Distributed chattering-free containment control for multiple Euler–Lagrange systems

This paper investigates the distributed chattering-free containment control problem for multiple Euler–Lagrange systems with general disturbances under a directed topology. It is considered that only a subset of the followers could receive the information of the multiple dynamic leaders. First, by combining a linear sliding surface with a nonsingular terminal sliding manifold, a distributed chattering-free asymptotic containment control method is proposed under the assumption that the upper bounds of the general disturbances are known. Further, based on the high-order sliding mode control technique, an improved distributed chattering-free finite-time containment control algorithm is developed. Besides, adaptive laws are designed to estimate the unknown upper bounds of the general disturbances. It is demonstrated that all the followers could converge into the convex hull spanned by the leaders under both proposed control algorithms by graph theory and Lyapunov theory. Numerical simulations and comparisons are provided to show the effectiveness of both algorithms.     

Consensus for multiple heterogeneous Euler–Lagrange systems with time-delay and jointly connected topologies

In this paper, we consider the consensus problem of multiple agents modeled by Euler–Lagrange (EL) equation, among which two classes of agents are addressed, i.e., some agents with exactly known parameters and the others with parametric uncertainties. We propose a distributed consensus protocol for the heterogeneous EL systems in which both time-delay and jointly connected topologies are taken into consideration. Based on graph theory, Lyapunov theory and Barbalat?s lemma, the stability of the controller is proved. A distinctive feature of this work is to investigate the consensus problem of EL systems with heterogeneous dynamics, time-delay and jointly connected topologies in a unified theoretical framework. Simulation results are also provided to illustrate the effectiveness of the obtained results.     

Two-layer distributed hybrid affine formation control of networked Euler–Lagrange systems

This paper tackles a distributed hybrid affine formation control (HAFC) problem for Euler–Lagrange multi-agent systems with modelling uncertainties using full-state feedback in both time-varying and constant formation cases. First, a novel two-layer framework is adopted to define the HAFC problem. Using the property of the affine transformation, we present the sufficient and necessary conditions of achieving the affine localizability. Because only parts of the leaders and followers can access to the desired formation information and states of the dynamic leaders, respectively, we design a distributed finite-time sliding-mode estimator to acquire the desired position, velocity, and acceleration of each agent. In the sequel, combined with the integral barrier Lyapunov functions, we propose a distributed formation control law for each leader in the first layer and a distributed affine formation control protocol for each follower in the second layer respectively with bounded velocities for all agents, meanwhile the adaptive neural networks are applied to compensate the model uncertainties. The uniform ultimate boundedness of all the tracking errors can be guaranteed by Lyapunov stability theory. Finally, corresponding simulations are carried out to verify the theoretical results and demonstrate that with the proposed control approach the agents can accurately and continuously track the given references.     

Leader-following bipartite consensus with disturbance rejection for uncertain multiple Euler–Lagrange systems over signed networks

In this paper, the leader-following bipartite consensus is investigated for a group of uncertain multiple Euler–Lagrange systems with disturbances. An innovative adaptive distributed observer is developed without requiring that followers surely acquire the leader’s auxiliary state and system matrix. A directed signed network satisfying the principle of structural balance is exploited to describe the interaction among agents. Then a novel bipartite consensus control protocol is proposed to solve the bipartite consensus problem of multiple Euler–Lagrange systems. The theoretical proof is provided via constructing a Lyapunov function and applying Barbalat lemma to analyze the convergence problem. Finally, a numerical simulation is utilized to demonstrate the effectiveness of proposed method.     

Finite-time event-triggered containment control of multiple Euler–Lagrange systems with unknown control coefficients

This paper researches the finite-time event-triggered containment control problem of multiple Euler–Lagrange systems (ELSs) with unknown control coefficients. To realize an accurate convergence time, the settling-time performance function is employed to ensures the steady-state and dynamic properties of the containment errors in the resulting system. Meanwhile, to handle unknown control coefficients, adaptive neural networks (ANNs) with an additional saturated term are designed, which removes the requirement of full rank control coefficients in traditional control methods. By establishing an event-triggered mechanism, a novel finite-time event-triggered containment control law is designed, which yields the semi-global practical finite-time stable (SGPFS) of the resulting closed-loop system without Zeno phenomenon according to the finite-time stability criterion. The effectiveness of the designed methodology is verified by simulation.     

Leader-following rendezvous for uncertain Euler–Lagrange multi-agent systems by output feedback

In this paper, we investigate the problem of output feedback tracking for a class of Euler–Lagrange multi-agent systems with unmeasurable velocity and input disturbances. By proposing a novel dynamic velocity observer, an adaptive output feedback consensus algorithm is proposed such that the tracking errors of all agents can converge to an arbitrarily small neighborhood of zero by tuning the design parameters. A numerical example is presented to illustrate the effectiveness of the controller.     

