Adaptive Optimal Output Regulation of Interconnected Singularly Perturbed Systems With Application to Power Systems

This article studies the adaptive optimal output regulation problem for a class of interconnected singularly perturbed systems(SPSs) with unknown dynamics based on reinforcement learning(RL).Taking into account the slow and fast characteristics among system states,the interconnected SPS is decomposed into the slow time-scale dynamics and the fast timescale dynamics through singular perturbation theory.For the fast time-scale dynamics with interconnections,we devise a decentralized optimal control strategy by selecting appropriate weight matrices in the cost function.For the slow time-scale dynamics with unknown system parameters,an off-policy RL algorithm with convergence guarantee is given to learn the optimal control strategy in terms of measurement data.By combining the slow and fast controllers,we establish the composite decentralized adaptive optimal output regulator,and rigorously analyze the stability and optimality of the closed-loop system.The proposed decomposition design not only bypasses the numerical stiffness but also alleviates the high-dimensionality.The efficacy of the proposed methodology is validated by a load-frequency control application of a two-area power system.

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

This paper investigates the robust cooperative output regulation problem for a class of heterogeneousuncertain linear multi-agent systems with an unknown exosystem via event-triggered control (ETC). By utilizingthe internal model approach and the adaptive control technique, a distributed adaptive internal model isconstructed for each agent. Then, based on this internal model, a fully distributed ETC strategy composed ofa distributed event-triggered adaptive output feedback control law and a distributed dynamic event-triggeringmechanism is proposed, in which each agent updates its control input at its own triggering time instants. It isshown that under the proposed ETC strategy, the robust cooperative output regulation problem can be solvedwithout requiring either the global information associated with the communication topology or the bounds ofthe uncertain or unknown parameters in each agent and the exosystem. A numerical example is provided toillustrate the effectiveness of the proposed control strategy.

Robust output regulation problem with prescribed performance for nonlinear strict feedback systems

This paper investigates the problem of robust output regulation control with prospected transient property for strict feedback systems.By employing the internal model principle,the robust output regulation problem with a prospected property can be transformed to a robust stabilization problem with a new output constraint.Then,by constructing the speed function and adopting barrier Lyapunov function technique,the dynamic feedback controller can be designed not only to drive error output of the closed-loop system entering into a prescribed performance bound within a given finite time,but also to achieve that the error output converges to zero asymptotically.The effectiveness of the results is illustrated by a simulation example.

Robust Leader-Following Output Regulation of Uncertain Multi-Agent Systems With Time-Varying Delay

In this paper, the robust analysis and design of leader-following output regulation for multi-agent systems described by general linear models is given in presence of timevarying delay and model uncertainty. To this aim, a new regulation protocol for the closed-loop multi-agent system under a directed graph is proposed. An important specification of the proposed protocol is to guarantee the leader-following output regulation for uncertain multi-agent systems with both stable and unstable agents. Since many signals can be approximated by a combination of the stationary and ramp signals, the presented results work for adequate variety of the leaders. The analysis and design conditions are presented in terms of certain matrix inequalities. The method proposed can be used for both stationary and ramp leaders. Simulation results are presented to show the effectiveness of the proposed method.

Control design for the nonlinear benchmark problem via the output regulation method

The problem of designing a feedback controller to achieve asymptotic disturbance rejection / attenuation while maintaining good transient response in the RTAC system is known as a benchmark nonlinear control problem, which has been an intensive research subject since 1995. In this paper, we will further investigate the solvability of the robust disturbance rejection problem of the RTAC system by the measurement output feedback control based on the robust output regulation method. We have obtained a design by overcoming two major obstacles: find a closed-form solution of the regulator equations; and devise a nonlinear internal model to account for non-polynomial nonlinearities.

