Stability analysis of discrete-time cyclic switched systems under improved cyclic switching regularity

The stability issue of discrete-time switched systems governed by cyclic switching laws is discussed in this paper. By establishing inverse-timer-based multiple Lyapunov functions (ITBMLFs), which are less conservative than traditional MLFs, limitations of the existing findings on discrete-time cyclic switched systems (DTCSSs) are well relaxed. Furthermore, from the perspective of computational complexity adjustment, the proposed ITBMLFs are confirmed to be more flexible than the previous ones, which is especially meaningful for the DTCSSs consisting of a large number of subsystems. Based on the cycle-dependent average dwell time (CD-ADT) concept and the ITBMLF approach, newly enhanced stability conditions are launched for DTCSSs where subsystems can be entirely or partially stable, or even completely unstable. Moreover, robust stability of DTCSSs can be achieved when norm-bounded and time-varying parameter uncertainties (NBTVPUs) are taken into account. Finally, the effectiveness and superiority of the proposed technologies are expounded through numerical examples.     

New stability conditions for discrete-time switched positive linear time-varying systems

In this note, we will devote to investigate the stability of discrete-time switched positive linear time-varying systems (PLTVSs). Firstly, a new asymptotic stability criterion of discrete-time PLTVSs is obtained by using time-varying copositive Lyapunov functions (TVCLFs) and this criterion is then extended to the switched case based on the multiple TVCLFs. Furthermore, the sufficient conditions are derived for stability of discrete-time switched PLTVSs with stable subsystems by means of function-dependent average dwell time and function-dependent minimum dwell time. In addition, the stability sufficient conditions are drawn for the switched PLTVSs which contain unstable subsystems. It is worth noting that the difference of TVCLFs and multiple TVCLFs are both relaxed to indefinite in our work. The theoretical results obtained are verified by two numerical examples.     

Observer-based quantized control for discrete-time switched systems with infinitely distributed delay

This paper studies the globally almost surely exponential stabilization of discrete-time switched systems (DSSs) with infinitely distributed delay. On account of the limitation of communication resources in the actual environment, a novel class of observer-based quantized control scheme is designed that incorporates the quantization of three kinds of signals: the measurement output, the state of observer, and the measurement output of observer. By employing S-procedure and some matrix inequality techniques, an algorithm is given to design the controller parameters. To reduce the conservativeness of the obtained results, new multiple Lyapunov–Krasovskii functionals (LKFs) with negative terms are proposed to deal with the infinitely distributed delay and mode-dependent average dwell time (MDADT) switching based on transition probability (TP) is introduced to study the stabilization of DSSs with both stable and unstable modes. It is worth highlighting that the improved stabilization conditions for DSSs can release the restriction on the length of dwell time (DT) of stable and unstable subsystems. Finally, a simulation example is presented to demonstrate the validity of the proposed method.     

Design of optimal PID controller for multivariable time-varying delay discrete-time systems using non-monotonic Lyapunov-Krasovskii approach

This paper is concerned with stability analysis and stabilization of time-varying delay discrete-time systems in Lyapunov-Krasovskii stability analysis framework. In this regard, a less conservative approach is introduced based on non-monotonic Lyapunov-Krasovskii (NMLK) technique. The proposed method derives time-varying delay dependent stability conditions based on Lyapunov-Krasovskii functional (LKF), which are in the form of linear matrix inequalities (LMI). Also, a PID controller designing algorithm is extracted based on obtained NMLK stability condition. The stability of the closed loop system is guaranteed using the designed controller. Another property that is important along with the stability, is the optimality of the controller. Thus, an optimal PID designing technique is introduced in this article. The proposed method can be used to design optimal PID controller for unstable multi-input multi-output time-varying delay discrete-time systems. The proposed stability and stabilization conditions are less conservative due to the use of non-monotonic decreasing technique. The novelty of the paper comes from the consideration of non-monotonic approach for stability analysis of time-varying delay discrete-time systems and using obtained stability conditions for designing PID controller. Numerical examples and simulations are given to evaluate the theoretical results and illustrate its effectiveness compared to the existing methods.     

