A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as ’large’ as possible. An example is provided to demonstrate the effectiveness of the new method.     

Further improvement of stability criterion and BRL for Markovian jump systems with interval time-varying delay

This paper deals with delay-dependent stochastic stability and bounded real lemma(BRL)for Markovian jump linear systems with interval time-varying delays.By constructing some new Lyapunov functionals and using the Jensen’s integral inequality method,the free weighting matrix method,the convex combination method and the delay decomposition approach integratedly,some less conservative delay-dependent stability criteria and BRL are established. Numerical examples are given to show the effectiveness of the proposed method.     

Reconstruction of measurements in state estimation strategy against deception attacks for cyber physical systems

Without the known state equation, a new state estimation strategy is designed to be against malicious attacks for cyber physical systems. Inspired by the idea of data reconstruction, the compressive sensing (CS) is applied to reconstruction of residual measurements after the detection and identification scheme based on the Markov graph of the system state, which increases the resilience of state estimation strategy against deception attacks. First, the observability analysis is introduced to decide the triggering time of the measurement reconstruction and the damage level from attacks. In particular, the dictionary learning is proposed to form the over completed dictionary by K singular value decomposition (K SVD), which is produced adaptively according to the characteristics of the measurement data. In addition, due to the irregularity of residual measurements, a sampling matrix is designed as the measurement matrix. Finally, the simulation experiments are performed on 6 bus power system. Results show that the reconstruction of measurements is completed well by the proposed reconstruction method, and the corresponding effects are better than reconstruction scheme based on the joint dictionary and the traditional Gauss or Bernoulli random matrix respectively. Especially, when only 29% available clean measurements are left, performance of the proposed strategy is still extraordinary, which reflects generality for five kinds of recovery algorithms.     

Security control of positive semi‑Markovian jump systems with actuator faults

Actuator faults usually cause security problem in practice. This paper is concerned with the security control of positive semi-Markovian jump systems with actuator faults. The considered systems are with mode transition-dependent sojourntime distributions, which may also lead to actuator faults. First, the time-varying and bounded transition rate that satisfies the mode transition-dependent sojourn-time distribution is considered. Then, a stochastic co-positive Lyapunov function is constructed. Using matrix decomposition technique, a set of state-feedback controllers for positive semi-Markovian jump systems with actuator faults are designed in terms of linear programming. Under the designed controllers, stochastic stabilization of the systems with actuator faults are achieved and the security of the systems can be guaranteed. Furthermore, the proposed results are extended to positive semi-Markovian jump systems with interval and polytopic uncertainties. By virtue of a segmentation technique of the transition rates, a less conservative security control design is also proposed. Finally, numerical examples are provided to demonstrate the validity of the presented results.     

Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.     

Robust H-infinity control for uncertain discrete-time Markovian jump systems with actuator saturation

The design of robust H-infinity controller for uncertain discrete-time Markovian jump systems with actuator saturation is addressed in this paper. The parameter uncertainties are assumed to be norm-bounded. Linear matrix inequality (LMI) conditions are proposed to design a set of controllers in order to satisfy the closed-loop local stability and closed-loop H-infinity performance. Using an LMI approach, a set of state feedback gains is constructed such that the set of admissible initial conditions is enlarged and formulated through solving an optimization problem. A numerical example is given to illustrate the effectiveness of the proposed methods.     

A unified approach to output synchronization of heterogeneous multi-agent systems via L2-gain design

In this paper, a unified design procedure is given for output synchronization of heterogeneous multi-agent systems (MAS) on communication graph topologies, using relative output measurements from neighbors. Three different control protocols, namely, full-state feedback, static output-feedback, and dynamic output-feedback, are designed for output synchronization. It is seen that a unified design procedure for heterogeneous MAS can be given by formulation and solution of a suitable local $\mathcal{L}{_2}$-gain design problem. Sufficient conditions are developed in terms of stabilizing the local agents'' dynamics, satisfying a certain small-gain criterion, and solving the output regulator equations. Local design procedures are presented for each agent to guarantee that these sufficient conditions are satisfied. The proposed control protocols require only one copy of the leader''s dynamics in the compensator, regardless of the dimensions of the outputs. This results in lower-dimensional compensators for systems with high-order outputs, compared to the $p$-copy internal model approach. All three proposed control protocols are verified using numerical simulations.     

