非线性系统的鲁棒采样控制

研究在汽车转向控制中遇到的、具有输出约束的一类非线性不确定系统的鲁棒采样控制和鲁棒采样最优控制问题,结果表示为一些矩阵不等式.最后基于线性矩阵不等式,给出了一个迭代算法和算例.数值计算实例证明了该算法的有效性.     

非线性系统的鲁棒采样最优控制

采样系统控制作为一种数字控制的直接设计方法,近年来引起了广泛的重视,另一方面系统的时域约束在工业控制中是不可避免的。利用实用稳定性理论,研究了具有输出约束的一类非线性系统的鲁棒采样最优控制问题,结果表示为一些矩阵不等式,最后给了出了一个迭代算法。     

凸多面体不确定系统的符号稳定性分析

针对一类凸多面体描述的连续线性不确定系统研究其符号稳定性条件,从而从符号稳定的角度探索一种新的不确定系统鲁棒控制器设计方法.在矩阵符号稳定定义和必要条件的基础上,给出了矩阵集合符号稳定的定义和完整同源稳定符号型集合的概念,得到了凸多面体不确定系统符号稳定的充分必要条件.进一步分析了符号稳定凸多面体不确定系统的特征根分布与主对角线元素的关系,提出了基于符号稳定的不确定系统状态反馈镇定控制综合方法.相比于基于Lyapunov稳定性理论的不确定系统鲁棒控制方法,本文所提方法避免了求解线性矩阵不等式,并且更符合工程设计的习惯.通过一类三轴稳定卫星姿态控制问题的算例和仿真验证了所提方法的有效性.     

Robust Input Covariance Constraint Control for Uncertain Polytopic Systems

In this paper, the robust input covariance constraint (ICC) control problem with polytopic uncertainty is solved using convex optimization with linear matrix inequality (LMI) approach. The ICC control problem is an optimal control problem that optimizes the output performance subjected to multiple constraints on the input covariance matrices. This control problem has significant practical implications when hard constraints need to be satisfied on control actuators. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the robust ICC control problem for polytopic uncertain systems. Both continuous‐ and discrete‐time systems are considered. Parameter‐dependent and independent Lyapunov functions have been used for robust ICC controller synthesis. Numerical design examples are presented to illustrate the effectiveness of the proposed approach.     

Robust Stability and Stabilization of Positive Interval Systems Subject to Actuator Saturation

This paper addresses the stabilization problem for a class of uncertain positive linear systems (PLSs) in the presence of saturating actuators. The objective is to obtain sufficient conditions for the robust stability of PLSs and to design robust state feedback control laws such that the closed‐loop uncertain system is asymptotically stable and positive at the origin with a large domain of attraction. Several sufficient conditions for robust stabilization and positivity are derived via the Lyapunov function approach and convex analysis method for both the discrete‐time and the continuous‐time cases, respectively. The state feedback controller design and the estimation of the domain of attraction are presented by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints. A numerical example is given to show the effectiveness of the proposed methods.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

不确定时滞线性系统的采样控制

采样控制作为一种数字控制的直接设计方法,近年来引起了广泛的重视,目前采样控制不易处理模型的不确定性和时滞,本语文给不确定时滞系统的采样控制算法,结果表示为一些矩阵不等式,并给中用ＬＭＩ求解的迭代算法。     

Robustness of linear uncertain sampled‐data control systems with generalized sampled‐data hold functions

This paper investigates robust stability of linear time‐invariant (LTI) uncertain sampled‐data control systems with generalized sampled‐data hold functions (GSHFs). A new sufficient condition for robust stability of such systems is developed. Unlike that of most of the previous works, it directly uses the data of the continuous‐time plant and therefore it is less conservative. The condition is expressed in terms of the spectral radius of a certain matrix and is shown to be a unimodal function of a free parameter. This property enabled us to use standard one‐dimensional optimization algorithm to perform the proposed test. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust one-step receding horizon control for constrained systems

This paper proposes a robust receding horizon control scheme for discrete-time uncertain linear systems with input and state constraints. The control scheme is based on the minimization of the worst-case one-step finite horizon cost with a finite terminal weighting matrix. It is shown that the proposed receding horizon control robustly asymptotically stabilizes uncertain constrained systems under some matrix inequality conditions on the terminal weighting matrices. This robust receding horizon control scheme has a larger feasible initial-state set and a more general structure than existing robust receding horizon controls for uncertain constrained systems under the same design parameters. The proposed controller is obtained using semidefinite programming. Copyright © 1999 John Wiley & Sons, Ltd.     

