Necessary and sufficient conditions for bounded distributed mean square tracking of multi‐agent systems with noises

This paper is concerned with the distributed control problem of second‐order agents under directed network topology. The control input of each agent only depends on its own state and the states of its neighbors corrupted by white noises. By using the algebraic graph theory and stochastic analysis method, necessary and sufficient conditions are presented for mean square bounded tracking. Finally, several simulation examples are given to illustrate the results. Copyright © 2015 John Wiley & Sons, Ltd.     

Output tracking control for an omnidirectional rehabilitative training walker with incomplete measurements and random parameters

In this study, we propose a model and an output feedback tracking control for an omnidirectional rehabilitative training walker (ODW) with unmeasurable speed, incomplete measurements of position output, and random structural parameters. A stochastic model and an incomplete measurement model were proposed to describe the motion of an ODW subject to random structural parameters and to account for any incomplete data transmission phenomenon caused by possible sensor ageing or failures. A speed observer and a state observer were designed to estimate the unmeasurable speed and the incomplete measurements of position output. Moreover, a dynamic output feedback controller was constructed to ensure the exponential stability in mean square of the tracking error system. Furthermore, the results verify that the choice of appropriate design parameters can result in the mean square of the tracking error becoming arbitrarily small. A simulation example was provided to illustrate the effectiveness of the proposed design procedures.     

A predictive control strategy for norm‐bounded LPV discrete‐time systems with bounded rates of parameter change

A novel predictive control strategy for input‐saturated norm‐bounded linear parameter varying discrete‐time systems is proposed. The solution is computed by minimizing an upper bound to the ‘worst‐case’ infinite horizon quadratic cost under the constraint of steering the future state evolutions, emanating from the current state, into a feasible and positive invariant set. It will be shown that the ‘size’ of this terminal set depends on the rate of change of the scheduling parameter, which is assumed to be bounded and measurable. Copyright © 2007 John Wiley & Sons, Ltd.     

Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H_∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.     

Distributed consensus and tracking control of second‐order time‐varying nonlinear multi‐agent systems

In this paper, the distributed consensus and tracking protocols are developed for the second‐order time‐varying nonlinear multi‐agent systems under general directed graph. Firstly, the consensus and tracking problems can be converted into a conventional stabilization control problem. Then a state transformation is employed to deal with the time‐varying nonlinearities. By choosing an appropriate time‐varying parameter and coupling strengths, exponential consensus and tracking of second‐order nonlinear multi‐agent systems can be achieved. Finally, a simulation is given to illustrate the effectiveness of the proposed consensus and tracking protocols. Copyright © 2017 John Wiley & Sons, Ltd.     

Finite‐horizon robust Kalman filtering for uncertain discrete time‐varying systems with state‐delay

A finite‐horizon robust estimator design approach is developed for a class of discrete time‐varying uncertain systems with state‐delay. It extends the Kalman filter to the case in which the considered system is subject to norm‐bounded uncertainties in both state and output matrices. The state and gain matrices of the designed filter are optimized to give a minimal upper bound such that the estimation error variance is guaranteed to lie within a certain bound for all admissible uncertainties. A simulation example is presented to show the effectiveness of the proposed approach by comparing to the traditional Kalman filtering method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Connectivity maintenance and distributed tracking for double‐integrator agents with bounded potential functions

In this paper, we develop a set of decentralized control laws with bounded potential functions. The basic control law is a combination of attractive, repulsive, and alignment forces, which can keep connectivity, avoid collision, synchronize all agents, and further track a constant moving leader. Furthermore, we investigate the distributed tracking problem with a varying‐velocity leader, where the acceleration of the leader can not be measured. Two cases are considered; the acceleration of the leader is bounded, and the acceleration function satisfies Lipschitz condition. In the first case, the relative velocities of neighbors are integrated and transmitted as a new variable to account for the uncertain time‐varying acceleration. In the second case, two distributed estimators are added for the leader's position and velocity. Finally, some simulations are presented to show the effectiveness of the proposed algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Guaranteed cost finite‐time control for semi‐Markov jump systems with event‐triggered scheme and quantization input