RISE-based prescribed performance control of Euler–Lagrange systems

In this study, we addressed the problem of design of high-performance tracking controller for uncertain systems described by the Euler–Lagrange formulation. The main objective was to combine the advantages of the robust integral of the sign of the error (RISE) controller with those of the prescribed performance (PP) controller. In particular, we aimed to obtain asymptotic tracking for the uncertain systems through a continuous control command while ensuring the transient performance. Two controllers were developed. First, the PP property was injected into the RISE controller assuming no constraint on the actuation amplitude existed, and then this property was incorporated into the saturated RISE controller. The performance of the proposed controllers was validated through experimental and simulation tests.     

Disturbance observer-based fixed-time leader-following consensus control for multiple Euler–Lagrange systems: A non-singular terminal sliding mode scheme

This paper focuses on the fixed-time leader-following consensus problem for multiple Euler–Lagrange (EL) systems via non-singular terminal sliding mode control under a directed graph. Firstly, for each EL system, a local fixed-time disturbance observer is introduced to estimate the compound disturbance (including uncertain parameters and external disturbances) within a fixed time under the assumption that the disturbance is bounded. Next, a distributed fixed-time observer is designed to estimate the leader’s position and velocity, and the consensus problem is transformed into a local tracking problem by introducing such an observer. On the basis of the two types of observers designed, a novel non-singular terminal sliding surface is proposed to guarantee that the tracking errors on the sliding surface converge to zero within a fixed time. Furthermore, the presented control algorithm also ensures the fixed-time reachability of the sliding surface, while avoiding the singularity problem. Finally, the effectiveness of the proposed observers and control protocol is further verified by a numerical simulation.     

Adaptive sliding mode control for uncertain Euler–Lagrange systems with input saturation

In this paper, the tracking control problem of uncertain Euler–Lagrange systems under control input saturation is studied. To handle system uncertainties, a leakage-type (LT) adaptive law is introduced to update the control gains to approach the disturbance variations without knowing the uncertainty upper bound a priori. In addition, an auxiliary dynamics is designed to deal with the saturation nonlinearity by introducing the auxiliary variables in the controller design. Lyapunov analysis verifies that based on the proposed method, the tracking error will be asymptotically bounded by a neighborhood around the origin. To demonstrate the proposed method, simulations are finally carried out on a two-link robot manipulator. Simulation results show that in the presence of actuator saturation, the proposed method induces less chattering signal in the control input compared to conventional sliding mode controllers.     

Dynamic output feedback H∞ control for fractional-order linear uncertain systems with actuator faults

This paper is concerned with the problem of robust fault-tolerant H_∞ dynamic output feedback control for fractional-order linear uncertain systems with the order satisfying 0 < α < 1 in the presence of actuator faults. A new linear matrix inequality (LMI) formulation corresponding to the H_∞ norm of fractional-order linear systems is proposed. Based on the new formulation and by introducing a new linearizing change of variables, sufficient conditions for robust fault-tolerant H_∞ dynamic output feedback controller designs are derived in term of LMIs. Furthermore, the proposed controller not only enables the system to keep robust stabilization, but also achieves a better H_∞ performance compared with the existing methods. Numerical examples are given to illustrate the design procedure and its effectiveness.     

Event-driven fully distributed optimal coordinated control for Euler–Lagrange multi-agent systems with connectivity preservation

This paper studies the distributed optimal coordinated control problem for Euler–Lagrange multi-agent systems with connectivity preservation. The aim is to force agents to achieve the optimal solution minimizing the sum of the local objective functions while guaranteeing the connectivity of the communication graph. For practical purposes, the gradient vector of the local objective function is allowed to use only at the real-time generalized position instead of at the auxiliary system state. To make the control parameters independent of the global information and guarantee the fully distributed manner of controller, the adaptive control is introduced to update the coupling weights of the relative states among neighbors. Moreover, to reduce the resource for control updates, the event-driven communication is employed for the updates of both the relative states and the gradient of the connectivity-preserving potential function. Based on the Lyapunov analysis framework, it is proved that agents can converge to the optimal solution with connectivity preservation and Zeno behavior is excluded for the two event-triggering conditions. Finally, the effectiveness of the proposed method is verified by a numerical simulation example.     

Adaptive actuator fault-tolerant control for a three-dimensional Euler–Bernoulli beam with output constraints and uncertain end load

This paper studied an adaptive actuator fault-tolerant control scheme for the flexible Euler–Bernoulli beam in the three-dimensional space with output constraints and uncertain end load. The dynamic models are represented by partial differential equations (PDEs) and ordinary differential equations (ODEs). When part of the actuator fails, an adaptive control scheme is designed to regulate the vibration and stabilize the flexible three-dimensional Euler–Bernoulli beam. Barrier Lyapunov Function (BLF) is adopted to realize output constraints of the system. Adaptive control law with projection mapping operator is designed to compensate for the end load which is uncertain and bounded. The goal of this paper is to suppress the displacement of the flexible three-dimensional Euler–Bernoulli beam which can be constrained in given bounds under actuator fault and uncertain, bounded end load. It is confirmed that the proposed control scheme can deal with the vibration, adaptive actuator fault-tolerant control, uncertain and bounded end load and output constraints of the system simultaneously. Finally, numerical simulations illustrate the effectiveness and feasibility of the method.     