Parametric estimation of interconnected nonlinear systems described by input-output mathematical models

In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems,which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.     

Markov跳变线性奇异摄动系统鲁棒H∞控制

In this paper, we study the robust control for uncertain Markov jump linear singularly perturbed systems (MJLSPS), whose transition probability matrix is unknown. An improved heuristic algorithm is proposed to solve the nonlinear matrix inequalities. The results of this paper can apply not only to standard, but also to nonstandard MJLSPS. Moreover, the proposed approach is independent of the perturbation parameter and therefore avoids the ill-conditioned numerical problems.     

Robust stabilization for nonholonomic systems with state delay and nonlinear drifts

This paper presents a control strategy for stabilization of the nonholonomic control systems with strongly nonlinear drifts and state delay.Applying a novel Lyapunov functional and backstepping recursive method,the design of robust nonlinear state feedback controllers is proposed,which can guarantee the stability of the closed-loop systems.Finally,a numerical example is provided to show the effectiveness of the method.     

State estimation for discrete-time Markov jump linear systems with multiplicative noises and delayed mode measurements

In this paper, the state estimation problem for discrete-time Markov jump linear systems affected by multiplicative noises is considered. The available measurements for the system under consideration have two components: the first is the model measurement and the second is the output measurement, where the model measurement is affected by a fixed amount of delay. Using Bayes' rule and some results obtained in this paper, a novel suboptimal state estimation algorithm is proposed in the sense of minimum mean-square error under a lot of Gaussian hypotheses. The proposed algorithm is recursive and does not increase computational and storage load with time. Computer simulations are carried out to evaluate the performance of the proposed algorithm.     

Almost sure estimation and synthesis of ultimate bounds for discrete-time Markov jump linear systems

This paper is concerned with the problems of almost sure ultimate bound estimation and controller design for Markov jump linear systems with bounded stochastic disturbances. By utilising a Lyapunov-based scheme proposed in this paper, an almost sure estimation of ellipsoidal ultimate bound (EUB) of the system is obtained through tractable matrix inequalities. On the basis of the estimation results, the problem of designing mode-dependent state feedback controllers that make the closed-loop system admit a prescribed ellipsoid as an EUB is considered. The obtained results on estimation and synthesis are then extended to the case of systems with deficient mode information. Finally, a practical example in DC motor devices is presented to demonstrate the applicability of the obtained results.     

Markov跳变系统的有限时间状态反馈镇定

讨论一类含有限能量未知扰动的线性Markov跳变系统的有限时间镇定问题.针对连续系统和离散系统两种情况,利用构造的Lyapunov-Krasovskii函数,并结合线性矩阵不等式方法,分别证明并给出了跳变系统有限时间镇定控制器有解的充分条件.采用该方法设计的镇定控制器可使连续系统和离散系统对所有满足条件的未知扰动是有限时问有界和有限时间镇定的.最后通过数值示例表明了该设计方法的有效性.     

Stabilization of Markov jump linear systems using quantized state feedback

This paper addresses the stabilization problem for single-input Markov jump linear systems via mode-dependent quantized state feedback. Given a measure of quantization coarseness, a mode-dependent logarithmic quantizer and a mode-dependent linear state feedback law can achieve optimal coarseness for mean square quadratic stabilization of a Markov jump linear system, similar to existing results for linear time-invariant systems. The sector bound approach is shown to be non-conservative in investigating the corresponding quantized state feedback problem, and then a method of optimal quantizer/controller design in terms of linear matrix inequalities is presented. Moreover, when the mode process is not observed by the controller and quantizer, a mode estimation algorithm obtained by maximizing a certain probability criterion is given. Finally, an application to networked control systems further demonstrates the usefulness of the results.     

