Robust stability analysis and stabilization for uncertain linear neutral delay systems

This paper considers the problem of robust stability analysis and robust stabilization for uncertain neutral delay systems. The system under consideration is subject to norm-bounded parameter uncertainty appearing in all the matrices of the state-space model. Both delay-dependent and -independent robust stability conditions are obtained in terms of linear matrix inequalities. Based on these, the corresponding conditions for the exsitence of robust stabilizing state feedback controllers are developed. When these conditions are feasible, the desired state feedback controller gain matrices can be obtained via convex optimization.     

Constrained control of uncertain nonhomogeneous Markovian jump systems

This paper addresses the problem of robust stabilization for uncertain systems subject to input saturation and nonhomogeneous Markovian jumps, where the uncertainties are assumed to be norm bounded and the transition probabilities are time‐varying and unknown. By expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the time‐varying transition probabilities inside a polytope, we establish conditions under which the closed‐loop system is asymptotically stable. On the basis of these conditions, the problem of designing the state feedback gains for achieving fast transience response with a guaranteed size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by numerical examples including the application to a DC motor speed control example. Copyright © 2017 John Wiley & Sons, Ltd.     

具有闭环极点和方差约束的不确定离散系统鲁棒控制

对一类具有范数有界不确定性的离散时间系统,研究了使得闭环系统的所有极点位于一给定圆盘,且稳定状态方差不超过给定上界的状态反馈鲁棒方差控制律设计问题,基于线性矩阵不等式的处理方法,导出了鲁棒方差控制律的存在条件,并用一组线性矩阵不等式的珂行解给出了鲁棒方差控制律的一个参数化表示,进而,通过建立和求解一个凸优化问题,给出了具有最泸控制能量的鲁棒方差控制律设计方法。     

变时滞不确定关联系统的分散鲁棒容错控制

针对一类不确定项具有数值界的变时滞不确定关联系统,运用线性矩阵不等式（LMI）方法对其分散鲁棒容错控制问题进行研究。首先提出以一组LMIs有解作为系统可分散鲁棒容错控制的充分条件,并给出了在此条件下的控制律,它对执行器发生故障时具有完整性;然后求解一个具有LMIs约束的凸优化问题,作为设计具有尽可能小反馈增益的分散鲁棒容错控制律的系统化方法,从而得到更符合实际的满意的分散容错控制律。     

饱和约束系统的鲁棒模型预测控制

针对饱和约束系统提出了一种鲁棒模型预测控制算法,分别考虑了多面体不确定性和结构反馈不确定性.考虑无穷时域的最坏二次性能指标,通过采用带有饱和特性的反馈控制结构,将控制律的求解转化为一个在线的线性矩阵不等式优化问题.初始时刻优化问题的可行性保证了闭环控制系统的鲁棒稳定性.最后的仿真结果说明了算法的优越性.     

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.     

Output feedback MPC with guaranteed robust stability

This paper focuses on the issues of robust stability of model predictive control (MPC). The control problem is formulated as linear matrix inequalities (LMI) optimization problem. A suboptimal solution for the output feedback control problem is proposed. The size of the resulting MP controller is reduced by using a suitable state-space representation of the process. Guaranteed stability conditions for the output feedback MPC are enforced via a Lyapunov type constraint. An iterative algorithm is developed resulting in a pair of coupled LMI optimization problems which provide a robustly stable output feedback gain. Model uncertainties are considered via a polytopic set of process models. The methodology is illustrated with the simulation of the control problem of two chemical processes. The results show that the proposed strategy eliminates the need to detune the MP controller improving the performance for most of the cases considered.     

基于线性矩阵不等式的分散鲁棒跟踪控制器设计

应用线性矩阵不等式（ＬＭＩ）方法研究不确定性关联大系统的分散鲁棒输出跟踪控制问题。系统中不确定项具有数值界,可不满足匹配条件。基于不确定基项的表达形式,给出了存在分散控制鲁棒跟踪控制器的ＬＭＩ条件。在此基础上,通过建立求解受ＬＭＩｓ约束的凸优化问题,提出了具有较小反馈增益ＬＭＩ设计方法,使受控系统渐近跟踪给定的参考输入。ＬＭＩ方法求解简单,最后用示例说明了该方法的应用。     

