Reliable sliding mode finite‐time control for discrete‐time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities

This paper focuses on the problem of finite‐time $H_{\infty }$ control for one family of discrete‐time uncertain singular Markovian jump systems with sensor fault and randomly occurring nonlinearities through a sliding mode approach. The failure of sensor is described as a general and practical continuous fault model. Nonlinear disturbance satisfies the Lipschitz condition and occurs in a probabilistic way. Firstly, based on the state estimator, the discrete‐time close‐loop error system can be constructed and sufficient criteria are provided to guarantee the augment system is sliding mode finite‐time boundedness and sliding mode $H_{\infty }$ finite‐time boundedness. The sliding mode control law is synthesized to guarantee the reachability of the sliding surface in a short time interval, and the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities through a decoupling technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

state estimation with fading measurements,randomly varying nonlinearities and probabilistic distributed delays

In this paper, the state estimation problem is investigated for a class of discrete‐time stochastic systems in simultaneous presence of three network‐induced phenomena, namely, fading measurements, randomly varying nonlinearities and probabilistic distributed delays. The channel fading is characterized by the ?th‐order Rice fading model whose coefficients are mutually independent random variables with given probability density functions. Two sequences of random variables obeying the Bernoulli distribution are utilized to govern the randomly varying nonlinearities and probabilistic distributed delays. The purpose of the problem addressed is to design an state estimator such that the dynamics of the estimation errors is stochastically stable and the prespecified disturbance rejection attenuation level is guaranteed. Through intensive stochastic analysis, sufficient conditions are established under which the addressed state estimation problem is recast as a convex optimization one that can be solved via the semi‐definite program method. Finally, a simulation example is provided to show the usefulness of the proposed state estimation scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive asymptotic stabilization of switched parametric strict‐feedback systems with switched control

This paper is concerned with the problem of adaptive stabilization for a class of switched linear‐parametric nonlinear systems under arbitrary switching. The traditional adaptive backstepping control is successfully extended to switched systems from nonswitched ones where the asymptotic regulation of system state is not destroyed due to rapid or abrupt changes of switching parameters. A new switched adaptive controller is designed by exploiting a common high‐order Lyapunov function with a σ‐modification mechanism, which can reflect sufficiently the changes of plant by designing different adaptive laws and control laws for different subsystems. An explicit formula for constructing a continuous and piecewise virtual control function is given to remove the restriction where some bound functions have to be constructed blindly by designers in the existing results, which may be somewhat too strict to be applied. A numerical example is provided to validate the proposed approach.     

Dynamic output‐feedback control for continuous‐time singular Markovian jump systems

This paper considers a dynamic output‐feedback control for continuous‐time singular Markovian jump systems, whereas the existing research studies in literature focused on state‐feedback or static output‐feedback control. While they have only provided the sufficient conditions, this paper successfully obtains the necessary and sufficient condition for the existence of the dynamic output‐feedback control. Furthermore, this condition is expressed with linear matrix inequalities by the so‐called replacement technique. Two numerical examples show the validity of the resulting control.     

Discrete‐time output feedback for Markov jump systems with uncertain transition probabilities

This article addresses the output feedback control for discrete‐time Markov jump linear systems. With fully known transition probability, sufficient conditions for an internal model based controller design are obtained. For the case where the transition probabilities are uncertain and belong to a convex polytope with known vertices, we provide a sufficient LMI condition that guarantees the norm of the closed‐loop system is below a prescribed level. That condition can be improved through an iterative procedure. Additionally, we are able to deal with the case of cluster availability of the Markov mode, provided that some system matrices do not vary within a given cluster, an assumption that is suitable to deal with packet dropout models for networked control systems. A numerical example shows the applicability of the design and compares it with previous results. Copyright © 2012 John Wiley & Sons, Ltd.     

