Output Regulation Error Research Articles

Estimator-based event-triggered output synchronization for heterogeneous multi-agent systems under denial-of-service attacks and actuator faults

This paper studies the output synchronization problem with an event-triggered communication scheme for a class of heterogeneous multi-agent systems under denial-of-service (DoS) attacks and actuator faults. DoS attacks may render the followers incapable of acquiring the leader's states and actuator faults may cause the actuators to not perform the control operation well. Comparing with the previous studies adopting the continuous communication mechanism, a novel switching estimator with an event-triggered communication strategy is designed to estimate the leader's states for each follower. By using the Lyapunov stability theory and the average dwell time method, sufficient conditions for the upper bound of the frequency of DoS attacks are derived. The estimation error system is proved to be exponentially stable. Besides, in order to compensate for actuator faults, a distributed adaptive fault-tolerant controller is proposed. The conditions for the stability of the output regulation error when the systems suffer from DoS attacks and actuator faults are given. A simulation example is proposed to prove the effectiveness of the main results.

Event‐triggered cooperative control for uncertain multi‐agent systems and applications

AbstractThis paper investigates the event‐triggered cooperative output regulation problem for uncertain multi‐agent systems, demonstrating that the output regulation error of the uncertain multi‐agent system can converge to a small neighborhood of the origin. The proposed method has several notable features. Firstly, both the leader and follower systems contain unknown parameters, and follower systems can be heterogeneous. Secondly, the controller only requires the relative output of each agent, rather than the absolute output or state. Thirdly, the controller is fully distributed, which implies that it does not rely on any global information. In order to achieve the above purpose, a fully distributed reduced‐order observer is proposed with new adaptive laws. Furthermore, new adaptive event‐triggered mechanisms are designed on the basis of the neighborhood regulation error (NRE) and the observational regulation error (ORE). Finally, the proposed approach is validated through simulation and experiment on a multi‐joint robot manipulator.

Fuzzy Output Regulation of Nonlinear Time-Delay Distributed Parameter Systems With Quantization and Actuator Failures: Application to Hot Strip Mill Cooling Process

The output regulation of nonlinear distributed parameter systems (DPSs) with time-varying delay is studied in this article. By employing the Takagi–Sugeno (T–S) fuzzy model, the nonlinear time-delay DPSs are described as a fuzzy partial differential equation. To deal with the limited capability of communication channels, the state information and output regulation error are quantized by a kind of dynamic quantizer. The actuator failures which occur frequently in practice are considered in two cases: to be unknown and to follow the Bernoulli stochastic distribution. Then, the boundary-control-based output regulation controllers are designed based on the derived T–S fuzzy model. And fuzzy controller design strategies are proposed to ensure the system state and the output regulation error are finite-time bounded. By constructing appropriate Lyapunov functionals, sufficient conditions for the control gains and the quantizer’s adjusting parameters are provided in forms of linear matrix inequalities. Finally, an application of the output regulation strategies into the cooling process in a hot strip mill is explored. The feasibility and effectiveness of the design strategies are indicated through the simulation results.

Integral sliding‐mode‐based robust output‐regulation for constrained and uncertain linear systems

AbstractThis article proposes a solution to the output regulation problem for uncertain linear systems with input saturation, state constraints, and external disturbances. The proposed robust control is composed of a linear and a nonlinear part. Each part of the control can be designed independently due to the use of an integral sliding‐mode control approach. The linear control, whose design is based on the barrier Lyapunov function and the attractive ellipsoid method, considers the input saturation, the state constraints, and the parameter uncertainties. The nonlinear part is based on an integral sliding‐mode control approach and it can compensate the effect of some matched disturbances. Also, a safe set where the system trajectories do not transgress the state constraints and input saturation, is provided. The proposed scheme guarantees asymptotic convergence to zero of the output regulation error coping with the system constraints and disturbances. A constructive and simple method, based on linear matrix inequalities, is proposed to compute the controller gains. Some simulation results illustrate the feasibility of the proposed scheme.