Distributed multiple model estimation for jump Markov linear systems with missing measurements

This paper is concerned with distributed multiple model estimation for jump Markov linear systems with missing measurements over a sensor network. Two independent Markov chains are used to describe the switching of dynamic models and the missing of measurements, respectively. Under the assumption that each sensor can only communicate with its neighbours, a distributed filter is developed by applying the basic interacting multiple model (IMM) approach in the Bayesian estimation framework. To circumvent the difficulty of exponentially growing filters by exchanging local measurements between neighbouring sensors, the mode-conditioned estimates are exchanged instead of local measurements and the covariance intersection method is adopted to fuse mode-conditioned estimates. A multi-sensor manoeuvering target tracking example is provided to verify the effectiveness of the proposed filter.     

Adaptive control of linear Markov jump systems

Stabilization of linear Markov jump systems via adaptive control is considered in this paper. The switching law is assumed to be unobservable Markov process. A sufficient condition is obtained for the stochastic stabilizability based on common quadratic Lyapunov functions (QLFs). The constructive proof provides a method to construct a sampling adaptive stabilizer. An example is used to describe the design of adaptive control, which stabilizes the system.     

On almost sure stability of continuous-time Markov jump linear systems

In this paper, we study the almost sure stability of continuous-time jump linear systems with a finite-state Markov form process. A sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches. It is shown that, if the system is exponentially almost sure stable, there exists a finite m such that the criterion is satisfied. In order to evaluate the expected value appearing in the condition, an efficient Monte Carlo algorithm is worked out.     

Linear state estimation for Markov jump linear system with multi-channel observation delays and packet dropouts

This paper is to investigate the linear minimum mean square error estimation for Markovian jump linear system subject to unknown Markov chains, multi-channel mode and observation delays, and packet losses. The reorganisation method is employed to convert the delayed measurement system into an equivalent delay-free one and a new state variable is introduced, by which the original state estimation with transmission delays and data losses is transformed into the new state estimation for the reorganised delay-free system with jumping parameters and multiplicative noises. The new state estimation is derived via the innovation analysis method, and an analytical solution to the estimator is given in terms of a set of generalised Riccati difference equations based on a set of coupled Lyapunov equations. Then the original state estimation will be obtained via the jumping property. Finally, we show that the difference Riccati equations converge to a set of generalised algebraic Riccati equations under appropriate assumptions, which result in an optimal stationary filter.     

带有乘性过程噪声和模式观测时滞离散马氏跳线性系统的状态估计

研究受乘性过程噪声干扰的离散马氏跳线性系统状态估计问题. 系统可得到的观测包括两部分: 模式观测和输出观测, 其中模式观测受到固定时滞的影响. 利用贝叶斯定理及所得到的一些结果, 提出一种新颖的最小均方误差意义下次优状态估计算法. 该次优算法是回归的, 并且不随着时间增加而加重计算存储负荷. 通过计算机仿真来评估所提出次优算法的性能, 仿真结果验证了该算法的优越性.

     

Risk-sensitive filtering for jump Markov linear systems

In this paper, a risk-sensitive multiple-model filtering algorithm is derived using the reference probability methods. First, the approximation of the interacting multiple-model (IMM) algorithm is identified in the reference probability domain. Then, the same type of approximation is used to derive the finite-dimensional risk-sensitive filtering algorithm. The derived algorithm reduces to the IMM filter when the risk-sensitive parameter goes to zero and reduces to the risk-sensitive filter for linear Gauss-Markov systems when the number of models is unity. The algorithm performs better in a simulated uncertain parameter scenario than the IMM filter.