New interpolation solution and application in system modeling and optimal control with prescribed distance to instability

We present a system theoretic interpretation of a two‐sided interpolation problem with a stable rational matrix U (interpolant) without constraints on its norm. It is known that all solutions U of that problem can be expressed as U = U _h+ U _p, where U _h ranges in the set of all solutions of the associated homogeneous problem, and U _p is a particular solution. We present a new solution for U _p and prove that it is actually the minimal ‐norm interpolant in the set of all interpolants. We apply these results in system modeling and in optimal control of one‐block plants, with a prescribed bound on the distance to instability of the closed‐loop system. The applications are illustrated by examples. Interesting connections to the augmented basic interpolation problem, to Nehari's problem, and to the stability of one‐block plants with multiple unstable invariant zeros are given. Copyright © 2015 John Wiley & Sons, Ltd.     

H∞ model predictive control for constrained discrete‐time piecewise affine systems

This paper investigates stability analysis for piecewise affine (PWA) systems and specifically contributes a new robust model predictive control strategy for PWA systems in the presence of constraints on the states and inputs and with l₂ or norm‐bounded disturbances. The proposed controller is based on piecewise quadratic Lyapunov functions. The problem of minimization of the cost function for model predictive control design is changed to minimization of the worst case of the cost function. Then, this objective is reduced to minimization of a supremum of the cost function subject to a terminal inequality by considering the induced l₂‐norm. Finally, the predictive controller design problem is turned into a linear matrix inequality feasibility exercise with constraints on the input signal and state variables. It is shown that the closed‐loop system is asymptotically stable with guaranteed robust performance. The validity of the proposed method is verified through 3 well‐known examples of PWA systems. Simulation results are provided to show good convergence properties along with capability of the proposed controller to reject disturbances.     

Weighted control with ‐stability constraint for switched positive linear systems

This paper is concerned with the problem of control with ‐stability constraint for a class of switched positive linear systems. The ‐stability means that all the poles of each subsystem of the resultant closed‐loop system belong to a prescribed disk in the complex plane. A sufficient condition is derived for the existence of a set of state‐feedback controllers, which guarantees that the closed‐loop system is not only positive and exponentially stable with each subsystem ‐stable but also has a weighted performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuous‐time and discrete‐time cases are considered, and all of the obtained conditions are formulated in terms of linear matrix inequalities, whose solution also yields the desired controller gains and the corresponding minimal average dwell time. Numerical examples are given to illustrate the effectiveness of the presented approach.Copyright © 2012 John Wiley & Sons, Ltd.     

Dissipativity‐based asynchronous control of discrete‐time Markov jump systems with mixed time delays

This paper addresses the problem of dissipativity‐based asynchronous control for a class of discrete‐time Markov jump systems. A unified framework to design a controller for discrete‐time Markov jump systems with mixed time delays is proposed, which is fairly general and can be reduced to a synchronous controller or a mode‐independent controller. Based on a stochastic Lyapunov function approach, which fully utilizes available information of the system mode and the controller, a sufficient condition is established to ensure the stochastic stability and strictly ( , , ) dissipative performance of the resulting closed‐loop system. Finally, the effectiveness and validity of the proposed method are illustrated with a simulation example.     

State and output feedback control of time‐delay switched linear systems

In this paper, we propose contributions on the stabilization and control of switched linear systems subject to time‐delays through the assignment of the switching law. As a first step, based on previous results related to switched linear systems with no time‐delays and exploiting the concept of piecewise quadratic Lyapunov–Krasovskii functionals, we solve the problem of finding suitable state‐dependent switching laws ensuring the prescribed control objectives. Secondly, we extend such results and present a strategy to construct an output feedback switching law, based on the available measurements made on the system. In both cases, the design of the control strategy is done by computing a feasible solution to a set of matrix inequalities associated to the modes of the switched linear system. Copyright © 2011 John Wiley & Sons, Ltd.     

