Robust sliding mode control of general time-varying delay stochastic systems with structural uncertainties

This paper presents a new robust sliding mode control （SMC） method with well-developed theoretical proof for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise （Wiener process）. The key features of the proposed method are to apply singular value decomposition （SVD） to all structural uncertainties and to introduce adjustable parameters for control design along with the SMC method. It leads to a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems via linear matrix inequality （LMI） forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1. Furthermore, it is theoretically proved that the proposed method with the SVD and adjustable parameters is less conservatism than the method without the SVD. The paper is mainly to provide all strict theoretical proofs for the method and results.     

Optimal linear estimators for systems with random measurement delays

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible the largest delay is bounded. Based on this new model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. A simulation example shows the effectiveness of the proposed algorithms.     

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.     

Max-plus-linear model-based predictive control for constrained hybrid systems：linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-linear （MPL） systems is obtained. And then, model predictive control （MPC） framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem （ELCP） were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling （MMPS） functions （using the operations maximization, minimization, addition and scalar multiplication） with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.     

具有干扰输入的不确定奇异系统的有限时间控制器设计

The concept of finite-time stability for linear singular system isinduced in this paper. Finite-time control problem is considered for linear singular systems with time-varying parametricuncertainties and exogenous disturbances. The disturbance satisfies a dynamical system with parametric uncertainties. Asufficient condition is presented for robust finite-ime stabilization via state feedback. The condition is translated to a feasibility problem involving restricted linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, an example is given to show the validity of the results.     

Adaptive control of linear multivariable systems with high frequency gain matrix hurwitz

A new adaptive control scheme is proposed for multivariable model reference adaptive control （MRAC） systems based on the nonlinear backstepplng approach with vector form. The assumption on a priori knowledge of the high frequency gain matrix in existing results is relaxed and the new required condition for the high frequency gain matrix can be easily checked for certain plants so that the proposed method is widely applicable. This control scheme guarantees the global stability of the closed-loop systems and the tracking error can be arbitrary small. The simulation result for an application example shows the validity of the proposed nonlinear adaptive scheme.     

Sliding mode control of uncertain systems with distributed time-delay： parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.     

Shaping of Output PDF Based on the Rational Square-root B-spline Model

This paper presents a new method for the modeling and control of the output probability density functions (PDFs) of linear stochastic systems.At first,a new PDF approximation method, namely the rational square-root B-spline model is proposed and the innovative concept of pseudo- weights is introduced.The new model is then compared with the existing B-spline models in terms of feasible domains.Next,a controller is developed to realize the output PDF tracking performance. An alternative minimal entropy control strategy is also provided for the case that no target PDF is available.Finally,illustrative examples indicate the effectiveness of the proposed algorithms.     

基于有理平方根B样条模型的概率密度函数形状控制

This paper presents a new method for the modeling and control of the output probability density functions (PDFs) of linear stochastic systems. At first, a new PDF approximation method, namely the rational square-root B-spline model is proposed and the innovative concept of pseudoweights is introduced. The new model is then compared with the existing B-spline models in terms of feasible domains. Next, a controller is developed to realize the output PDF tracking performance. An alternative minimal entropy control strategy is also provided for the case that no target PDF is available. Finally, illustrative examples indicate the effectiveness of the proposed algorithms.     

LMI-based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.     

New approach to stochastic stability and controller design for networked control systems

This paper addresses the random time-delays and packet losses issues of networked control systems (NCS) within the framework of jump linear systems with mode-dependent time-delays.A new delay-dependent condition on the stochastic stability is proposed by a new stochastic Lyapunov-Krasovskii functional.The condition is formulated as a set of coupled linear matrix inequalities (LMIs).As an example to verify the proposed method,an inverted-pendulum system with network is considered.The simulation results demonstrate the effectiveness of the method.     

A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances

This paper is concerned with the state feedback control problem for a class of discrete-time stochastic systems involving sector nonlinearities and mixed time-delays. The mixed time-delays comprise both discrete and distributed delays, and the sector nonlinearities appear in the system states and all delayed states. The distributed time-delays in the discrete-time domain are first defined and then a special matrix inequality is developed to handle the distributed time-delays within an algebraic framework. An effective linear matrix inequality (LMI) approach is proposed to design the state feedback controllers such that, for all admissible nonlinearities and time-delays, the overall closed-loop system is asymptotically stable in the mean square sense. Sufficient conditions are established for the nonlinear stochastic time-delay systems to be asymptotically stable in the mean square sense, and then the explicit expression of the desired controller gains is derived. A numerical example is provided to show the usefulness and effectiveness of the proposed design method.     