Formation consensus for discrete-time heterogeneous multi-agent systems with link failures and actuator/sensor faults

In this paper, a distributed control protocol is presented for discrete-time heterogeneous multi-agent systems in order to achieve formation consensus against link failures and actuator/sensor faults under fixed and switching topologies. A model equivalent method is proposed to deal with the heterogeneous system consists of arbitrary order systems with different parameters. Based on graph theory and Lyapunov theory, stability conditions to solve formation consensus problem are developed for the underlying heterogeneous systems with communication link failures. In order to tolerate actuator/sensor faults, a distributed adaptive controller is proposed based on fault compensation. The desired control is designed by linear matrix inequality approach together with cone complementarity linearisation algorithm. After applying the new control scheme to heterogeneous systems under the directed topologies with link failures and faults, the resulting closed-loop heterogeneous system is validated to be stable. The effectiveness of the new formation consensus control strategy and its robustness are verified by simulations.     

Hybrid control strategy for positive switched delay systems with unstable modes

In this paper, the problem of hybrid control strategy (HCS) for time-varying delay positive switched linear systems (PSLS) with unstable modes is studied. Firstly, the HCS, which includes minimum switching strategy and discretized state feedback controller, is applied to PSLS with time-varying delay for the first time. Secondly, by using the discretized multiple linear copositive Lyapunov-Krasovskii functional, a sufficient condition of globally uniformly asymptotically stable (GUAS) under the HCS is given. Finally, the HCS is extended to discrete-time positive switched time delay systems, and a delay independent stabilization condition is obtained in the discrete system. The effectiveness of the HCS is verified by two simulation examples.     

Subspace-based spectrum estimation in innovation models by mixed norm minimization

In this paper, identification of discrete-time power spectra of multi-input/multi-output (MIMO) systems in innovation models from output-only time-domain measurements is considered.A hybrid identification algorithm unifying mixed norm minimization with subspace estimation method is proposed. The proposed algorithm first estimates a covariance matrix from measurements. A significant dimension reduction is achieved in this step. Next, a regularized nuclear norm optimization problem is solved to enforce sparsity on the selection of most parsimonious model structure. A modification of the covariance estimates in the proposed algorithm generates yet another algorithm capable of handling data records with sequentially and intermittently missing values. The new and the modified identification algorithms are tested on a numerical study and a real-life application example concerned with the estimation of joint power spectral density (PSD) of parallel road tracks.     

Solving future equation systems using integral-type error function and using twice ZNN formula with disturbances suppressed

In this paper, for solving future equation systems, two novel discrete-time advanced zeroing neural network models are proposed, analyzed and investigated. First of all, by using integral-type error function and twice zeroing neural network (or termed, Zhang neural network) formula, as the preliminaries and bases of future problems solving, two continuous-time advanced zeroing neural network models are presented for solving continuous time-variant equation systems. Secondly, a one-step-ahead numerical differentiation rule termed 5-instant discretization formula is presented for the first-order derivative approximation with higher computational precision. By exploiting the presented 5-instant discretization formula to discretize the continuous-time advanced zeroing neural network models, two novel discrete-time advanced zeroing neural network models are proposed. Theoretical analyses on the convergence and precision of the discrete-time advanced zeroing neural network models are proposed. In addition, in the presence of disturbance, the proposed discrete-time advanced zeroing neural network models still possess excellent performance. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed discrete-time advanced zeroing neural network models for solving the future equation systems.     

Fractional-order partial pole assignment for time-delay systems based on resonance and time response criteria analysis

In this paper, a novel fractional-order partial pole assignment (FPPA) control algorithm is proposed for systems with time-delay. The FPPA control algorithm is essentially an extension of the original pole assignment, which could change undesired pole locations into desired pole locations. The presented control scheme can be used on open loop poorly damped or unstable systems, which is superior to most other time-delay compensation schemes. The discussion on choosing desirable pole locations is presented based on stability and resonance conditions in the frequency domain. The controlled system is also studied in the time domain based on different transient performance indicators, namely overshoot, settling time, and rising time. In addition, the parameters of the proposed FPPA control algorithm are tunable, thus the control scheme can be used to satisfy different control requirements. Simulation results of stable and unstable fractional-order plants with time-delay are shown to verify the effectiveness and practicability of the FPPA control algorithm.     

