unknown Linear Discrete-Time Systems

In this article, we investigate the optimal output tracking problem for linear discrete-time systems with unknown dynamics using reinforcement learning (RL) and robust output regulation theory. This output tracking problem only allows to utilize the outputs of the reference system and the controlled system, rather than their states, and differs from most existing works that depend on the state of the system. The optimal tracking problem is formulated into a linear quadratic regulation problem by proposing a family of dynamic discrete-time controllers. Then, it is shown that solving the output tracking problem is equivalent to solving output regulation equations, whose solution, however, requires the knowledge of the complete and accurate system dynamics. To remove such a requirement, an off-policy RL algorithm is proposed using only the measured output data along the trajectory of the system and the reference output. By introducing reexpression error and analyzing the rank condition of the parameterization matrix, we ensure the uniqueness of the proposed RL-based optimal control via output feedback.

Distributed Fault-Tolerant Bipartite Output Synchronization of Discrete-Time Linear Multiagent Systems.

This article studies the distributed fault-tolerant bipartite output synchronization problem of discrete-time linear multiagent systems (MASs) with process faults under a general directed signed graph. The reference signal is generated by an autonomous exosystem, which can also be seen as a leader. All followers are divided into two subgroups with antagonistic interactions, and the followers in each subgroup are cooperative. We aim to solve the bipartite fault-tolerant control (FTC) problem via the output regulation theory such that bipartite output synchronization can be achieved in the presence of process faults, that is, the outputs of followers with different subgroups can approach the output of exosystem with the same magnitude and the opposite sign regardless of process faults. To estimate the states and the faults of each follower, a simultaneous state and fault estimator based on the neighboring signed output estimation error and the standard discrete-time algebraic Riccati equation (ARE) is designed. Besides, a new exosystem observer with two classes of convergence conditions relying on the respective solutions of standard and modified AREs is provided. All eigenvalues of the exosystem matrix can lie completely outside the unit circle. Based on these estimations, we present a distributed fault-tolerant output feedback controller, which can overcome the no-loops constraint. Finally, simulation results are given to demonstrate the analytic results.

Semiglobal Leader-Following Output Consensus of Discrete-Time Heterogeneous Linear Systems Subject to Actuator Position and Rate Saturation

Motivated by the fact that physical systems are usually subject to actuator position and rate saturation, we consider in this article the semiglobal leader-following output consensus problem of a group of discrete-time heterogeneous linear systems with position and rate-limited actuators by output feedback control law. Distributed observers are designed for followers to estimate the state of the leader and the follower itself, based on which a novel distributed control law is proposed. We show that, via the low gain feedback design technique and output regulation theory, the semiglobal leader-following output consensus of discrete-time heterogeneous linear systems can be achieved by the consensus protocol if each follower is reachable from the leader in a directed communication topology.

Cooperative Output Feedback Tracking Control of Stochastic Linear Heterogeneous Multiagent Systems

We study cooperative output feedback tracking control of stochastic linear heterogeneous leader- following multiagent systems. Each agent has a conti- nuous-time linear heterogeneous dynamics with incompletely measurable state, and there are additive and multiplicative noises along with information exchange among agents. We propose a set of admissible distributed observation strategies for estimating the leader’s and the followers’ states and a set of admissible cooperative output feedback control strategies based on the certainty equivalence principle. By output regulation theory and stochastic analysis, we show that for observable leader’s dynamics and stabilizable and detectable followers’ dynamics, if the intensity coefficient of multiplicative noises multiplied by the sum of real parts of the leader’s unstable modes is less than one-fourth of the minimum nonzero eigenvalue of graph Laplacian, then there exist admissible distributed observation and cooperative control strategies to ensure mean square bounded output tracking, provided the associated output regulation equations are solvable. Finally, the effectiveness of our control strategies is demonstrated by a numerical simulation.