Analysis and design for continuous-time string-connected Takagi–Sugeno systems

Distributed systems consist of interconnected, lower-dimensional subsystems. For such systems, distributed analysis and design present several advantages, such as modularity, easier analysis and design, and reduced computational complexity. A special case of distributed systems is when the subsystems are connected in a string. Applications include distributed process control, traffic and communication networks, irrigation systems, hydropower valleys, etc. By exploiting such a structure, in this paper, we propose conditions for the distributed stability analysis of Takagi–Sugeno fuzzy systems connected in a string. These conditions are also extended to observer and controller design and illustrated on numerical examples.     

T–S fuzzy control for dithered nonlinear singularly perturbed systems with multiple time delays

This paper is concerned with the stability problem of nonlinear multiple time-delay singularly perturbed (NDSP) systems. To overcome the effect of modeling error between the reduced-order model of the NDSP plant and Takagi–Sugeno (T–S) fuzzy models, a robustness design of model-based fuzzy control is proposed in this study. A stability criterion in terms of Lyapunov’s direct method is derived to guarantee the asymptotic stability of NDSP systems. According to this criterion, a model-based fuzzy controller is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the NDSP system. If the designed fuzzy controller cannot stabilize the NDSP system, a high-frequency signal, commonly referred to as dither, is simultaneously introduced to stabilize it. Based on the relaxed method, the NDSP system can be stabilized by regulating appropriately the parameters of dither. If the dither’s frequency is high enough, the output of the dithered reduced system and that of its corresponding mathematical model – the relaxed reduced system – can be made as close as desired. This makes it possible to obtain a rigorous prediction of the stability of the dithered reduced system based on the one of the relaxed reduced system.     

Stabilization of positive Takagi–Sugeno fuzzy discrete-time systems with multiple delays and bounded controls

This paper deals with the problem of stabilization by state feedback control of Takagi–Sugeno (T–S) fuzzy discrete-time systems with multiple fixed delays while imposing positivity in closed-loop. The obtained results are presented under linear programming (LP) form. In particular, the synthesis of state feedback controllers is first solved in terms of Linear programming for the unbounded controls case. This result is then extended to the stabilization problem by nonnegative controls, and stabilization by bounded controls. The stabilization conditions are derived using the single Lyapunov–Krasovskii functional (LKF). An example of a real plant is studied to show the advantages of the design procedure. A comparison between linear programming and LMI approaches is presented.     

H∞ finite-time control for LPV systems with parameter-varying time delays and external disturbance via observer-based state feedback

This paper is concerned with the observer-based H_∞ finite-time control problem for linear parameter-varying (LPV) systems with parameter-varying time delays and external disturbance. The main contribution is to design an observer-based H_∞ finite-time controller such that the resulting closed-loop system is uniformly finite-time bounded and satisfies a prescribed H_∞ disturbance attenuation level in a finite-time interval. By using the delay- and parameter-dependent multiple Lyapunov–Krasovskii functional approach, sufficient criteria on uniform H_∞ finite-time stabilization via observer-based state feedback are presented for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the validity of the proposed theoretical results.     

Absolute stability and Lyapunov–Krasovskii functionals for switched nonlinear systems with time-delay

We derive conditions for the existence of Lyapunov–Krasovskii functionals for a number of classes of nonlinear switched systems with time-delay. In particular, we first give conditions for systems of retarded type that relax those recently described in Sun and Wang (2013) [18]. Using similar techniques, related results are then derived for coupled differential-difference systems and for systems of neutral type. Finally, we briefly note some corresponding results for discrete-time systems.     

Active fault tolerant control of wind turbine systems based on DFIG with actuator fault and disturbance using Takagi–Sugeno fuzzy model

This paper presents an active fault tolerant control (FTC) for doubly fed induction generator (DFIG) with actuator fault and disturbance using Takagi–Sugeno (TS) fuzzy model. The control structure has two parts: fault and disturbance estimation part and FTC part. First, a TS fuzzy model is used to describe the DFIG system. Using a special linear transformation, the original system is decoupled into three independent subsystems: state subsystem without fault and disturbance, disturbance subsystem without fault, and fault subsystem without disturbance. By solving linear matrix inequalities (LMIs), a TS fuzzy observer is designed for the state subsystem without fault and disturbance. Second, estimations of faults and disturbance are obtained using the other subsystem models. Third, an active FTC scheme is developed to reduce the effect of disturbance and actuator faults. Finally, the performance of the proposed FTC is tested for a wind turbine system based on DFIG with actuator faults and disturbance. The simulation results demonstrate that the new FTC scheme makes possible to obtain an efficient fault and disturbance estimation and to reduce the peak current in the transient process.