线性不确定时滞系统的可靠保成本控制

讨论了执行器故障下,线性不确定时滞系统的可靠保成本控制问题。提出了更实际、更一般的执行器故障模型;给出了以LMI表达的故障系统渐近隐定以及成本函数有上界的充分条件;进一步对执行器故障情况下的成本函数上界进行了优化,该优化是通过一个LMI组的最小化问题来实现的,对扰动输入具有一定的衰减性能。仿真实例验证了所得结果的有效性。     

Sequential LMI approach for the design of a BMI‐based robust observer state feedback controller with nonlinear uncertainties

This paper aims at developing a robust observer–based estimated state feedback control design method for an uncertain dynamical system that can be represented as a linear time‐invariant system connected with an integral quadratic constraint–type nonlinear uncertainty. Traditionally, in existing design methodologies, a convex semidefinite constraint is obtained at the cost of conservatism and unrealistic assumptions. This paper avoids such assumptions and formulates, the design of the robust observer state feedback controller as the feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP‐hard problem in general. The applicability of a linearization method, such as the variable change method and the congruence transformation, depends on the specific structure of the problem at hand and cannot be generalized. This paper transforms the feasibility analysis of the BMI constraint into an eigenvalue problem and applies the convex‐concave–based sequential linear matrix inequality optimization method to search for a feasible solution. Furthermore, an augmentation of the sequential linear matrix inequality algorithm to improve its numerical stability is presented. In the application part, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real‐world estimated state feedback control design problem and the necessity of the augmentation for numerical stability.     

Operator‐based robust control for nonlinear plants with uncertain non‐symmetric backlash

This paper presents an operator‐based robust nonlinear control method for nonlinear plants with uncertain non‐symmetric backlash. The control design is achieved by introducing operator‐based robust right coprime factorization. In more detail, using an operator‐theoretic approach, the uncertain non‐symmetric backlash is described as a generalized Lipschitz operator and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new robust condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the uncertain backlash. As a result, based on the proposed robust condition, a stabilized plant is obtained. For eliminating the effect from the parasitic term to ensure the output tracking performance, a nonlinear tracking controller is designed. Simulation results are presented to validate the effectiveness of the proposed control design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

不确定有损网络控制系统的鲁棒镇定

The data packet dropouts phenomenon is usually inevitable when information transmitted among communication networks. In this paper, the robust stabilization problem for uncertain networked control systems with data packet dropouts is studied. First, an uncertain discrete-time switching system model is presented to describe these networked control systems. The stability equivalence is then proved between this switching system and an uncertain impulsive difference system. Moreover, a sufficient condition is obtained for the asymptotical stability of the nonlinear impulsive difference system. From this condition the robust stabilization problem is dealt with for the uncertain impulsive system. Main results are given in linear matrix inequalities. Finally a numerical example is given to illustrate the theoretical results.     

Robust Stabilization of Uncertain Networked Control Systems with Data Packet Dropouts

The data packet dropouts phenomenon is usually inevitable when information transmit- ted among communication networks.In this paper,the robust stabilization problem for uncertain networked control systems with data packet dropouts is studied.First,an uncertain discrete-time switching system model is presented to describe these networked control systems.The stability equiv- alence is then proved between this switching system and an uncertain impulsive difference system. Moreover,a sufficient condition is obtained for the asymptotical stability of the nonlinear impulsive difference system.From this condition the robust stabilization problem is dealt with for the uncertain impulsive system.Main results are given in linear matrix inequalities.Finally a numerical example is given to illustrate the theoretical results.     

