Coordinated tracking for networked robotic systems via model-free controller–estimator algorithms

This paper mainly focuses on two classes of coordinated tracking problems for networked robotic systems, including semi-global coordinated tracking (SCT) problem and global coordinated tracking (GCT) problem. Considering that the dynamics of the networked robotic system can be unattainable, several novel model-free controller-estimator algorithms are proposed to solve the SCT and GCT problems, as well as to reject the input disturbances contained in the system dynamics. By invoking nonsmooth analysis and Lyapunov argument, a number of novel criteria (including sufficient criteria, necessary and sufficient criteria) for semi-global and global asymptotic stability of the presented algorithms are established. Finally, simulation experiments are carried out to verify the theoretical results.     

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.     

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.     

Fully distributed observer-based tracking control for Lur’e systems with event-triggered communication

This paper investigates the problem of cooperative tracking for Lur’e systems under directed spanning tree topology. First, a control protocol is proposed to achieve cooperative tracking consensus by a distributed observer, which utilizes only the states of neighboring agents based on the event-triggering conditions with mixed node and edge. Then, an improved tracking protocol is developed by considering the case that only the outputs of neighbors can be obtained. With the aid of adaptive updating parameters, the two protocols do not utilize the minimum eigenvalue of Laplacian matrix, and can deal with the nonlinear dynamics of Lur’e systems in a fully distributed manner. Moreover, with the Lyapunov analysis framework, the tracking errors can be proved to converge to zero in both cases. Zeno behavior is excluded from the event-triggering conditions containing states and outputs of neighbors. Finally, the effectiveness of the proposed protocols is verified by two numerical simulations.     

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.     

Non-fragile quantized H∞ output feedback control for nonlinear systems with quantized inputs and outputs

This paper is concerned with non-fragile $H_{\infty }$ control problems for a class of continuous-time nonlinear systems with unknown nonlinearity and quantized inputs and outputs. The construction of both static output feedback (SOF) and observer-based output feedback (OBOF) control laws in the presence of additive interval-bounded controller coefficient variations can be divided into two parts, linear and nonlinear parts. The linear part plays a role in achieving the $H_{\infty }$ performance, while the nonlinear part is used to reduce the quantization effect. However, it should be pointed out that the effect of input and output quantization can be eliminated fully for SOF case by requiring knowledge of all signs of the states, but only the effect of input quantization can be eliminated for OBOF case. It is worth mentioning that three novel alternative methods with strict linear matrix inequality (LMI) conditions are proposed to design both SOF and OBOF controllers. In particular, these three new methods do not introduce any other auxiliary constraints as many existing results do where a matrix equality constraint between system matrix and Lyapunov matrix is often inserted. Finally, the effectiveness and advantages of the proposed control methods are demonstrated by a numerical example.     

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.     

H∞ tracking control for a class of asynchronous switched nonlinear systems with uncertain input delay

This paper studies the problems of stability and H∞ model reference tracking performance for a class of asynchronous switched nonlinear systems with uncertain input delay. First, it is assumed switched controller and corresponding piecewise Lyapunov function are unknown but the derivative of piecewise Lyapunov function has a condition; this condition implies that the nominal system (system without input delay and disturbance) is exponentially stable by any switched controller which satisfies this condition. With this assumption, a proper Lyapunov–Krasovskii functional is constructed. By employing this new functional and average dwell time technique, the delay-dependent input-to-state stability criteria are derived under a certain delay bound; in addition, a mechanism which finds the upper bound of input delay is proposed. Finally, a kind of state feedback control law which fulfils condition of aforesaid piecewise Lyapunov function is introduced to guarantee the input-to-state stability and H∞ model reference tracking performance. Simulation examples are presented to demonstrate the efficacy of results.     

Hierarchical type stability and stabilization of networked control systems with event-triggered mechanism via canonical Bessel–Legendre inequalities

This paper is studied with the hierarchical type stability and stabilization of networked control systems (NCSs) with event-triggered mechanism (ETM). In the cause of reducing the amount of data transmission and saving the limited network bandwidth, ETM is introduced into NCSs, and the closed-loop time-delay NCSs model with ETM is presented. An improved Lyapunov–Krasovskii functional (LKF), containing delay-product-type terms and being appropriate for the canonical BesselLegendre inequality (BLI), is first constructed. Then, by utilizing the canonical BLI and the extended reciprocally convex matrix inequality (ERCMI) to deal with the single integral terms of the derivative of LKF, a sufficient condition on asymptotically stable is derived for NCSs. Based on above N-dependent stability criteria, a co-design method is developed, which can be capable of calculating the control gain of controller and the weighting matrix of the ETM. Finally, the feasibility and superiority of the results are verified by two examples.     

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.     

New robust H∞ control for uncertain stochastic Markovian jumping systems with mixed delays based on decoupling method

This paper considers the problems of robust stochastic stabilization and robust $H_{\infty }$ controller design for a class of stochastic Markovain jumping systems with mixed time delays and polytopic parameter uncertainties. Both the interval time-varying delay and distributed time delay are simultaneously considered. Some new delay-dependent sufficient conditions, which differs greatly from the most existing results, are obtained based on the decoupling method and some advanced techniques. A numerical example is provided to illustrate the effectiveness of the proposed criteria.     

Novel master–slave synchronization criteria of chaotic Lur’e systems with time delays using sampled-data control

This paper investigates the problem of master–slave synchronization of chaotic Lur’e systems (CLSs) with time delays by sampled-data control. First, a novel Lyapunov–Krasovskii functional (LKF) is constructed with some new augmented terms, which can fully capture the system characteristics and the available information on the actual sampling pattern. In comparison with existing results, the constraint condition of the positive definition of the LKF is more relax, since it is positive definite only requiring at sampling instants. Second, based on the LKF, a less conservative synchronization criterion is established. Third, the desired estimator gain can be designed in terms of the solution to linear matrix inequalities (LMIs). The obtained conditions ensure the master–slave synchronization of CLSs under a longer sampling period than remarkable existing works. Finally, three numerical simulations of Chua’s circuit and neural network are provided to show the effectiveness and advantages of the proposed results.     

Optimal stabilization for differential systems with delays - Malkin’s approach

The paper considers a process controlled by a system of delayed differential equations. Under certain assumptions, a control function is determined such that the zero solution of the system is asymptotically stable and, for an arbitrary solution, the integral quality criterion with infinite upper limit exists and attains its minimum value in a given sense. To solve this problem, Malkin’s approach to ordinary differential systems is extended to delayed functional differential equations, and Lyapunov’s second method is applied. The results are illustrated by examples, and applied to some classes of delayed linear differential equations.     

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.     

Formation-containment control for multi-robot systems with two-layer leaders via hierarchical controller–estimator algorithms

This paper studies the formation-containment control for multi-robot systems with two-layer leaders in the presence of parametric uncertainties, input disturbances and directed interaction topologies. To cope with the aforementioned issues, we establish a novel formation-containment control framework, where the analysis of the systems is carried out step by step. A hierarchical controller–estimator (HCE) algorithm, containing distributed sliding-mode estimators in each sub-algorithm, is proposed for the two-layer leaders system. Moreover, by invoking finite-time stable and input-to-state stable theories, the sufficient conditions for convergence of the proposed HCE algorithm are presented. Finally, numerous simulations are performed to demonstrate the validity of the theoretical results.