Stochastic fault tolerant control of networked control systems

A problem of stabilization about uncertain networked control systems (NCSs) with random but bounded delays is discussed in this paper. By using augmented state-space method, this class of problems can be modeled as discrete-time jump linear systems governed by finite-state Markov chains. A new switched model based on probability is proposed to research problems of reliable control when actuators become ageing or partially disabled. Using improved V-K iteration algorithm, a class of reliable controllers are designed to make systems asymptotically mean square stable under several stochastic disturbances such as random time-delay and stochastic actuator failure and the maximal redundancy degree is given through this method.     

Fault detection for discrete-time systems with randomly occurring nonlinearity and data missing: A quadrotor vehicle example

This paper concerns the fault detection (FD) problem for a class of discrete-time systems subject to data missing and randomly occurring nonlinearity modeled by two independent Bernoulli distributed random variables. We propose to design a set of fault detection filters, or residual generation systems, corresponding to each of the fault components, to guarantee that each subsystem is mean square stable and satisfies a prescribed disturbance attenuation level. Sufficient conditions are established in the form of linear matrix inequalities (LMIs). System faults can be effectively detected by generating the residues and comparing them with the dynamic fault thresholds. A quadrotor vehicle example with faults on angles and angular rates illustrates and verifies the effectiveness of the proposed algorithm.     

Non-fragile control of positive Markovian jump systems

This paper investigates the non-fragile control for positive Markovian jump systems both in continuous-time and discrete-time cases with actuator uncertainty. It is assumed that the coefficient matrices of the non-fragile controller is unknown and bounded. The state-feedback controller gain consists of nominal controller gain and gain perturbation. First, a set of state-feedback controllers for the considered system are designed by using a stochastic co-positive Lyapunov function integrated with linear programming approach. Under the designed controllers, the resulting closed-loop systems are positive and stochastically stable. Then, the proposed controller design approach is extended to discrete-time systems. Through comparisons, it is shown that existing results are special cases of the presented ones in the paper. Finally, two examples are given to illustrate the effectiveness of the proposed design.     

Discrete-time adaptive fuzzy speed regulation control for induction motors with input saturation via command filtering

A discrete-time adaptive fuzzy control method is introduced to achieve the speed regulation for induction motors (IMs) with input saturation via command filtering in this paper. First, the continuous model of IMs drive system is transformed into discrete-time form by using Euler formula. Then, the fuzzy logic systems are used to approximate the unknown nonlinear functions in the discrete-time drive system. In addition, the command filtering control method is introduced to overcome the “explosion of complexity” problem in the design process of traditional backstepping method. It is verified that all the closed-loop signals are bounded and the outputs can track the given reference signals well. Finally, simulation results illustrate the validity of the discrete-time control method.     

Stabilization for multi-group coupled models with dispersal by feedback control based on discrete-time observations in diffusion part

In this paper, we study the almost surely stabilization for a class of unstable multi-group coupled models with dispersal (MGMs, in short) by feedback control design based on discrete-time observations in diffusion part. Specifically, we show that the corresponding stochastically controlled system is almost surely exponentially stable when the stochastic MGM is almost surely exponentially stable within a duration of time. Finally, an example is given to illustrate the obtained theoretical results.     

State estimation for networked systems with Markovian communication constraints and multiple packet dropouts

In this paper, the state estimation problem for discrete-time networked systems with communication constraints and random packet dropouts is considered. The communication constraint is that, at each sampling instant, there is at most one of the various transmission nodes in the networked systems is allowed to access a shared communication channel, and then the received data are transmitted to a remote estimator to perform the estimation task. The channel accessing process of those transmission nodes is determined by a finite-state discrete-time Markov chain, and random packet dropouts in remote data transmission are modeled by a Bernoulli distributed white sequence. Using Bayes’ rule and some results developed in this study, two state estimation algorithms are proposed in the sense of minimum mean-square error. The first algorithm is optimal, which can exactly compute the minimum mean-square error estimate of system state. The second algorithm is a suboptimal algorithm obtained under a lot of Gaussian hypotheses. The proposed suboptimal algorithm is recursive and has time-independent complexity. Computer simulations are carried out to illustrate the performance of the proposed algorithms.     