多时滞Lurie控制系统的时滞相关鲁棒稳定性

时滞Lurie控制系统的稳定性条件与Lyapunov函数的选取有关.本文对多时滞Lurie控制系统进行了变换,然后选择一个适当的Lyapunov函数,利用Lyapunov稳定性方法并结合Moon引理,得到了多时滞Lurie控制系统的时滞相关鲁棒稳定性判别条件,该条件是以线性矩阵不等式(LMI)给出的,可用Matlab求解.最后用一个算例验证了所得方法的有效性.     

MISO 系统基于正交匹配追踪算法的参数与时滞联合估计

在有限采样情况下, 研究具有时滞的多输入单输出受控自回归系统的参数辨识和时滞估计问题. 当采样次数少于未知变量数时, 描述系统的方程组是欠定的, 对其目标函数求解是NP-hard 问题, 传统方法无法有效辨识出系统参数. 受压缩感知理论的启发, 基于参数向量所具有的稀疏特性, 提出一种新的阈值正交匹配追踪算法辨识系统的参数和时滞. 仿真实验表明, 所提出的算法能在少量采样时有效地辨识系统参数、估计未知时滞, 同时验证了算法的有效性.

     

Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities

This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality–based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired controller gains is derived. An illustrative example is provided to show the usefulness and effectiveness of the proposed method.     

Singular linear-quadratic optimal control problem for a class of discrete singular systems with multiple time-delays

The singular linear-quadratic optimal control problem for a class of discrete-time linear singular systems with multiple time-delays is investigated. The equivalent relationship between this problem and the non-singular linear-quadratic problem for standard state-space discrete-time linear systems without time-delay is derived, and the necessary and sufficient condition guaranteeing this equivalent relationship is also given. The optimal control is synthesized as state feedback, and the closed-loop system is regular, impulse-free and without time-delay. An example is given to show the validity of the proposed method.     

Fault detection for a class of nonlinear stochastic systems with Markovian switching and mixed time-delays

This article is concerned with the fault detection (FD) problem for a class of nonlinear stochastic systems with Markovian switching and mixed time-delays. The stochastic system under consideration contains discrete and distributed mode-dependent delays, nonlinearities as well as Markovian switching. Considering a new sensor fault model, which can express the failures of the loss of effectiveness and the outage, a novel FD scheme is proposed such that it is valid for this class of sensor faults. In addition, delay-dependent conditions, which include some existing results, that capture the sensitivity performance and attenuation performance are derived. Then the FD filter gains are characterised in terms of the solutions to a convex optimisation problem. Finally, an aircraft application is given to demonstrate the effectiveness of the proposed method.     

网络控制系统稳定性的图理论

针对具有有界时延和数据包丢失的网络控制系统,提出了一种新的稳定性判据.基于Lyapunov方法和图论理论,给出非线性离散和连续刚络控制系统渐近稳定的充分条件,获得保持这两类系统稳定的最大允许时延界.得到控制器设计方法.并且,利用区间矩阵的谱特征.给出网络控制系统区间稳定的充分条件.设计算法,获得比例积分反馈控制器增益.算例表明所提方法的有效性.     

高速率通信网络下时变系统的有限时域H∞控制

针对高速率通信网络和Round-Robin（RR）协议影响下网络化时变系统的有限时域[H∞]控制问题，考虑到系统中存在乘性噪声、随机时滞和量化效应，提出了一种基于观测器的有限时域[H∞]控制器的设计方法。利用李雅普诺夫稳定性理论和线性矩阵不等式（Linear Matrix Inequality，LMI）技术得到有限时域[H∞]控制器存在的充分条件。基于锥补线性化（Cone Complementarity Linearization，CCL）方法通过求解一组递归矩阵不等式得到观测器和控制器参数。所设计的控制器保证闭环网络化时变系统在给定的时域内稳定，且满足预定的[H∞]性能指标。数值仿真验证了所提方法的有效性。     

Fault detection for discrete piecewise linear systems with infinite distributed time-delays

In this paper, the fault detection problem is investigated for a class of discrete-time piecewise linear systems with external disturbances and infinite distributed time-delays. As a modelling framework, piecewise linear system often arise when piecewise linear components are encountered, such as dead-zone, saturation, relays and hysteresis. The time-delays are assumed to be infinitely distributed in the discrete-time domain. The aim of this paper is to detect the possible faults and to estimate the system state. For this purpose, firstly, stability analysis is given based on a piecewise smooth Lyapunov function. Afterward, an appropriate approach of fault detection and filter design problem is provided to achieve a satisfactory balance between the disturbances attenuation level γ and the sensitivity to the fault for piecewise linear systems. As a consequence, a sufficient condition is obtained in terms of the linear matrix inequalities such that, for all admissible infinite distributed time-delays and external disturbances, the system is guaranteed to be asymptotically stable and the residual is guaranteed to satisfy H_∞ filtering performance and fault detection performance. At last, a simulation example is provided to demonstrate the applicability and effectiveness of the fault detection filtering scheme proposed in this paper.