In this paper, the guaranteed cost finite‐time control for semi‐Markov jump systems with unknown transition rates is addressed. An event‐triggered scheme is constructed to automatically monitor the data transmission and the input quantization is involved to reduce the cost of control. Different from the existing general transition rates in the semi‐Markov jump systems, the upper and lower bounds of transition rates are not given in advance but obtained through the stability criteria. The stability criteria are established to verify the stochastic finite‐time boundedness of the closed‐loop event‐triggered system and estimate the performance index of the given cost function. A guaranteed cost optimal controller is also proposed to stabilize the considered system. Finally, the vertical take‐off and landing helicopter model is introduced to verify the effectiveness of the main algorithms.     

Uniform bounded input bounded output stability of fractional‐order delay nonlinear systems with input

The bounded input bounded output (BIBO) stability for a nonlinear Caputo fractional system with time‐varying bounded delay and nonlinear output is studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input bounded output stability criteria are derived. Also, explicit and independent on the initial time bounds of the output are provided. Uniform BIBO stability and uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system's dynamic response, and demonstrate the effectiveness of our theoretical results.     

Recursive state estimation for discrete‐time nonlinear systems with event‐triggered data transmission,norm‐bounded uncertainties and multiple missing measurements

In this paper, we consider the recursive state estimation problem for a class of discrete‐time nonlinear systems with event‐triggered data transmission, norm‐bounded uncertainties, and multiple missing measurements. The phenomenon of event‐triggered communication mechanism occurs only when the specified event‐triggering condition is violated, which leads to a reduction in the number of excessive signal transmissions in a network. A sequence of independent Bernoulli random variables is employed to model the multiple measurements missing in the transmission. The norm‐bounded uncertainties that could be considered as external disturbances which lie in a bounded set. The purpose of the addressed filtering problem is to obtain an optimal robust recursive filter in the minimum‐variance sense such that with the simultaneous presence of event‐triggered data transmission, norm‐bounded uncertainties, and multiple missing measurements; the filtering error is minimized at each sampling time. By solving two Riccati‐like difference equations, the filter gain is calculated recursively. Based on the stochastic analysis theory, it is proved that the estimation error is bounded under certain conditions. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

In this paper, distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays and general disturbances is investigated under directed topology by using sliding‐mode control technique. We consider that the information of dynamic leaders can be obtained by only a portion of the followers. Firstly, a nonsingular fast terminal sliding surface is selected to achieve the finite‐time convergence for the error variables. Then, a distributed finite‐time containment control algorithm is proposed where the neural network is utilized to approximate the model uncertainties and external disturbances of the systems. Furthermore, considering that error constraint method can improve the performance of the systems, a distributed finite‐time containment control algorithm is developed by transforming the error variable into another form. It is demonstrated that the containment errors are bounded in finite time by using Lyapunov theory, graph theory, and finite‐time stability theory. Numerical simulations are provided to show the effectiveness of the proposed methods.     

Adaptive finite‐time control for nonlinear teleoperation systems with asymmetric time‐varying delays

This paper addresses the adaptive finite‐time control problem of nonlinear teleoperation system in the presence of asymmetric time‐varying delays. To achieve the finite‐time position tracking, a novel adaptive finite‐time coordination algorithm based on subsystem decomposition is developed. By introducing a switching‐technique‐based error filtering into our design framework, the complete closed‐loop master (slave) teleoperation system is modeled as a special class of switched system, which is composed of two subsystems. To analyze such system, a finite‐time state‐independent input‐to‐output stability criterion is first developed for some normal switched nonlinear delayed systems. Then based on the classical Lyapunov–Krasovskii method, the stability of complete closed‐loop systems is obtained. It is shown that the proposed scheme can make the position errors converge into a deterministic domain in finite time when the robots continuously contact with human operator and/or the environment in the presence of asymmetric time‐varying delays. Finally, the simulation results are given to demonstrate the effectiveness. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive dynamic surface control of nonaffine nonlinear system with time‐varying state constraints