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

This paper addresses the passivity‐based control problem for a class of time‐varying delay systems subject to nonlinear actuator faults and randomly occurring uncertainties via fault‐tolerant controller. More precisely, the uncertainties are described in terms of stochastic variables, which satisfies Bernoulli distribution, and the existence of actuator faults are assumed not only linear but also nonlinear, which is a more general one. The main objective of this paper is to design a state feedback‐reliable controller such that the resulting closed‐loop time‐delay system is stochastically stable under a prescribed mixed and passivity performance level γ>0 in the presence of all admissible uncertainties and actuator faults. Based on Lyapunov stability method and some integral inequality techniques, a new set of sufficient conditions is obtained in terms of linear matrix inequality (LMI) constraints to ensure the asymptotic stability of the considered system. Moreover, the control design parameters can be computed by solving a set of LMI constraints. Finally, two examples including a quarter‐car model are provided to show the efficiency and usefulness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

A mixed numerical–analytical stable pseudo‐inversion method aimed at attaining an almost exact tracking

This paper considers the problem of computing the input u(t) of an internally asymptotically stable, possibly non‐minimum phase, linear, continuous time system Σ yielding a very accurate tracking of a pre‐specified desired output trajectory . The main purpose of the new approach proposed here is to alleviate some limitations that inherent the classical methods developed in the framework of the preview‐based stable inversion, which represents an important reference context for this class of control problems. In particular, the new method allows one to deal with arbitrary and possibly uncertain initial conditions and does not require a pre‐actuation. The desired output to be exactly tracked in steady state is here assumed to belong to the set of polynomials, exponential, and sinusoidal time functions. The desired transient response is specified to obtain a fast and smooth transition toward the steady‐state trajectory , without under and/or overshoot in the case of a set point reset. The transient control input u_t(t) is a priori assumed to be given by a piecewise polynomial function. Once has been specified, this allows the computation of the unknown u_t(t) as the approximate least squares solution of the Fredholm's integral equation corresponding to the explicit formula of the output forced response. The steady‐state input u_s(t) is analytically computed exploiting the steady‐state output response expressions for inputs belonging to the same set of . Copyright © 2013 John Wiley & Sons, Ltd.     

Dual approaches to strictly positive real controller synthesis with a performance using linear matrix inequalities

The synthesis of controllers that minimize a performance index subject to a strictly positive real (SPR) constraint is considered. Two controller synthesis methods are presented that are then combined into an iterative algorithm. Each method synthesizes optimal SPR controllers by posing a convex optimization problem where constraints are enforced via linear matrix inequalities. Additionally, each method fixes the controller state‐feedback gain matrix and finds an observer gain matrix such that an upper bound on the closed‐loop ‐norm is minimized and the controller is SPR. The first method retools the standard ‐optimal control problem by using a common Lyapunov matrix variable to satisfy both the criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the performance and the SPR constraint by employing a completing the square method and an overbounding technique. Both synthesis methods are used within an iterative scheme to find optimal SPR controllers in a sequential manner. Comparison of our synthesis methods to existing methods in the literature is presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Decentralized weighted control for a class of large‐scale systems with multi‐modes

In this paper, the control synthesis problem for a class of large‐scale systems with multi‐modes that are called large‐scale switched systems is addressed. By introducing the concept of decentralized switching signal and the relevant decentralized average dwell time, the asymptotic stability and weighted ?₂ gain performance are investigated. It should be noted that the decentralized switching covers general switching cases for large‐scale switched systems, namely, it admits both time‐dependent switching signal and arbitrary switching signal blended in the decentralized switching. Then, on the basis of the analysis results, the decentralized weighted control scheme including state feedback controller gains and switching signals is studied. Several design algorithms are proposed to meet different controller design problems. Finally, numerical examples are provided to illustrate theoretical findings within this paper. Copyright © 2013 John Wiley & Sons, Ltd.     

Stabilization of stochastic coupled systems with Markovian switching via feedback control based on discrete‐time state observations

This study investigates the stabilization issue of stochastic coupled systems with Markovian switching via feedback control. A state feedback controller based on the discrete‐time observations is applied for the stabilization purpose. By making use of the graph theory and the Lyapunov method, we establish both Lyapunov‐ and coefficient‐type sufficient criteria to guarantee the stabilization in the sense of stability, and then, we further develop the mean‐square asymptotical stability. In particular, the upper bound of the duration between 2 consecutive state observations is well formulated. Applications to a concrete stabilization problem of stochastic coupled oscillators with Markovian switching and some numerical analyses are presented to illustrate and to demonstrate the easy verifiability, effectivity, and efficiency of our theoretical findings.     