Efficiency analysis of a filtering algorithm for discrete-time linear stochastic systems with polynomial measurements

A filtering algorithm is presented for discrete-time linear stochastic systems with polynomial measurements. The techniques to evaluate its efficiency are proposed. The algorithm performance is demonstrated by solving two navigation data processing problems, map-aided navigation using geophysical fields and single-beacon navigation for an autonomous underwater vehicle. The designed polynomial filter is compared to the extended Kalman filter, which is commonly used in practice. The simulation results reveal advantages of the polynomial algorithm. The obtained conclusions are reported.     

Decentralized neural identification and control for uncertain nonlinear systems: Application to planar robot

This paper presents a discrete-time decentralized neural identification and control for large-scale uncertain nonlinear systems, which is developed using recurrent high order neural networks (RHONN); the neural network learning algorithm uses an extended Kalman filter (EKF). The discrete-time control law proposed is based on block control and sliding mode techniques. The control algorithm is first simulated, and then implemented in real time for a two degree of freedom (DOF) planar robot.     

Stabilization of networked periodic piecewise linear systems under asynchronous switching with packet dropouts

In this paper, the networked stabilization of discrete-time periodic piecewise linear systems under transmission package dropouts is investigated. The transmission package dropouts result in the loss of control input and the asynchronous switching between the subsystems and the associated controllers. Before studying the networked control, the sufficient conditions of exponential stability and stabilization of discrete-time periodic piecewise linear systems are proposed via the constructed dwell-time dependent Lyapunov function with time-varying Lyapunov matrix at first. Then to tackle the bounded time-varying packet dropouts issue of switching signal in the networked control, a continuous unified time-varying Lyapunov function is employed for both the synchronous and asynchronous subintervals of subsystems, the corresponding stabilization conditions are developed. The state-feedback stabilizing controller can be directly designed by solving linear matrix inequalities (LMIs) instead of iterative optimization used in continuous-time periodic piecewise linear systems. The effectiveness of the obtained theoretical results is illustrated by numerical examples.     

False data injection attacks on sensors against state estimation in cyber-physical systems

In this paper, the problem about the false data injection attacks on sensors to degrade the state estimation performance in cyber-physical systems(CPSs) is investigated. The attack strategies for unstable systems and stable ones are both designed. For unstable systems, based on the idea of zero dynamics, an unbounded attack strategy is proposed which can drive the state estimation error variations to infinity. The proposed method is more general than existing unbounded attack strategies since it relaxes the requirement for the initial value of the estimation error. For stable systems, it is difficult to bring unbounded impacts on the estimation error variations. Therefore, in this case, an attack strategy with adjustable attack performance which makes the estimation error variations track predesigned target values is proposed. Furthermore, a uniform attack strategy which aims to deteriorate state estimation for both stable systems and unstable ones is derived. Finally, simulations are provided to illustrate the effectiveness of the proposed attack strategies.     

Model-free algorithm for consensus of discrete-time multi-agent systems using reinforcement learning method

In this work, we investigate consensus issues of discrete-time (DT) multi-agent systems (MASs) with completely unknown dynamic by using reinforcement learning (RL) technique. Different from policy iteration (PI) based algorithms that require admissible initial control policies, this work proposes a value iteration (VI) based model-free algorithm for consensus of DTMASs with optimal performance and no requirement of admissible initial control policy. Firstly, in order to utilize RL method, the consensus problem is modeled as an optimal control problem of tracking error system for each agent. Then, we introduce a VI algorithm for consensus of DTMASs and give a novel convergence analysis for this algorithm, which does not require admissible initial control input. To implement the proposed VI algorithm to achieve consensus of DTMASs without information of dynamics, we construct actor-critic networks to online estimate the value functions and optimal control inputs in real time. At last, we give some simulation results to show the validity of the proposed algorithm.