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.     

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.     

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.     

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.     

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.     

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.     

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.     

Collision-avoiding formation for multiple Euler–Lagrange systems against external disturbances and actuator faults

In this paper, for multiple Euler–Lagrange systems embodying external disturbances and unknown uncertainties, the problems of collision-avoiding formation (CAF) are investigated. With regard to Euler–Lagrange systems under healthy actuator condition and under actuator failures, two distributed collision-avoiding formation (DCAF) control laws are proposed. In one case, which the systems are under healthy actuator condition, firstly, a robust continuous term with adaptive variable gain is utilized to reduce the influence of external disturbances under unknown range. In addition, in order to handle the uncertainties of dynamical systems and collision avoidance, both the estimations for uncertain terms and repulsive potential functions are established in design of algorithms. For the other case, the systems under actuator failures, by utilizing the Lyapunov function and relevant adaptive updating laws, the effects subjected to partial loss of actuator effectiveness can be eliminated. Eventually, two distributed algorithms are proposed to achieve the expected formation configuration with no collision occurred. Numerical simulations are conducted to illustrate the validities of the presented control methodologies.     

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.     

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.     

Actuator saturation control of continuous-time positive switched T–S fuzzy systems

The saturated control problem is investigated for positive switched Takagi–Sugeno (T–S) fuzzy systems with partially controllable subsystems in this paper. Based on the parallel distribution compensation (PDC) algorithm and the convex hull technology, new fuzzy control schemes are proposed for continuous-time positive switched T–S fuzzy systems (PSTSFSs) with actuator saturation. By the multiple linear co-positive Lyapunov function and the slow-fast combined mode-dependent average dwell time (MDADT) approach, sufficient conditions for the stability of continuous-time closed-loop PSTSFSs are developed, which is an extension of the results in previous literature. Furthermore, the least conservative estimation of the attraction domain of PSTSFSs is transformed into an optimization problem. Finally, three simulation examples are given to illustrate the effectiveness of the proposed saturated control schemes.     

Model transformation based sliding mode control of discrete-time two-dimensional Fornasini–Marchesini systems

This paper investigates the problem of sliding mode control (SMC) for discrete-time two-dimensional (2-D) systems subject to external disturbances. Given a 2-D Fornasini–Marchesini (FM) local state space model, attention is focused on designing the 2-D sliding surface and sliding mode controller, which guarantees the resultant closed-loop system to be asymptotically stable. Particularly, this problem is solved using the model transformation based method. First of all, sufficient conditions are formulated for the existence of a linear sliding surface guaranteeing the asymptotic stability of the equivalent sliding mode dynamics. Based on this, a sliding mode controller is synthesized to ensure that the associated 2-D FM system satisfies the reaching condition. The efficiency of the proposed 2-D SMC law design is shown by a numerical example. This paper extends the idea of model transformation to the 2-D systems and solves the SMC problem of a more general 2-D model in FM type for the first time.     

ISS control synthesis of T–S fuzzy systems with multiple transmission channels under denial of service

This paper investigates the input-to-state stabilizing (ISS) problem for Takagi–Sugeno (T–S) fuzzy systems with multiple transmission channels under denial-of-service (DoS) attacks. To achieve ISS, time-triggered data update logics on different channels are determined by linear matrix inequalities (LMIs). Under DoS attacks, a switched fuzzy dynamic output feedback controller which takes the security of premise variables into consideration is constructed. A novel time division mechanism is proposed to deal with the uncertainties caused by DoS attacks at different time periods. The proposed mechanism considers all cases of DoS attacks, which is more general compared to the existing method. Then, sufficient conditions are given to ensure the ISS of T–S fuzzy systems under DoS attacks. Finally, two examples are given to illustrate the effectiveness and merits of the proposed method.     

Nonlinear control design based on generalized Takagi–Sugeno fuzzy systems

This paper is concerned with control design for a generalized Takagi–Sugeno fuzzy system. The Takagi–Sugeno fuzzy system generally describes nonlinear systems by employing local linear system representations, while a generalized fuzzy system to be considered in this paper describes even a wider class of nonlinear systems by representing locally nonlinear systems. For such a generalized system, a stabilizing controller design method is proposed by introducing a new class of non-PDC controllers. A non-PDC controller is a generalized controller of PDC one, which is a traditional fuzzy controller. Stabilizing controller design conditions are given in terms of a set of linear matrix inequalities (LMIs), which are easily numerically solvable. A relaxation method is used to reduce the conservatism of design conditions. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.     

Event-triggered ε level H∞ probabilistic control of uncertain systems

In this paper, a new event-trigger based probabilistic controller is designed using a scenario optimization approach for the robust stabilization of uncertain systems subject to nonlinear and unbounded uncertainties. Sufficient probabilistic stabilization conditions are derived under which the closed-loop system is ε level robust probabilistic stable. Based on these conditions, the design of the gains of the event-triggered state feedback controller is formulated and solved as an optimization problem involving linear matrix inequality. The applicability of theoretical results obtained is illustrated by a numerical example.     

Probabilistic-constrained control of interval type-2 T–S fuzzy systems under the multi-node round-robin scheduling protocol

This work concentrates on the control design of interval type-2 (IT2) T–S fuzzy systems under probabilistic saturation constraints. The actual control signals are allowed to exceed some preset thresholds with a certain frequency. Meanwhile, the sensors are governed by the multi-node round-robin scheduling protocol, which permits more than one sensors to transmit their information at every moment. The main objective is to synthesize a fuzzy controller such that the closed-loop system is locally stochastically stable under probabilistic saturated constraints and the multi-node round-robin scheduling protocol. To this end, the probabilistic saturation constraints are characterized by a Bernoulli-distributed stochastic process, and the received state at the controller side is formulated based on an updating rule and a compensation strategy. By constructing new membership functions, a token-dependent control law is subsequently designed. The stability analysis is facilitated by a modified sector condition dealing with the saturation nonlinearities. With suitable selection of initial states, sufficient conditions are derived to achieve the local stochastic stability of the closed-loop IT2 T–S fuzzy system. A larger domain of stochastic stability can be obtained via a searching algorithm. Finally, the proposed method is illustrated via a simulation example.