Observer-Based Adaptive Inverse Optimal Output Regulation for a Class of Uncertain Nonlinear Systems

This paper addresses the adaptive inverse optimal output regulation problem for a class of uncertain nonlinear systems driven by an exosystem. The unknown parameters, internal disturbances, and unmeasured states are contained in the nonlinear system. Firstly, the output regulation problem is decomposed into a feedforward control design problem which can be solved by the internal model based on the output regulation theory, and an adaptive inverse optimal stabilization problem. Then an auxiliary system is designed, and a new state observer related to the auxiliary system is given. By combining adaptive control technology and inverse optimal control method, a novel adaptive output feedback inverse optimal controller is developed to make the output of the system track the reference signal fast. With this control strategy, all the signals of the closed-loop system are uniformly ultimately bounded (UUB), and the newly well-defined cost functional which is connected with the auxiliary system and the controller can be minimized. Finally, a simulation case is put forward to verify the feasibility of the newly raised controller and the state observer.

Saturated Output Regulation of Distributed Parameter Systems with Collocated Actuators and Sensors⋆

This paper addresses the problem of output regulation of infinite-dimensional linear systems subject to input saturation. We focus on strongly stabilizable linear dissipative systems with collocated actuators and sensors. We generalize the output regulation theory for finite-dimensional linear systems subject to input saturation to the class of considered infinite-dimensional linear systems. The theoretic results are illustrated with an example where we consider the output regulation of a flexible satellite model that is composed of two identical flexible solar panels and a center rigid body.

On the Output Regulation for an Underactuated Inverse Pendulum When the Exosystem Is a High-Gain Observer

This paper is devoted to solving the output regulation problem on the basis of the new Francis equations for arbitrary reference/disturbance signals, whose model are obtained by High-Gain observers, providing in this way, the regulation of unmodeled but measurable reference signals. The design is given by fixing a steady state globally attractive by means of LMIs which allows controlling the decay rate by considering input bounds; while the regulation problem is solved by computing the steady-state input based on a modified set of the regulation equations, when the exosystem is constructed upon High-Gain observers, extending in this way, the classical output regulation theory for unmodeled reference/disturbance signal. The Furuta pendulum is used to illustrate the viability of the proposed approach.

Output regulation for general heterodirectional linear hyperbolic PDEs coupled with nonlinear ODEs

This paper considers general heterodirectional linear hyperbolic PDEs with boundary actuation and collocated measurement, that are bidirectionally coupled with nonlinear ODEs at the unactuated boundary. An output feedback regulator is designed to have the control output track a reference in the presence of disturbances, with a nonlinear signal model generating the reference and the disturbances. This leads to new challenges for both the observer and controller design. The regulator design makes use of results from output regulation theory for nonlinear lumped-parameter and distributed-parameter systems. The derivation of the state feedback regulator requires solving a new type of regulator equations, which consist of a Cauchy problem for linear and semilinear hyperbolic PDEs. A key component of the novel observer design is a nonlinear retarded observer for a finite-dimensional subsystem. Both the controller and the observer design are systematic in nature and derived in several successive steps, that include backstepping transformations and, most notably, predictions of PDE and ODE states. The latter are shown to be the unique solution of general nonlinear Volterra integro-differential equations. Combining the observer with the state feedback regulator is proven to achieve output regulation for the closed-loop system. A numerical example illustrates and confirms the theoretical results.

A demand side controller of electrolytic aluminum industrial microgrids considering wind power fluctuations

Direct wind power purchase for large industrial users is a meaningful way to improve wind power consumption and decrease industrial production costs. Short-term wind power fluctuations may lead to large-scale wind power curtailment problems. To promote use of wind energy, a demand side control method is proposed based on output regulator theory for a grid-connected industrial microgrid with electrolytic aluminum loads to continuously track and respond to wind power fluctuations. The control model of the EALs and the dominant frequencies of the wind power fluctuation signals are analyzed and incorporated into the demand side control plant. The feedback control signals with active power deviations on the tie-line are used to design the demand side controller. Simulations are conducted for an actual industrial microgrid to validate the feasibility and effectiveness of the proposed method. The results demonstrate that the proposed controller based on output regulator theory is able to effectively track wind power fluctuations.