Output regulation for the parametric strict-feedback system via the event-triggered adaptive updating algorithm

In this paper, the adaptive event-triggered output regulation problem for the parametric strict feedback system is addressed. The adaptive control strategy over the plant-control communication network is developed and governed by the transmission sampled data of the plant, completely. By introducing an augment dynamic to compensate the event-triggered measurement errors, the event-triggered mechanism is developed independent on the stability of the adaptive algorithm. Therefore, a more flexible and robust event-triggered mechanism is proposed than the existing method where the threshold coefficients are constrained with the closed-loop system stable requirement. It is proved that, the asymptotical output regulation error upper bound is continuously dependent on the event-triggered threshold coefficient, but independent on the upper bound of unknown parameters. Therefore, the output regulation error upper bound can be modified by the feedback gains and threshold coefficients without considering the bounded unknown parameters. What’s more, the Zeno phenomenon is discussed carefully and excluded. Finally, the event-triggered adaptive control method is applied to control the double-rod electro-hydraulic servo system. It is shown that, the proposed scheme has smaller output regulation error than the existing methods with less communication times.

Adaptive Backstepping Control of Uncertain Gear Transmission Servosystems With Asymmetric Dead-Zone Nonlinearity

In this paper, an adaptive backstepping control scheme is presented to solve the position control problem for a gear transmission servosystem with unknown asymmetric sandwiched dead-zone nonlinearity. All the parameters involved in both the system and dead-zone models are allowed to be totally unknown. In contrast to the previous results where the effects of symmetric dead zone can be treated as additive disturbances in a transformed system, most of the unknown parameters of the transformed system are now time varying and dependent on the real-time value of relative displacement between the driving and driven gears. To deal with the above issue, new compensating terms in the quadratic form are introduced in the design of the virtual control signal for each recursive step. With the adaptive laws modified correspondingly, we can still show that all the closed-loop signals are ensured to be bounded and the output regulation error will converge to a compact set. Simulation results are provided to show the effectiveness of the proposed adaptive control scheme.

Distributed Adaptive Consensus Control and Disturbance Suppression of Unknown Nonlinear Multi-Agent Systems

This paper considers consensus control of unknown nonlinear multi-agent systems with unknown disturbance under undirected networks. The expected output signal of the leader is not available to all subsystems, only some subsystems can obtain it, and other subsystems will obtain the output regulation error through the network connections. The critical contribution of this paper is to develop a new distributed adaptive control protocol and disturbance observer based on relative output information to achieve the consensus control objective of the subsystems. Since only the relative output information is used, the adaptive control protocol we proposed is distributed. Also, a new lemma is proposed for the first time to analyze the stability of the subsystems. Comparing to current results, the challenge exists in this paper is that the external disturbance is unknown and does not have explicit expression. Based on this, designing a disturbance observer based on relative output information to achieve consensus output regulation is the motivation of this paper. Different from the existing disturbance suppression methods, only the relative output information is used for disturbance suppression, and only the part of disturbance that affects the common trajectory will be suppressed. The stability analysis of the systems is carried out by using algebraic graph theory, Lyapunov function, and Barbalat lemma. The outcome of the paper is that all variables of the systems are bounded and the output regulation errors of the subsystems converge to zero asymptotically. Finally, a numerical simulation is given to demonstrate the effectiveness of the proposed method.

Adaptive Approximation-Based Regulation Control for a Class of Uncertain Nonlinear Systems Without Feedback Linearizability.

In this paper, for a general class of uncertain nonlinear (cascade) systems, including unknown dynamics, which are not feedback linearizable and cannot be solved by existing approaches, an innovative adaptive approximation-based regulation control (AARC) scheme is developed. Within the framework of adding a power integrator (API), by deriving adaptive laws for output weights and prediction error compensation pertaining to single-hidden-layer feedforward network (SLFN) from the Lyapunov synthesis, a series of SLFN-based approximators are explicitly constructed to exactly dominate completely unknown dynamics. By the virtue of significant advancements on the API technique, an adaptive API methodology is eventually established in combination with SLFN-based adaptive approximators, and it contributes to a recursive mechanism for the AARC scheme. As a consequence, the output regulation error can asymptotically converge to the origin, and all other signals of the closed-loop system are uniformly ultimately bounded. Simulation studies and comprehensive comparisons with backstepping- and API-based approaches demonstrate that the proposed AARC scheme achieves remarkable performance and superiority in dealing with unknown dynamics.