Mixed control of hidden Markov jump systems

In this work, we study the mixed control for Markov jump linear systems with hidden Markov parameters. The hidden Markov process is denoted by , where the nonobservable component θ(k) represents the mode of operation of the system, whereas represents the observable component provided by a detector. The goal is to obtain design techniques for mixed control problems, with the controllers depending only on the estimate , for problems formulated in 3 different forms: (i) minimizing an upper bound on the norm subject to a given restriction on the norm; (ii) minimizing an upper bound on the norm, while limiting the norm; and (iii) minimizing a weighted combination of upper bounds of both the and norms. We propose also new conditions for synthesizing robust controllers under parametric uncertainty in the detector probabilities and in the transition probabilities. The so‐called cluster case for the mixed control problem is also analyzed under the detector approach. The results are illustrated by means of 2 numerical examples.     

A novel three‐dimensional guidance law implementation using only line‐of‐sight azimuths

A novel three‐dimensional guidance law using only line‐of‐sight azimuths based on input‐to‐state stability and robust nonlinear observer is proposed for interception of maneuvering targets. The proposed guidance law does not need any prior information of unknown bounded target maneuvers and uncertainties. Since in practice the line‐of‐sight rate is difficult for a pursuer to measure accurately, a nonlinear robust observer is introduced to estimate it. A three‐dimensional guidance law with bearing only measurement is obtained for interception of maneuvering targets. The presented algorithm is tested using computer simulations against a maneuvering target. Copyright © 2014 John Wiley & Sons, Ltd.     

H∞‐output regulation of linear heterogeneous multiagent systems over switching graphs

In this paper, we analyze H_∞‐output regulation of linear heterogeneous multiagent systems. The agents are subject to modeled and unmodeled disturbances and communicate over a switching graph. We derive a sufficient condition that guarantees H_∞ output regulation for the mentioned setup. This sufficient condition places requirements on both the single‐agent systems and the switching graph. The requirement on the single‐agent systems is an H_∞‐criterion that should be satisfied by a proper design of the controller. Meanwhile, the switching graph needs to be maximally connected. Moreover, we derive an upper bound for the overall ‐gain of the output synchronization error with respect to the unmodeled disturbances over a fixed communication graph. We illustrate our technical developments by a simulation example.     

Distributed filtering in sensor networks with randomly occurring saturations and successive packet dropouts

This paper is concerned with the distributed filtering problem for a class of nonlinear systems with randomly occurring sensor saturations (ROSS) and successive packet dropouts in sensor networks. The issue of ROSS is brought up to account for the random nature of sensor saturations in a networked environment of sensors, and accordingly, a novel sensor model is proposed to describe both the ROSS and successive packet dropouts within a unified framework. Two sets of Bernoulli distributed white sequences are introduced to govern the random occurrences of the sensor saturations and successive packet dropouts. Through available output measurements from not only the individual sensor but also its neighboring sensors, a sufficient condition is established for the desired distributed filter to ensure that the filtering dynamics is exponentially mean‐square stable and the prescribed performance constraint is satisfied. The solution of the distributed filter gains is characterized by solving an auxiliary convex optimization problem. Finally, a simulation example is provided to show the effectiveness of the proposed filtering scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive dynamic surface control for pure‐feedback systems

This paper proposes a novel dynamic surface control algorithm for a class of uncertain nonlinear systems in completely non‐affine pure‐feedback form. Instead of using the mean value theorem, we construct an affine variable at each design step, and then neural network is employed to deduce a virtual control signal or an actual control signal. As a result, the unknown control directions and singularity problem raised by the mean value theorem is circumvented. The proposed scheme is able to overcome the explosion of complexity inherent in backstepping control and guarantee the tracking performance by introducing an initialization technique based on a surface error modification. Simulation results are presented to demonstrate the efficiency of the proposed scheme. Copyright © 2011 John Wiley & Sons, Ltd.