Decentralized robust controller design for uncertain large-scale systems with control delays

This paper presents a decentralized robust controller design for a class of interconnected dynamic systems with control delays and parametric uncertainty. The parameter uncertainties are considered unknown but norm bounded. By applying the Lyapunov stability theorem, two new delay-dependent sufficient conditions are established in terms of linear matrix inequalities, and linear memoryless state feedback controllers are designed to maintain the robust stability for the class of systems under study. It is shown that either no tuning procedure is required or only one parameter from each inequality needs to be tuned. An example is presented to demonstrate the application of the results presented here.     

一类复杂控制系统分散自适应鲁棒控制器设计

基于模糊逻辑系统具有充分利用语言信息和逼近连续函数性质的思想,分析研究了一类非线性不确定复杂系统的自适应控制问题.利用系统的数学模型和模糊逻辑系统对不确定性的输出信息,设计出了复杂系统的分散自适应鲁棒控制器和模糊逻辑系统参数估计的自适应律,在较弱的假设条件下,证明了这种控制器使被控系统的状态及参数估计误差一致终极有界.仿真实例表明,所提出的方法是有效的.     

Decentralized adaptive controller design of large-scale uncertain robotic systems

In this paper, we develop a decentralized neural network control design for robotic systems. Using this design, it is not necessary to derive the robotic dynamical system (robotic model) for the control of each of the robotic components, as in traditional robot control. The advantage of the proposed neural network controller is that, under a mild assumption, unknown nonlinear dynamics such as inertia matrix and Coriolis/centripetal matrix and friction, as well as interconnections with arbitrary nonlinear bounds can be accommodated with on-line learning.     

Robust controller design for uncertain multiple-delay systems with unknown actuator parameters

This paper considers the controller design problem for a class of uncertain systems with unknown actuator parameters. The considered systems are with multiple time delays and nonlinear uncertainties, and the uncertain nonlinearities are bounded by nonlinear functions with unknown coefficients. The actuator parameters are time-varying and their bounds are unknown, moreover the signs of them are not available. To deal with unknown actuator parameters problem, we decompose the system into two subsystems. For the resultant system, we develop the corresponding tolerant controller design method with the help of Nussbaum function. By constructing the Lyapunov Krasovskii functional, we prove the asymptotical stability of the closed-loop system. Finally, simulations are performed on a chemical reactor system to show the effectiveness of the proposed method.     

The variable structure controller design for a class of nonlinear uncertain systems based on robust observer

The variable structure controller is designed for a class of nonlinear uncertain time-delay system by using robust observer, and incorporating H-infinity control technique, the controller can guarantee the H-infinity performance of sliding mode dynamics and satisfy the reaching condition, which also does not require uncertainties to satisfy matching condition and linear boundary condition. The simulation example is given to illustrate the method.     

时变不确定系统鲁棒控制器设计的新方法

基于包含两个二次项的分段Lyapunov函数,研究了线性时变不确定系统的鲁棒控制器设计问题.所考虑的系统由两个矩阵的凸组合构成,通过引入一个附加矩阵,推导出鲁棒控制器存在的充分条件.该控制器的状态反馈增益的求解问题可以转化为一组带有两个比例参数的线性矩阵不等式的凸优化问题.最后的数值示例说明了该设计方法的可行性.     

Vector control design for robust stabilization of a class of uncertain systems

We consider a state-space control system such that the elements of the system matrix and the matrix of the control term are functionals having arbitrary nature. By using a quadratic Lyapunov function, a stabilizing vector control is designed such that it does not depend on the form of the elements of the system matrix, but rather on the bounds of their possible variations.     

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.     

An asymptotically stable robust controller formulation for a class of MIMO nonlinear systems with uncertain dynamics

In this work, we present a novel continuous robust controller for a class of multi-input/multi-output nonlinear systems that contains unstructured uncertainties in their drift vectors and input matrices. The proposed controller compensates uncertainties in the system dynamics and achieves asymptotic tracking while requiring only the knowledge of the sign of the leading principal minors of the input gain matrix. A Lyapunov-based argument backed up with an integral inequality is applied to prove the asymptotic stability of the closed-loop system. Simulation results are presented to illustrate the viability of the proposed method.     