Output feedback receding horizon control of constrained systems

This paper considers output feedback control of linear discrete-time systems with convex state and input constraints which are subject to bounded state disturbances and output measurement errors. We show that the non-convex problem of finding a constraint admissible affine output feedback policy over a finite horizon, to be used in conjunction with a fixed linear state observer, can be converted to an equivalent convex problem. When used in the design of a time-varying robust receding horizon control law, we derive conditions under which the resulting closed-loop system is guaranteed to satisfy the system constraints for all time, given an initial state estimate and bound on the state estimation error. When the state estimation error bound matches the minimal robust positively invariant (mRPI) set for the system error dynamics, we show that this control law is time-invariant, but its calculation generally requires solution of an infinite-dimensional optimization problem. Finally, using an invariant outer approximation to the mRPI error set, we develop a time-invariant control law that can be computed by solving a finite-dimensional tractable optimization problem at each time step that guarantees that the closed-loop system satisfies the constraints for all time.     

Reliability-based robust Pareto design of linear state feedback controllers using a multi-objective uniform-diversity genetic algorithm (MUGA)

In this paper, fuzzy threshold values, instead of crisp threshold values, have been used for optimal reliability-based multi-objective Pareto design of robust state feedback controllers for a single inverted pendulum having parameters with probabilistic uncertainties. The objective functions that have been considered are, namely, the normalized summation of rising time and overshoot of cart (S_RO–C) and the normalized summation of rising time and overshoot of pendulum (S_RO–P) in the deterministic approach. Accordingly, the probabilities of failure of those objective functions are also considered in the reliability-based design optimization (RBDO) approach. A new multi-objective uniform-diversity genetic algorithm (MUGA) is presented and used for Pareto optimum design of linear state feedback controllers for single inverted pendulum problem. In this way, Pareto front of optimum controllers is first obtained for the nominal deterministic single inverted pendulum using the conflicting objective functions in time domain. Such Pareto front is then obtained for single inverted pendulum having probabilistic uncertainties in its parameters using the statistical moments of those objective functions through a Monte Carlo simulation (MCS) approach. It is shown that multi-objective reliability-based Pareto optimization of the robust state feedback controllers using MUGA with fuzzy threshold values includes those that may be obtained by various crisp threshold values of probability of failures and, thus, remove the difficulty of selecting suitable crisp values. Besides, the multi-objective Pareto optimization of such robust feedback controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust state feedback controllers can be compromisingly chosen from the Pareto frontiers.     

含状态时滞及执行器饱和不确定系统反馈镇定及L2增益分析

研究了具有控制饱和状态时滞不确定系统的L2控制问题,提出了状态反馈方法,利用Lyapunov函数可获得时滞相关的线性矩阵不等式.线性矩阵不等式条件可保证闭环系统无干扰时鲁棒内稳定性和在某椭球内预先给定的有干扰时L2性能水平,该不等式通过引入辅助矩阵解除了执行器饱和对系统的影响而更易于实现且减小了保守性.采用线性矩阵不等式技术,将控制器存在的充分条件转化为凸优化问题.在此基础上设计了系统的状态反馈控制器,最后用数值仿真验证了所提出方法的可行性.     

基于线性矩阵不等式的不确定关联系统的分散鲁棒镇定

应用线性矩阵不等式（LMI）方法研究不确定性关联大系统的分散便棒镇定问题。系统中不稳定项具有数值界,可不满足匹配条件。基于不确定项的表达形式,给出了其可分散状态反馈镇定的充分条件,即一组LMIs有解。在此基础上,通过求第一凸优化问题,提出了具有较小反馈增益的分散稳定化状态反馈控制律的设计方法。仿真示例说明了该方法的有效性和优越性。     

一类不确定线性时滞系统的输出反馈鲁棒镇定

研究一类不确定线性时滞系统的输出反馈鲁棒镇定问题,其中不确定性不必满足匹配条件。以二次Lyapunov泛函保证系统的渐近稳定性,利用线性矩阵不等式给出了系统可以利用动态输出反馈鲁棒镇定的充分条件。当此条件成立时,基于线性矩阵不等式的解构造了全阶动态输出反馈镇定控制器。     

Offline Robust Model Predictive Control for Lipschitz Non‐Linear Systems Using Polyhedral Invariant Sets