Stabilisation of asymmetrically structured back‐to‐back static synchronous compensator system with non‐linear damping control

This study describes a new back-to-back static synchronous compensator (BTB STATCOM) system with asymmetrically structured converters and develops its mathematical model. BTB STATCOM uses pulse-width modulation technology for a rectifier station along with multipulse technology for an inverter station. The authors propose a control strategy for the following three control variables: DC voltage and both active and reactive rectifier powers. In the rectifier station, input–output linearisation via the feedback control law is applied for independent control of the active and reactive powers. Conversely, the controller is not applicable for maintaining the DC voltage because of its irregularity. They design an alternative indirect damping controller for the reactive current within the inverter station. The proposed controller improves the stability margin and decreases the oscillation of DC voltage with a degraded reactive current tracking performance of the inverter. Using simulation, they validate the proposed method, comparing its effectiveness to that of a proportional-plus-integral-plus-derivative controller. They investigate the semi-globally exponential stability of the damped internal dynamics using a parameter-dependent Lyapunov (PDL) function. Using a composite Lyapunov function based on the PDL function, the uniform boundedness of the output regulation error as well as the closed-loop stability is established.

Containment control of heterogeneous linear multi-agent systems

In this note, we study the containment control problem of heterogeneous linear multi-agent systems based on output regulation framework. Motivated by leader–follower output regulation problems, the leaders are assumed to be exosystems. In controller design approach for each follower, we utilize a distributed dynamic state feedback control scheme. To achieve the objective of this work, we modify the conventional output regulation error in such a way that it can handle more than one leader, and we also introduce a dynamic compensator. Our work is based on a new formulation for containment error that guarantees the convergence of all follower agents to the dynamic convex hull spanned by the leaders, and also enables us to use output regulation techniques with some modifications to solve the containment problem. Finally, a numerical example is given to illustrate the validity of theoretical results.

Simple Integral Fuzzy Control for Converters with Highly Nonlinear Dynamics

A simple integral Takagi-Sugeno (T-S) fuzzy control scheme suitable for many types of converters is proposed in this paper. A converter with highly nonlinear characteristics, called active high power factor correction (AHPFC), is taken as an example to show the control scheme. Indeed, we can derive a linear controller to achieve zero output regulation error for the AHPFC converter. First, we include an integral error signal to form an augmented system. After translating the coordinate to the regulated point, we obtain the stabilization model. The model-based fuzzy approach is then used to handle the nonlinear system. The system stability is proven by Lyapunov theorem. The feedback gains are obtained by solving linear matrix inequalities (LMIs). A surprised property is that the gains are identical for every fuzzy control rule. This result greatly simplifies the controller to be a linear state feedback one. Finally, the simulation and experimental results show the satisfactory performance, which is better than the converter using a proportional integral (PI) controller.

Disturbance cancellation for linear systems by adaptive internal models

The adaptive disturbance cancellation problem is considered for single-input, single-output, linear systems when the linear exosystem which generates the disturbances to be rejected and/or the reference signals to be tracked is unknown, that is both its order 2r+1 and its parameters {ω1,…,ωr} are unknown. The proposed regulator makes use of two observers and contains an adaptive internal model which tunes m internal parameters on the basis of the output regulation error. It is shown that: if m≥r, that is the adaptive internal model can reproduce the required input, the regulation error tends exponentially to zero; if m<r, that is the adaptive internal model can only approximate the required input within an approximation error ϵ, the regulation error tends exponentially into a closed ball whose radius is proportional to ϵ, provided that ϵ is sufficiently small so that singularities are avoided.

Tuning of a TS Fuzzy Output Regulator Using the Steepest Descent Approach and ANFIS

The exact output regulation problem for Takagi-Sugeno (TS) fuzzy models, designed from linear local subsystems, may have a solution if input matrices are the same for every local linear subsystem. Unfortunately, such a condition is difficult to accomplish in general. Therefore, in this work, an adaptive network-based fuzzy inference system (ANFIS) is integrated into the fuzzy controller in order to obtain the optimal fuzzy membership functions yielding adequate combination of the local regulators such that the output regulation error in steady-state is reduced, avoiding in this way the aforementioned condition. In comparison with the steepest descent method employed for tuning fuzzy controllers, ANFIS approximates the mappings between local regulators with membership functions which are not necessary known functions as Gaussian bell (gbell), sigmoidal, and triangular membership functions. Due to the structure of the fuzzy controller, Levenberg-Marquardt method is employed during the training of ANFIS.

Uniform output regulation via approximated input–output linearisation for lightly damped internal dynamics

We present a general framework for the design of a damping controller to tame lightly damped internal dynamics and to assess the stability of an approximate input–output linearised closed-loop system. In nonlinear systems, conclusions cannot be drawn regarding the stability of internal dynamics even though the zero dynamics is globally stable. Here, we investigated the sufficient conditions with a parameter-dependent Lyapunov (PDL) function for semi-globally exponential stability of damped internal dynamics. Using a composite Lyapunov function based on the PDL function, the uniform boundedness of the output regulation error is established within a region of interest. Controllability and observability analyses offer a theoretical guideline as to how a damping controller can be designed in the view of control effort and transient performance.