Adaptive fuzzy controller design with observer for a class of uncertain nonlinear MIMO systems

In this paper, an adaptive fuzzy control approach is proposed to stabilize a class of uncertain nonlinear MIMO systems with the unmeasured states and the external disturbances. The fuzzy logic systems are used to approximate the unknown functions. Because it does not required to assume that the system states are measurable, it needs to design an observer to estimate the system unmeasured states. The considered MIMO systems are more general, i.e. they consist of N subsystems and each subsystem is in the non‐affine form. The stability of the closed‐loop system is verified by using Lyapunov analysis method. Two simulation examples are utilized to verify the effectiveness of the proposed approach. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一类不确定参数系统鲁棒稳定界的解析分析与应用

研究一类具有不确定参数系统鲁棒性稳定界的解析分析方法.在定义了鲁棒稳定界的基础上,证明了鲁棒稳定界只与标称系统的最小特征值有关.利用这一结论不仅可以方便地分析多项式的稳定性,而且可以根据系统的不确定性设计闭环控制系统的期望极点,并进行极点配置.     

不确定奇异大系统分散鲁棒预测控制

针对一类不确定奇异关联大系统,讨论了当系统状态不可测时,基于输出反馈的分散鲁棒预测控制问题.通过构造Lyapunov函数以及应用线性矩阵不等式方法,将"min-max"优化问题转化为凸优化问题求解,从而得到了输出反馈分散控制器存在的充分条件和显示表达式.证明了优化问题在初始时刻的可行解能保证奇异闭环大系统渐近稳定且正则无脉冲.仿真结果验证了算法的有效性.     

不确定非线性环链系统的分散鲁棒控制

提出了环链系统和一类不确定非线性环链系统,利用线性代数理论,给出了实现环链系统的充要条件,运用李雅普诺夫稳定理论和矩阵理论研究了不确定非线性环链系统的鲁棒镇定,并给出了一种非线性鲁棒镇定控制器的设计,还考虑了一类非线性环链相似组合大系统,给出了分散鲁棒镇定条件,最后给出数值例子说明设计方法的有效性。     

一类离散非线性不确定互联系统的模糊分散控制

利用模糊控制方法研究一类离散非线性互联系统的分散控制问题.首先采用模糊(T-S)模型对离散非线性不确定互联系统进行模糊建模,应用并行分布补偿算法(PDC)给出状态反馈分散模糊控制方案,并基于李亚普诺夫函数方法证明了闭环系统的稳定性.然后当系统的状态不完全可测时,设计模糊分散观测器来估计各子系统的状态,从而给出基于观测器的状态反馈分散模糊控制设计的方法.因为该分散模糊控制设计问题是以线性矩阵不等式的形式给出,所以很容易用凸优化方法求解.仿真结果验证了所提出控制方法的有效性.     

Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.     

一类不确定性系统鲁棒H∞控制器

研究一类具有匹配不确定性系统鲁棒H∞控制问题,第一,基于矩阵不等式给出了二次稳定的条件并且对系统的H∞性能进行了分析;第二,给出了系统的鲁棒H∞控制器,该控制器不仅满足系统二次稳定的条件,而且也满足H∞性能约束条件;最后,数值算例说明了控制器的有效性和可行性。     

基于鲁棒可靠性的不确定时滞系统最优H∞控制器设计

用区间变量描述控制系统参数的不确定性,提出了不确定时滞系统鲁棒H_∞控制的鲁棒可靠性方法,基于鲁棒可靠性的不确定时滞系统最优状态反馈H_∞控制器设计方法,将系统的最优控制器设计归结为基于线性矩阵不等式(LMI)的优化问题．所设计的控制器可以在满足对所有不确定性鲁棒可靠的前提条件下,具有最优的H_∞鲁棒性能,并能在控制系统的设计中综合考虑控制性能、控制代价和鲁棒可靠性．数值算例说明了所提方法的有效性和可行性．     

Sampled-data controller design for uncertain systems

Presents a sampled-data controller design methodology for uncertain systems. A continuous system with bounded time-varying uncertainty is sampled at intervals of length T. The controller is designed using a Riccati equation approach by neglecting O(T²) uncertainty terms in the discretized system. Stability is verified for this choice of T with the U(T²) terms included. If there exists a stabilizing continuous controller, then there also exists a stabilizing sampled-data controller for a sufficiently small choice of T     

Decentralized robust PI controller design for an industrial boiler

This paper presents a new scheme to design decentralized robust PI controllers for uncertain LTI multivariable systems. Sufficient conditions for closed-loop stability and closed-loop diagonal dominance (almost decoupling) of a multivariable system are obtained. Satisfying these conditions and robust performance of the overall system are modeled as local robust performance problems. Then, by appropriately selecting the time constants of the closed-loop isolated subsystems in the IMC (Internal Model Control) strategy, the defined local robust performance problems are solved. To design a decentralized robust PI controller for a real industrial utility boiler, a control oriented nonlinear model for the boiler is identified. The nonlinearity of the system is modeled as uncertainty for a nominal LTI multivariable system. Using the new proposed method, a decentralized PI controller for the uncertain LTI model is designed. The designed controller is applied to the real system. The simulation results show the effectiveness of the proposed methodology.