In this paper the concept of maximal admissible set (MAS) for linear systems with polytopic uncertainty is extended to non‐linear systems composed of a linear constant part followed by a non‐linear term. We characterize the maximal admissible set for the non‐linear system with unstructured uncertainty in the form of polyhedral invariant sets. A computationally efficient state‐feedback RMPC law is derived off‐line for Lipschitz non‐linear systems. The state‐feedback control law is calculated by solving a convex optimization problem within the framework of linear matrix inequalities (LMIs), which leads to guaranteeing closed‐loop robust stability. Most of the computational burdens are moved off‐line. A linear optimization problem is performed to characterize the maximal admissible set, and it is shown that an ellipsoidal invariant set is only an approximation of the true stabilizable region. This method not only remarkably extends the size of the admissible set of initial conditions but also greatly reduces the on‐line computational time. The usefulness and effectiveness of the method proposed here is verified via two simulation examples.     

Robust LQR design for systems with probabilistic uncertainty

In this paper, we consider the design of robust quadratic regulators for linear systems with probabilistic uncertainty in system parameters. The synthesis algorithms are presented in a convex optimization framework, which optimize with respect to an integral cost. The optimization problem is formulated as a lower‐bound maximization problem and developed in the polynomial chaos framework. Two approaches are considered here. In the first approach, an exact optimization problem is formulated in the infinite‐dimensional space, which is solved approximately using polynomial‐chaos expansions. In the second approach, an approximate problem is formulated using a reduced‐order model and solved exactly. The robustness of the controllers from these two approaches are compared using a realistic flight control problem based on an F16 aircraft model. Linear and nonlinear simulations reveal that the first approach results in a more robust controller.     

含状态时滞及执行器饱和不确定系统反馈镇定及L2增益分析

研究了具有控制饱和状态时滞不确定系统的L₂控制问题, 提出了状态反馈方法, 利用Lyapunov函数可获得时滞相关的线性矩阵不等式. 线性矩阵不等式条件可保证闭环系统无干扰时鲁棒内稳定性和在某椭球内预先给定的有干扰时L₂性能水平, 该不等式通过引入辅助矩阵解除了执行器饱和对系统的影响而更易于实现且减小了保守性. 采用线性矩阵不等式技术, 将控制器存在的充分条件转化为凸优化问题. 在此基础上设计了系统的状态反馈控制器, 最后用数值仿真验证了所提出方法的可行性.     

基于输出反馈的不确定连续系统的鲁棒预测控制

运用线性矩阵不等式方法,研究一类基于输出反馈的线性连续时间范数有界参数不确定系统的鲁棒预测控制问题．基于变量变换的思想,将无限时域“最小—最大”优化问题转化为线性规划问题,得出分段连续的输出反馈控制律,并给出了控制律存在的充分条件,证明了优化问题在初始时刻的可行解保证闭环系统渐近稳定．仿真实例验证了此方法的有效性．     

连续时间多胞线性变参数系统变增益H∞/H2输出反馈控制

针对一类同时具有参数不确定性和外界干扰的非线性系统,提出了一种连续时间多胞线性变参数(LPV)系统变增益H_∞/H_2输出反馈控制方法.首先,对连续时间多胞LPV系统的变增益混合目标(H_∞/H_2指标和区域极点约束)输出反馈控制器综合方法进行了数学描述;其次,引入新的结构化松弛矩阵变量和参数依赖Lyapunov函数,将满足期望性能的混合目标鲁棒动态输出反馈控制问题转化为线性矩阵不等式框架内的有限维凸优化问题,进一步降低了所设计LPV控制器的保守性.最后,以四分之一车辆模型主动悬架系统为研究对象进行仿真,仿真结果验证了本文控制器的有效性.     

不确定广义系统的输出反馈鲁棒预测控制

针对一类具有范数有界不确定性的广义系统,当系统状态不可测时,提出了一种基于输出反馈的鲁棒预测控制器综合算法．采用ＬＭＩ方法以及变量变换思想,将无限时域“最小最大”优化问题转化为线性规划问题．确定出一组分段连续的输出反馈控制序列,给出了输出反馈控制律存在的充分条件,证明了优化问题在初始时刻的可行解可以保证广义闭环系统是渐近稳定且正则无脉冲的．仿真实例验证了所提出方法的有效性．     

Mixed‐Objective Robust Dynamic Output Feedback Controller Synthesis for Continuous‐Time Polytopic Lpv Systems

A robust dynamic output feedback controller synthesis algorithm considering H_∞/H₂ performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.