Composite nonlinear feedback control for output regulation problem of linear discrete-time systems with input saturation

Transient performance for output regulation problems of linear discrete-time systems with input saturation is addressed by using the composite nonlinear feedback（CNF） control technique. The regulator is designed to be an additive combination of a linear regulator part and a nonlinear feedback part. The linear regulator part solves the regulation problem independently which produces a quick output response but large oscillations. The nonlinear feedback part with well-tuned parameters is introduced to improve the transient performance by smoothing the oscillatory convergence. It is shown that the introduction of the nonlinear feedback part does not change the solvability conditions of the linear discrete-time output regulation problem. The effectiveness of transient improvement is illustrated by a numeric example.

Distributed Robust Containment Control of Linear Heterogeneous Multi-Agent Systems:An Output Regulation Approach

In this paper,we consider the robust output containment problem of linear heterogeneous multi-agent systems under fixed directed networks.A distributed dynamic observer based on the leaders’measurable output was designed to estimate a convex combination of the leaders’states.First,for the case of followers with identical state dimensions,distributed dynamic state and output feedback control laws were designed based on the state-coupled item and the internal model compensator to drive the uncertain followers into the leaders’convex hull within the output regulation framework.Subsequently,we extended theoretical results to the case where followers have nonidentical state dimensions.By establishing virtual errors between the dynamic observer and followers,a new distributed dynamic output feedback control law was constructed using only the states of the compensator to solve the robust output containment problem.Finally,two numerical simulations verified the effectiveness of the designed schemes.

Output regulation for linear multi-agent systems with unmeasurable nodes

The output regulation of linear multi-agent systems with partial unmeasurable agents is investigated in this paper. All the agents except the exosystem can be classified into two groups. Agents in the first group can be measured by themselves and their neighbors. State variables are not fully accessible for direct communication and full order Luenberger observers are constructed for the unmeasurable agents. We give a state feedback control law to solve the output regulation problem under the communication topologies based on both measurable and unmeasurable agents. The heterogeneous agents' synchronization problem is a general case of our results. Finally, examples are utilized to show the effectiveness of the obtained 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 co and the unknown parameter ju 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.

OUTPUT REGULATION OF THE GENERAL NONLINEARDISCRETE-TIME SYSTEM

With the use of centre manifold and dynamic system theory, the necessary and sufficient conditions are obtained for the solvabilities of the output regulator problems for the general nonlinear discrete-time system. This work generalizes and refines the corresponding results by Isidori and Byrnes on the affine nonlinear continuous-time 'system.

Global robust output regulation for a class of affine singular nonlinear systems

The global robust output regulation problem of the singular nonlinear system is investigated. Motivated by the input-output linearization of the normal affine nonlinear system, a global diffeomorphism map is designed under the assumption that the singular nonlinear system has a strong relative degree. The global diffeomorphism map transfers the singular nonlinear system into a new singular nonlinear system with a special structure. Attaching an internal model to the new singular nonlinear system yields an augmented singular nonlinear system and the global robust stabilization solution of the augmented system implies the global robust output regulation solution of the original singular nonlinear system. Then the global stabilization problem is solved by some appropriate assumptions and the solvability conditions of the global robust output regulation problem are established. Finally, a simulation example is given to illustrate the design approach.

Output regulation of nonaffine nonlinear systems using singular perturbation theory

A control synthesis method for output regulation based on singular perturbation theory combined with inverting design is considered for a class of nonaffine nonlinear systems. The resulting control signal is defined as a solution to ＂fast＂ dynamics which inverts a series error model, whose state is exponentially stable. It is shown that, under sufficient conditions being consistent with the assumptions of singular perturbation theory, this problem is solvable with （ε） tracking error if and only if a set of first-order nonlinear partial differential equations are solvable. The control law can be easily constructed and the simulations show the feasibility and effectiveness of the controller.

Output regulation of nonlinear singularly perturbed systems based on T-S fuzzy model

Based on the T-S model, the output regulation of nonlinear singularly perturbed systems via state feedback is discussed. It is shown that, under standard assumptions, this problean is solvable if and only if certain linear matrix equations are solvable. Once these equations are solvable, the state feedback regulator can easily be constructed.

