Observer-based reliable stabilization of uncertain linear systems subject to actuator faults,saturation, and bounded system disturbances

A matrix inequality approach is proposed to reliably stabilize a class of uncertain linear systems subject to actuator faults, saturation, and bounded system disturbances. The system states are assumed immeasurable, and a classical observer is incorporated for observation to enable state-based feedback control. Both the stability and stabilization of the closed-loop system are discussed and the closed-loop domain of attraction is estimated by an ellipsoidal invariant set. The resultant stabilization conditions in the form of matrix inequalities enable simultaneous optimization of both the observer gain and the feedback controller gain, which is realized by converting the non-convex optimization problem to an unconstrained nonlinear programming problem. The effectiveness of proposed design techniques is demonstrated through a linearized model of F-18 HARV around an operating point.     

Robust model predictive control for switched linear systems

Developed is a robust model predictive control scheme for a class of discrete-time switched linear systems. The system is described in linear fractional transformation form in the presence of model uncertainty and induced norm bounded disturbances. The objective is to minimize the upper bound of an infinite horizon cost function subject to a terminal inequality. A Lyapunov function analysis for the switched system shows guaranteed closed-loop stability. Taking into account the switching structure of the system, the predictive control design problem along with sufficient conditions for the existence of a solution is expressed in terms of Riccati–Metzler inequalities. Then, these inequalities are turned into a linear matrix inequality feasibility problem. Three cases are analyzed to demonstrate the performance and effectiveness of the proposed robust model predictive controller for switched discrete-time linear systems.     

Analytical development of a robust controller for smart structural systems

This paper aims at demonstrating the feasibility of active control of beams with a multiobjective state-feedback control technique. The multiobjective state-feedback controller is designed on a linear matrix inequality (LMI) approach for the multiobjective synthesis. The design objectives are to achieve a mix ofH _∞ performance andH ₂ performance satisfying constraints on the closed-loop pole locations in the face of model uncertainties. The controller is also designed to reject the effects of the noise and external of disturbances. For the theoretical analysis, the governing equation of motion is derived by Hamilton’s principle to describe the dynamics of a smart structural system. Numerical examples are presented to demonstrate the effectiveness of the integrated robust controller in damping out the multiple vibration modes of the piezo/beam system.     

Finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations

In this paper, the problem of finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations is investigated. By constructing a novel Lyapunov–Krasovskii functional and employing a new summation inequality named discrete Wirtinger-based inequality, reciprocally convex approach and zero equality, the improved finite-time stability criteria are derived to guarantee that the state of the system with time-varying delay does not exceed a given threshold when fixed time interval. Furthermore, the obtained conditions are formulated in forms of linear matrix inequalities which can be solved by using some standard numerical packages. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed method.     

一类网络控制系统的稳定性分析

在基于多包传输的网络控制系统中,传感器采用时间驱动,控制器和执行器采用事件驱动.假定传输时延可以忽略,则整个网络控制系统可以描述为一个具有N个事件的异步动态系统.该文针对受控对象状态均可测,控制律采用输出反馈的情况,利用双线性矩阵不等式方法,讨论了网络控制系统指数稳定的问题,并给出了稳定性的充分条件,最后通过仿真实验加以验证.     

双星编队构形保持抗干扰容错控制

为解决系统模型误差、外部干扰以及执行器故障引起的双星编队轨道控制精度低、稳定性差问题,设计一种基于观测器的抗干扰容错线性二次型调节器(LQR)控制策略。首先,根据编队双星相对运动动力学模型,设计基于双比例积分自适应律的增广观测器,同时实现对系统状态、间歇故障与快速时变故障、可建模干扰的快速精确估计,并采用H∞优化技术抑制不可建模干扰对控制系统的影响。其次,采用Lyapunov稳定性理论,保证动态误差系统渐近稳定。然后,在控制器中引入未知动态估计信息的前馈补偿项,设计闭环反馈抗干扰容错LQR控制律。最后实验结果表明,相比文献中控制方法,本文所提方法的编队卫星相对位置控制精度提高49.93%,验证了所设计的抗干扰容错LQR控制律的优越性,能够为双星编队构形保持提供精确控制策略。     

一种串联机器人的全局参数优化设计方法

针对串联机器人物理参数方程的非线性导致的只能对串联机器人进行局部优化的问题,提出了一种基于线性矩阵不等式的全局优化方法。该方法从串联机器人机构与控制协同设计的理念出发,通过将非线性动力学方程的求解转化为线性矩阵不等式的优化问题,以消耗能量最小的方式来分析串联机器人指定动作下的动态特性,进而从全局角度来获取质量、几何尺寸、惯量等最优物理参数。用该方法指导4自由度重载机器人样机设计,运行效果验证了该方法的有效性。     