基于积分二次约束不确定时滞大系统的鲁棒容错控制

针对一类不确定时滞大系统,研究执行器或传感器失效情况下的鲁棒容错控制。通过运用积分二次约束、线性矩阵不等式及Lyapunov函数的新分析方法,得到无摄动时滞大系统具有鲁棒容错控制的时滞依赖稳定性判据。通过推导获得不确定时滞大系统的时滞依赖稳定性判据,设计鲁棒容错控制器。     

A robust continuous‐time fixed‐lag smoother for nonlinear uncertain systems

This paper presents a scheme for the design of a robust fixed‐lag smoother for a class of nonlinear uncertain systems. The proposed approach combines a nonlinear robust estimator with a stable fixed‐lag smoother, to improve the estimation error covariance. The robust fixed‐lag smoother is based on the use of integral quadratic constraints and minimax linear quadratic regulator estimation and control theory. The state estimator uses a copy of the system nonlinearity in the estimator and combines an approximate model of the delayed states to produce a smoother signal. Also in this work, a characterization of the delay approximation error is presented, and the corresponding integral quadratic constraint is included in the design, which gives a guaranteed bound on the performance cost function. In order to see the effectiveness of the method, it is applied to a quantum optical phase estimation problem. Results show a significant improvement in the error covariance of the estimator when compared with a robust nonlinear filter. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust sampled‐data control for Itô stochastic Markovian jump systems with state delay

In this paper, the problem of robust sampled‐data control for Itô stochastic Markovian jump systems (Itô SMJSs) with state delay is investigated. Using parameters‐dependent Lyapunov functionals and some stochastic equations, we give stochastic sufficient stability criteria for polytopic uncertain Itô SMJSs. As a corollary, stochastic sufficient stability criteria are given for nominal Itô SMJSs. For this two cases of Itô SMJSs, based on the obtained stochastic stability criteria, their time‐independent sampled‐data controllers are designed, respectively. Then, for designing a time‐dependent sampled‐data controller for Itô SMJSs, a parameters‐dependent time‐scheduled Lyapunov functional is developed. New stochastic sufficient stability criteria are obtained for polytopic uncertain Itô SMJSs and nominal Itô SMJSs. Furthermore, their time‐dependent sampled‐data controllers are designed, respectively. Lastly, a numerical example is provided to illustrate the effectiveness of the proposed method.     

A new integral inequality and its applications to robust control problems of uncertain nonlinear systems

In this paper, a new integral inequality is presented. By combining this integral inequality with adaptive approach, new design methods can be developed to synthesize some adaptive robust control schemes for a large class of uncertain nonlinear systems and to deal with well the unknown nonlinearities appearing in uncertain nonlinear control dynamical systems. As an application of the presented integral inequality to control theory, the robust stabilization problem is considered for a class of uncertain strict‐feedback nonlinear systems with both time‐delay and unknown dead‐zone input nonlinearities. It is shown that there are two main merits in the design method based on the integral inequality presented in this paper. The first one is that one need not estimate and know the unknown nonlinearities to synthesize some stabilizing control schemes. The second one is that the resulting feedback control schemes have rather simple structure.     

时延网络控制系统的模型预测控制

针对有输入约束的不确定时延网络控制系统,提出鲁棒模型预测控制方法;其中,将不确定时延建模为范数有界的输入矩阵的不确定性．给出了鲁棒性能指标的上界和系统渐近稳定的充分条件,通过在线求解LMI凸优化问题得到状态反馈控制律．仿真例子验证了该方法的有效性．     

不匹配不确定线性时滞系统的鲁棒自适应控制

对一类同时具有匹配不确定性及结构确定不匹配不确定性的不确定时滞系统进行鲁棒自适应控制。首先,采用李雅谱诺夫函数方法,结合基于线性矩阵不等式的鲁棒控制器设计方法和变结构控制方法,设计鲁棒控制器,保证闭环系统的二次渐近稳定。利用自适应参数估计方法,设计具有匹配不确定性范数界估计能力的鲁棒自适应控制器,保证闭环系统的一致终结有界。结合算例,进行控制器的设计和仿真研究,验证所提出的设计方法的有效性。