Containment control for heterogeneous multi-agent systems with time delay via an output regulation approach

This paper presents the containment analysis and design of heterogeneous linear multi-agent systems(MAS)with time-delay under the output regulation.The leaders are treated as exosystems and an modified output regulation error is designed,which can deal with more than one leader in containment control,then the containment problem will be turned into an output regulation problem.A novel analysis framework of the output regulation is proposed to design a dynamic state feedback control law for containment error and distributed observer when the agents cannot receive external system signal,which guarantees the convergence of all follower agents to the dynamic convex hull spanned by the leaders.The system stability for time-delay containment is proved by the output regulation method instead of the Lyapunov method.Finally,a numerical example is given to illustrate the validity of the theoretical results.

New Results in Cooperative Adaptive Optimal Output Regulation

This paper investigates the cooperative adaptive optimal output regulation problem of continuous-time linear multi-agent systems.As the multi-agent system dynamics are uncertain,solving regulator equations and the corresponding algebraic Riccati equations is challenging,especially for high-order systems.In this paper,a novel method is proposed to approximate the solution of regulator equations,i.e.,gradient descent method.It is worth noting that this method obtains gradients through online data rather than model information.A data-driven distributed adaptive suboptimal controller is developed by adaptive dynamic programming,so that each follower can achieve asymptotic tracking and disturbance rejection.Finally,the effectiveness of the proposed control method is validated by simulations.

Cooperative Output Regulation of Heterogeneous Systems over Directed Graphs:A Dynamic Adaptive Event-Triggered Strategy

This paper investigates the cooperative output regulation problem of heterogeneous linear multi-agent systems over directed graphs with the constraint of communication bandwidth.Given that there exists an exosystem whose state information is not available to all agents,the authors develop distributed adaptive event-triggered observers for the followers based on relative information between neighboring agents.It should be pointed out that,two kinds of time-varying gains are introduced to avoid relying on any global information associated with the network,and dynamic triggering conditions are designed to get rid of continuous communications.On the basis of the designed observers,the authors devise a local controller for each agent.Compared with the existing related works,the main contribution of the current paper is that the cooperative output regulation problem for general directed graphs is solved requiring neither global information nor continuous communications.

Asynchronous Output Regulation Control for Continuous-Time Markovian Jump Systems with Colored-Noise

The output regulation control problem for the Markovian jump systems with colored-noise is proposed in this paper.Since the modes mismatch problem often exists in the Markovian switching system,the authors design a modes asynchronous controller with an internal model form,which can not only deal with external disturbance,but also reduce the influence of stochastic noise on the system,such that the mean square of the regulation error can be made arbitrarily small by turning the designed parameters.Meanwhile,a criterion of the m-th moment noise-to-state exponential stability is presented for continuous-time Markovian jump systems under the asynchronous control.

Output regulation for a class of uncertain nonlinear systems with nonlinear exosystems and its application

In this paper, we consider the global robust output regulation problem for a class of uncertain nonlinear systems with nonlinear exosystems. By employing the internal model approach, we show that this problem boils down to a global robust stabilization problem of a time-varying nonlinear system in lower triangular form, the solution of which will lead to the solution of the global robust output regulation problem. An example shows the effectiveness of the proposed approach.

Output regulation problem for discrete-time linear time-delay systems by output feedback control

In this paper, we study the output regulation problem of discrete linear time-delay systems by output feedback control. We have established some results parallel to those for the output regulation problem of continuous linear time-delay systems.

Sampled-Data Semi-Global Robust Output Regulation for a Class of Nonlinear Systems

This paper investigates the semi-global robust output regulation problem for a class of uncertain nonlinear systems via a sampled-data output feedback control law.What makes the results interesting is that the nonlinearities of the proposed system do not have to satisfy linear growth condition and the uncertain parameters of our system are allowed to belong to some arbitrarily large prescribed compact subset.Two cases are considered.The first case is that the exogenous signal is constant.The second case is that the exogenous signal is time-varying and bounded.For the first case,the authors solve the problem exactly in the sense that the tracking error approaches zero asymptotically.For the second case,the authors solve the problem practically in the sense that the steady-state tracking error can be made arbitrarily small.Finally,an example is given to illustrate the effectiveness of our approach.