不确定性双臂空间机器人自适应模糊优化控制

考虑空间环境存在惯性参数未知及外部扰动等不确定性因素,针对自由漂浮双臂空间机器人(DFFSR)关节角运动控制问题,提出了一种自适应模糊优化控制方法。首先,基于系统动量守恒关系及Lagrange方法,建立DFFSR系统关节空间的动力学方程;而后,考虑系统惯性参数未知导致惯性矩阵无法求解问题,利用模糊控制理论的万能逼近特性,通过在线参数辨识建立系统自适应模糊模型;由此,同时考虑系统存在外界扰动以及输出力矩的优化问题,基于SDRE优化控制理论,设计一种自适应模糊优化控制方法,实现了DFFSR系统关节角的精确运动控制。一组对比仿真验证了所提控制方法的可靠性。     

Observer-based robust control of one-sided Lipschitz nonlinear systems

This paper presents an observer-based controller design for the class of nonlinear systems with time-varying parametric uncertainties and norm-bounded disturbances. The design methodology, for the less conservative one-sided Lipschitz nonlinear systems, involves astute utilization of Young’s inequality and several matrix decompositions. A sufficient condition for simultaneous extraction of observer and controller gains is stipulated by a numerically tractable set of convex optimization conditions. The constraints are handled by a nonlinear iterative cone-complementary linearization method in obtaining gain matrices. Further, an observer-based control technique for one-sided Lipschitz nonlinear systems, robust against L₂-norm-bounded perturbations, is contrived. The proposed methodology ensures robustness against parametric uncertainties and external perturbations. Simulation examples demonstrating the effectiveness of the proposed methodologies are presented.     

Further results on delay-range-dependent stability with additive time-varying delay systems

In this paper, new conditions for the delay-range-dependent stability analysis of time-varying delay systems are proposed in a Lyapunov–Krasovskii framework. Time delay is considered to be time-varying and has lower and upper bounds. A new method is first presented for a system with two time delays, integral inequality approach (IIA) used to express relationships among terms of Leibniz–Newton formula. Constructing a novel Lyapunov–Krasovskii functional includes information belonging to a given range; new delay-range-dependent criterion is established in term of linear matrix inequality (LMI). The advantage of that criterion lies in its simplicity and less conservative. This paper also presents a new result of stability analysis for continuous systems with two additive time-variant components representing a general class of delay with strong application background in network-based control systems. Resulting criteria are then expressed in terms of convex optimization with LMI constraints, allowing for use of efficient solvers. Finally, three numerical examples show these methods reducing conservatism and improving maximal allowable delay.     

Adaptive backstepping sliding mode control of flexible ball screw drives with time-varying parametric uncertainties and disturbances

This paper presents a method to model and design servo controllers for flexible ball screw drives with dynamic variations. A mathematical model describing the structural flexibility of the ball screw drive containing time-varying uncertainties and disturbances with unknown bounds is proposed. A mode-compensating adaptive backstepping sliding mode controller is designed to suppress the vibration. The time-varying uncertainties and disturbances represented in finite-term Fourier series can be estimated by updating the Fourier coefficients through function approximation technique. Adaptive laws are obtained from Lyapunov approach to guarantee the convergence and stability of the closed loop system. The simulation results indicate that the tracking accuracy is improved considerably with the proposed scheme when the time-varying parametric uncertainties and disturbances exist.     

New results on delay-range-dependent stability analysis for interval time-varying delay systems with non-linear perturbations

This paper studies the problem of the stability analysis of interval time-varying delay systems with nonlinear perturbations. Based on the Lyapunov–Krasovskii functional (LKF), a sufficient delay-range-dependent criterion for asymptotic stability is derived in terms of linear matrix inequality (LMI) and integral inequality approach (IIA) and delayed decomposition approach (DDA). Further, the delay range is divided into two equal segments for stability analysis. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Two well-known examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.     