Output regulation of a class of continuous-time Markovian jumping systems

This paper studies output regulation for continuous-time Markovian jumping systems (MJSs), for which mode-dependent regulation equations are investigated. With the extension of regulation scheme to MJSs by stochastic Lyaponov–Krasovskii functional framework, sufficient conditions are, respectively, obtained for state feedback and error feedback. The resulting closed-loop system is guaranteed to be stochastically stable and the output regulation error almost asymptotically converges to zero. A semi-definite optimization approach via disciplined convex programming is adopted to ensure relaxed solutions of the regulation equations. Finally, two numerical simulations are given to illustrate the performance of the proposed approach.

Nonlinear dynamic allocator for optimal input/output performance trade-off: Application to the JET tokamak shape controller

In this paper, we revisit the dynamic allocation scheme for input redundant plants proposed in Zaccarian (2009). within a set-point regulation setting and propose generalizations that apply to cases where the plant under consideration is not input redundant but the control specifications allow us to modify the set-point regulation within certain bounds. In this case, the input allocator is extended to the nonredundant case by allowing it to improve the input allocation selection at the price of some output regulation error. We also establish here desirable convergence properties of the allocator, which were only addressed for the linear case in Zaccarian (2009). In particular, we design the allocator dynamics as the gradient of a cost function and establish its convergence to the minimum of the cost function under some mild conditions. The allocation scheme is applied to the JET tokamak shape controller by illustrating its capabilities to enforce coil currents selections that tend to move away from the saturation limits within the allowable degrees of freedom.

Output tracking of Markovian jumping systems via error feedback regulation

AbstractThis paper studies the output tracking problem of continuous-time Markovian jumping systems (MJSs) via error feedback scheme. With the extension of output regulation to MJSs, sufficient conditions are obtained based on stochastic Lyapunov-Krasovskii functional. The resulting closed-loop system is guaranteed to be stochastically stable and the output tracking is achieved almost asymptotically. Moreover, the output regulation error almost asymptotically converges to zero. In order to ensure the relaxed solutions of the regulation equations, we described the problem as a semi-definite optimization approach via disciplined convex programming. Simulation result is also given to illustrate the performance and effectiveness of the proposed approach.

Takagi-Sugeno Fuzzy Integral Control for Asymmetric Half-Bridge DC/DC Converter

In this paper, Takagi-Sugeno (TS) fuzzy integral control is investigated to regulate the output voltage of an asymmetric half-bridge (AHB) DC/DC converter; First, we model the dynamic characteristics of the AHB DC/DC converter with state-space averaging method and small perturbation at an operating point. After introducing an additional integral state of the output regulation error, we obtain the 5 th -order TS fuzzy model of the AHB DC/DC converter. Second, the concept of the parallel distributed compensation is applied to design the fuzzy integral controller, in which the state feedback gains are obtained by solving the linear matrix inequalities (LMIs). Finally, simulation results are presented to show the performance of the considered design method as the output voltage regulator and compared to the results for which the conventional loop gain method is used.

LMI-based Integral fuzzy control of DC-DC converters

In this paper, we propose a T-S fuzzy controller which combines the merits of: i) the capability for dealing with nonlinear systems; ii) the powerful LMI approach to obtain control gains; iii) the high performance of integral controllers; iv) the workable rigorous proof for exponential convergence of error signals; and v) the flexibility on tuning decay rate. The output regulation problems of a basic buck converter and a zero-voltage-transition (ZVT) buck converter are used as application examples to illustrate the control performance of the proposed methodology. First, we consider a general nonlinear system which can represent the large-signal models of the converters. After introducing an added integral state of output regulation error and taking coordinate translation on an equilibrium point, the resulting augmented system is represented into a Takagi-Sugeno (T-S) fuzzy model. Then, the concept of parallel distributed compensation is applied to design the control law whereby the control gains are obtained by solving linear matrix inequalities (LMIs). An interesting result is that the obtained control law is formed only by the linear state feedback signals weighted by grade functions. In addition, the robustness analysis is carried out when uncertainty and disturbance are taken into consideration. The performance of numerical simulations and practical experiments results is satisfactory.