Discrete time sliding mode control with reduced switching – a new reaching law approach

In this paper, a novel reaching law for discrete‐time variable structure systems is proposed. It ensures that the representative point (state) of the controlled plant approaches the switching plane in finite time and then crosses it in every subsequent step. Moreover, the proposed reaching law ensures that for the nominal plant the absolute value of the sliding variable asymptotically decreases to zero, and for the perturbed plant, it converges to a smaller interval around zero than with the application of previously proposed reaching laws. The control method proposed in this paper guarantees asymptotic stability of the nominal system and uniform ultimate boundedness of the perturbed one. Furthermore, the method ensures that the sliding variable rate of change (i.e. the difference between its values at any two subsequent sampling instants) is bounded by design parameters, which do not depend on the system initial conditions. This is a highly desirable property, as it results in a priori specified, ‘almost’ constant convergence rate of the sliding variable when the system state is far off the switching plane and helps enforce state constraints in the system. Copyright © 2014 John Wiley & Sons, Ltd.     

Exponential synchronization of nonlinear multi‐agent systems with time delays and impulsive disturbances

The problem of cooperative synchronization of nonlinear multi‐agent systems with time delays is investigated in this paper. Compared with the existing works about synchronization (or consensus) of multi‐agent systems, the method in this paper provides a more general framework by considering nonlinear multi‐agent systems with time delays and impulsive disturbances. The model in this paper is sufficiently general to include a class of delayed chaotic systems. Based on the Lyapunov stability theory and algebraic graph theory, sufficient conditions are presented to guarantee the cooperative exponential synchronization for these multi‐agent delayed nonlinear systems. These conditions are expressed in terms of linear matrix inequalities, which can easily be checked by existing software tools. It is seen that the Lyapunov functions must be constructed based on the graph topology to prove synchronization. The well‐known master–slave (drive‐response) synchronization of two chaotic delayed systems is a special case of this paper, and therefore, the results in this paper are also useful for practical applications in secure communication. Simulation results verify the effectiveness of the proposed synchronization control algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

Integrated adaptive robust control for multilateral teleoperation systems under arbitrary time delays

With the increasing industrial requirements such as bigger size object, stable operation, and complex task, multilateral teleoperation systems extended from traditional bilateral teleoperation are widely developed. In this paper, the integrated control design is developed for multilateral teleoperation systems, where n master manipulators are operated by human to remotely control n slave manipulators cooperatively handling a target object. For the first time, the control objectives of multilateral teleoperation including stability, synchronization, transparency, and internal force distribution are clarified systematically. A novel communication architecture is proposed to cope with communication delays, where the estimated environmental parameters are transmitted from the slave side to the master, to replace the traditional environmental force measurement in the communication channel. A kind of nonlinear adaptive robust control technique is used to deal with nonlinearities, unknown parameters, and modeling uncertainties existing in the master, slave, and environmental dynamics, so that the excellent tracking performance is achieved in both master and slave sides. The coordinated motion/force control is designed in the slave side by the optimal internal force distribution among n slave manipulators, and the impedance control is designed in the master side to realize the target transparency behavior. In summary, the proposed control algorithm can achieve the guaranteed robust stability, the excellent synchronization and transparency performance, and the optimal internal force distribution simultaneously for multilateral teleoperation systems under arbitrary time delays and various modeling uncertainties. The simulation is carried out on a 2‐master/2‐slave teleoperation system, and the results show the effectiveness of the proposed control design. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Finite‐time asynchronous filtering for discrete‐time Markov jump systems over a lossy network

This paper is concerned with the problem of finite‐time asynchronous filtering for a class of discrete‐time Markov jump systems. The communication links between the system and filter are assumed to be unreliable, which lead to the simultaneous occurrences of packet dropouts, time delays, sensor nonlinearity and nonsynchronous modes. The objective is to design a filter that ensures not only the mean‐square stochastic finite‐time bounded but also a prescribed level of performance for the underlying error system over a lossy network. With the help of the Lyapunov–Krasovskii approach and stochastic analysis theory, sufficient conditions are established for the existence of an admissible filter. By using a novel simple matrix decoupling approach, a desired asynchronous filter can be constructed. Finally, a numerical example is presented and a pulse‐width‐modulation‐driven boost converter model is employed to demonstrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Time‐multiplexed tiled projection system with improved pixel and spatial resolution

We propose two methods to increase the pixel and spatial resolution of Digital Micromirror Devices (DMD)‐based projectors by utilizing the large bandwidth provided by their high pattern rates. By varying the intensity of the illumination for each binary pattern displayed on the DMD, the time required to display an 8‐bit grayscale image can be reduced by up to factor 32 compared to using constant illumination and binary pulse‐width modulation (BPWM). The high image rate projection is then spatially separated by either using a galvanometer scanner or sequentially illuminating the DMD from different directions, thus creating multiple independently addressable projections which are then tiled to form a larger, higher resolution image.     

Consensus of a class of second‐order nonlinear heterogeneous multi‐agent systems with uncertainty and communication delay

In this paper, a consensus problem is studied for a group of second‐order nonlinear heterogeneous agents with non‐uniform time delay in communication links and uncertainty in agent dynamics. We design a class of novel decentralized control protocols for the consensus problem whose solvability is converted into stability analysis of an associated closed‐loop system with uncertainty and time delay. Using an explicitly constructed Lyapunov functional, the stability conditions or the solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities apart from a small number of scalar parameters that appear nonlinearly. Furthermore, the linear matrix inequalities are theoretically verified to be solvable when the communication delay is sufficiently small. The effectiveness of the proposed control protocol is illustrated by numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive event‐triggered control for nonlinear discrete‐time systems

This paper focuses on the analysis and the design of event‐triggering scheme for discrete‐time systems. Both static event‐triggering scheme (SETS) and adaptive event‐triggering scheme (AETS) are presented for discrete‐time nonlinear and linear systems. What makes AETS different from SETS is that an auxiliary dynamic variable satisfying a certain difference equation is incorporated into the event‐triggering condition. The sufficient conditions of asymptotic stability of the closed‐loop event‐triggered control systems under both two triggering schemes are given. Especially, for the linear systems case, the minimum time between two consecutive control updates is discussed. Also, the quantitative relation among the system parameters, the preselected triggering parameters in AETS, and a quadratic performance index are established. Finally, the effectiveness and respective advantage of the proposed event‐triggering schemes are illustrated on a practical example. Copyright © 2016 John Wiley & Sons, Ltd.     

Two general integral inequalities and their applications to stability analysis for systems with time‐varying delay

Integral inequalities have been widely used in stability analysis for systems with time‐varying delay because they directly produce bounds for integral terms with respect to quadratic functions. This paper presents two general integral inequalities from which almost all of the existing integral inequalities can be obtained, such as Jensen inequality, the Wirtinger‐based inequality, the Bessel–Legendre inequality, the Wirtinger‐based double integral inequality, and the auxiliary function‐based integral inequalities. Based on orthogonal polynomials defined in different inner spaces, various concrete single/multiple integral inequalities are obtained. They can produce more accurate bounds with more orthogonal polynomials considered. To show the effectiveness of the new inequalities, their applications to stability analysis for systems with time‐varying delay are demonstrated with two numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

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.