This paper investigates the problem of adaptive dynamic surface control for pure‐feedback time‐varying state constrained nonaffine nonlinear system. A continuous and semibounded condition is proposed of nonaffine function to ensure that the system can be controlled, and the invariant set is introduced for this mild condition. By employing the dynamic surface control technique, the “complexity explosion” problem caused by backstepping technique is averted in developed control method. Robust compensators are devised to weaken poor effect of disturbances and uncertainties. The time‐varying barrier Lyapunov functions are adopted to dispose the problem of time‐varying state constrains. Moreover, it is proved that the whole closed‐loop signals are bounded, the tracking error can converge to a small neighborhood of zero, and the system states are insured to maintain in the predefined compact sets. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed method.     

A robust constrained model predictive control scheme for norm‐bounded uncertain systems with partial state measurements

A robust model predictive control scheme for a class of constrained norm‐bounded uncertain discrete‐time linear systems is developed under the hypothesis that only partial state measurements are available for feedback. The proposed strategy involves a two‐phase procedure. Initialization phase is devoted to determining an admissible, though not optimal, linear memoryless controller capable to formally address the input rate constraint; then, during on‐line phase, predictive capabilities complement the designed controller by means of N steps free control actions in a receding horizon fashion. These additive control actions are obtained by solving semidefinite programming problems subject to linear matrix inequalities constraints. As computational burden grows linearly with the control horizon length, an example is developed to show the effectiveness of the proposed approach for realistic control problems: the design of a flight control law for a flexible unmanned over‐actuated aircraft, where the states of the flexibility dynamics are not measurable, is discussed, and a numerical implementation of the controller within a nonlinear simulation environment testifies the validity of the proposed approach and the possibility to implement the algorithm on an onboard computer.     

Finite‐horizon fault estimation under imperfect measurements and stochastic communication protocol: Dealing with finite‐time boundedness

In this paper, we analyze the finite‐horizon fault estimation issue for a kind of time‐varying nonlinear systems with imperfect measurement signals under the stochastic communication protocol (SCP). The imperfect measurements result from randomly occurring sensor nonlinearities obeying sensor‐wise Bernoulli distributions. The Markov‐chain‐driven SCP is introduced to regulate the signal transmission to alleviate the communication congestion. The aim of the considered issue is to propose the design algorithm of a group of time‐varying fault estimators such that the estimation error dynamics satisfies both the H_∞ and the finite‐time boundedness (FTB) performance requirements. First, sufficient conditions are set up to guarantee the existence of the satisfactory H_∞ FTB fault estimators through intensive stochastic analyses and matrix operations. Then, the gains of such fault estimators are explicitly parameterized by resorting to the solution to recursive linear matrix inequalities. Finally, the correctness of the devised fault estimation approach is demonstrated by a numerical example.     

Gain‐scheduled leader‐follower tracking control for interconnected parameter varying systems

This paper considers the gain‐scheduled leader‐follower tracking control problem for a parameter varying complex interconnected system with directed communication topology and uncertain norm‐bounded coupling between the agents. A gain‐scheduled consensus‐type control protocol is proposed and a sufficient condition is obtained, which guarantees a suboptimal bound on the system tracking performance under this protocol. An interpolation technique is used to obtain a protocol schedule, which is continuous in the scheduling parameter. The effectiveness of the proposed method is demonstrated using a simulation example. Copyright © 2015 John Wiley & Sons, Ltd.     

Asymptotic tracking control for constrained nonstrict‐feedback MIMO nonlinear systems via parameter compensations

This paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict‐feedback form. Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict‐feedback structure. In each step of the backstepping design, the symmetric barrier Lyapunov functions are designed to avoid the breach of the state constraints, and the issues of overparametrization and unknown control direction are settled via introducing two compensation functions and the property of Nussbaum function, respectively. Furthermore, an adaptive fuzzy asymptotic tracking control strategy is raised. Based on Lyapunov stability analysis, the developed control strategy can effectually ensure that all the system variables are bounded, and the tracking errors asymptotically converge to zero. Eventually, simulation results are supplied to verify the feasibility of the proposed scheme.