基于状态空间的制造网络输出预测与扰动因素分析

针对复杂多变的制造网络为一随机动态系统,在分析内外扰动因素对制造网络状态影响的基础上,从订单流的角度建立网络中订单概率转移矩阵;定义制造网络中制造单元的状态变量;从系统动态分析的角度选定在制品订单量作为制造网络全局最优控制的反馈状态变量,进而构建制造网络的状态空间动态模型。通过分析扰动因素对订单概率转移矩阵的影响,建立扰动状态转移方程,更新扰动因素作用下的订单概率转移矩阵,简化制造网络状态空间的求解复杂度;从控制论的角度出发,利用建立的状态空间输出方程预测制造网络扰动因素影响下的订单输出量,并采用典型输入信号分析制造单元对扰动因素的动态响应。以某结构件数控加工厂的制造网络为例,验证该模型与扰动分析方法的有效性。     

Towards a new schedulability technique of real-time systems modeled by P-time Petri nets

In this paper, a novel schedulability analysis technique of real-time systems is presented. The developed approach is based on the consideration of the reachability graph of the (untimed) underlying Petri net of the studied model. The schedulability analysis is then conducted in two steps. Once a feasible firing sequence (called occurrence sequence) is highlighted, this sequence is then described under an algebraic form of type Ax?≤?b. The particular features of matrix A lead to a bimonotone linear inequality system. A bimonotone linear inequality is a linear inequality with at most two nonzero coefficients that are of opposite signs (if both different from zero). Thus, deciding whether a firing sequence is schedulable or not takes the form of the solution of a single-source shortest path problem which can be polynomially solved via the Bellman–Ford algorithm.     

Stabilization of systems with interval time-varying delay based on delay decomposing approach

The paper considers the stabilization for systems with interval time-varying delay. By decomposing the delay interval into multiple equidistant subintervals and considering the triple integral terms, a novel Lyapunov-krasovskii functional(LKF) is defined. Then extended integral inequality and convex combination approach are used to estimate the derivative of the constructed functional, and as a result, the new stability criterion with less conservatism and decision variables is obtained. On this basis, the state feedback controller is designed, by using linearization method, the existence condition of controller is obtained in terms of linear matrix inequalities(LMIs), and the specific form of controller is also given, moreover, by selecting the appropriate parameter value, the stabilization time of the system can be reduced. Numerical examples are given to illustrate the effectiveness of the proposed method.     

Adaptive nonlinear robust relative pose control of spacecraft autonomous rendezvous and proximity operations

This paper studies relative pose control for a rigid spacecraft with parametric uncertainties approaching to an unknown tumbling target in disturbed space environment. State feedback controllers for relative translation and relative rotation are designed in an adaptive nonlinear robust control framework. The element-wise and norm-wise adaptive laws are utilized to compensate the parametric uncertainties of chaser and target spacecraft, respectively. External disturbances acting on two spacecraft are treated as a lumped and bounded perturbation input for system. To achieve the prescribed disturbance attenuation performance index, feedback gains of controllers are designed by solving linear matrix inequality problems so that lumped disturbance attenuation with respect to the controlled output is ensured in the L₂-gain sense. Moreover, in the absence of lumped disturbance input, asymptotical convergence of relative pose are proved by using the Lyapunov method. Numerical simulations are performed to show that position tracking and attitude synchronization are accomplished in spite of the presence of couplings and uncertainties.     

采用Matlablmi工具进行控制系统鲁棒分析

针对用线性矩阵不等式（ＬＭＩ）描述的Ｈ＾∞控制问题，本文介绍如何利用ＭＡＴＬＡＢ软件ｌｍｉ工具进行分析、设计。文中给出了算例和相应的计算程序，对控制系统的鲁棒设计，具有参考意义。     

基于T-S模型的集装箱装卸桥防摇保性能控制

基于T-S模型的保性能控制对控制带有不确定性的系统有很好的鲁棒性(如集装箱装卸桥防摇系统),将系统稳定和保性能控制转化为解一系列矩阵不等式的问题,得出最优的反馈矩阵,设计出基于T-S模型的最优保性能控制器,并将该方法进行仿真,结果表明此方法简单可行,并且具有很好的鲁棒性。     

An algorithm for robust noninteracting control of ship propulsion system

In this paper, a new algorithm for noninteracting control system design is proposed and applied to ship propulsion system control. For example, if a ship diesel engine is operated by consolidated control with controllable pitch propeller (CPP), the minimum fuel consumption is achieved satisfying the demanded ship speed. For this, it is necessary that the ship is operated on the ideal operating line which satisfies the minimum fuel consumption, and the both pitch angle of CPP and throttle valve angle are controlled simultaneously. In this context of view, this paper gives a controller design method for a ship propulsion system with CPP based on noninteracting control theory. Where, linear matrix inequality (LMI) approach is introduced for the control system design to satisfy the givenH _∞ constraint in the presence of physical parameter perturbation and disturbance input. To the end, the validity and applicability of this approach are illustrated by the simulation in the all operating ranges.