Decentralised memory static output feedback control for the nonlinear time-delay similar interconnected systems

In this paper, the problem of decentralised memory static output feedback control for a class of nonlinear time-delayed interconnected systems with similar structure is investigated, where both the linear and nonlinear state vectors involve time delay. The contributions of the paper include the following: (1) a new similar structure is presented via memory static output feedback; (2) by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, the decentralised memory static output derivative feedback controllers with similar structure are designed, which is dependent of time delays, to stabilise the interconnected systems uniformly asymptotically; and (3) the stability domain is estimated. The conservatism of the results obtained is reduced by full using the system output information. Finally, the numerical examples are given to demonstrate the effectiveness of the results obtained in this paper.     

线性不确定系统的给定阶最优控制器设计

为避免间接法设计降阶控制器的模型近似引起的性能下降,本文在静态输出反馈控制器设计的基础上,直接设计了线性不确定系统的给定阶混合H2/H∞动态反馈控制器.利用系统内外分解方法,得到了最优降阶状态观测器.通过求解降维状态观测器的静态输出反馈,可得到降阶控制的最优反馈增益阵.给定阶控制器由两个Ric cati方程和一个Lyapunov方程参数化表示.最后,通过一个例子,说明了本文提出的给定阶控制器设计方法.     

Delay-dependent decentralised control for a class of uncertain similar interconnected systems with state delay and input delay

In this paper, the problem of delay-dependent decentralised control for a class of uncertain similar interconnected systems is investigated, where not only the state vectors but also the input vectors involve time delay. The new similar structure is presented via state feedback, based on which, by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, the decentralised stabilization controllers are designed, which is dependent on time delays, to stabilise the interconnected systems uniformly asymptotically. The results show that the design is easy to calculate and the controllers have the similar structure, so it is easy to realise project. Finally, a numerical example is given to demonstrate the effectiveness of the results obtained in this paper.     

Decentralised variable gain robust controller design for a class of large-scale interconnected systems with mismatched uncertainties

In this paper, we propose an LMI-based design method of a decentralised variable gain robust controller for large-scale interconnected systems with mismatched uncertainties. The mismatched uncertainties under consideration are composed of the matched part and the mismatched one, and the proposed decentralised robust controller consists of a state feedback with a fixed gain and one with a variable gain tuned by parameter adjustment laws. Sufficient conditions for the existence of the proposed decentralised variable gain robust controller are given in terms of linear matrix inequalities (LMIs). Finally, a numerical example is illustrated to validate the proposed design procedure.     

Decentralised stabilisation for nonlinear time delay interconnected systems using static output feedback

In this paper, time delay interconnected systems are considered where the nominal isolated subsystems are fully nonlinear. The interconnections and the matched and mismatched disturbances are nonlinear and time-delayed. A decentralised static output feedback control strategy is proposed to stabilise the resulting interconnected system uniformly asymptotically. A novel approach is proposed to deal with the interconnections by introducing artificial interconnections, such that accessible information is fully exploited in the control design to reduce conservatism. Simulation results show the effectiveness of the proposed approach.     

Decentralised output feedback control of Markovian jump interconnected systems with unknown interconnections

The problem of decentralised output feedback control is addressed for Markovian jump interconnected systems with unknown interconnections and general transition rates (TRs) allowed to be unknown or known with uncertainties. A class of decentralised dynamic output feedback controllers are constructed, and a cyclic-small-gain condition is exploited to dispose the unknown interconnections so that the resultant closed-loop system is stochastically stable and satisfies an H_∞ performance. With slack matrices to cope with the nonlinearities incurred by unknown and uncertain TRs in control synthesis, a novel controller design condition is developed in linear matrix inequality formalism. Compared with the existing works, the proposed approach leads to less conservatism. Finally, two examples are used to illustrate the effectiveness of the new results.     

Output Feedback Stabilization for a Discrete-Time System With a Time-Varying Delay

This study employs the free-weighting matrix approach to investigate the output feedback control of a linear discrete-time system with an interval time-varying delay. First, the delay-dependent stability is analyzed using a new method of estimating the upper bound on the difference of a Lyapunov function without ignoring any terms; and based on the results, a design criterion for a static output feedback (SOF) controller is derived. Since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities, a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility SOF control problem. Furthermore, the problem of designing a dynamic output feedback controller is formulated as one of designing an SOF controller. Numerical examples demonstrate the effectiveness of the method and its advantage over existing methods.      

Non-fragile output feedback H∞ vehicle suspension control using genetic algorithm

This paper presents an approach to design static output feedback and non-fragile static output feedback H_∞ controllers for active vehicle suspensions by using linear matrix inequalities and genetic algorithms. A quarter-car model with active suspension system is considered in this paper. By suitably formulating the minimization problem of the sprung mass acceleration, suspension deflection and tyre deflection, a static output feedback H_∞ controller and a non-fragile static output feedback H_∞ controller are obtained. The controller gain is naturally constrained in the design process. The approach is validated by numerical simulation which shows that the designed static output feedback H_∞ controller can achieve good active suspension performance in spite of its simplicity, and the non-fragile static output feedback H_∞ controller has significantly improved the non-fragility characteristics over controller gain variations.     

Reduced-order observer-based decentralised control of non-linear interconnected systems

The output feedback-based asymptotic stabilisation problem for a class of non-linear interconnected systems is considered, where the non-linear interconnections between subsystems satisfy quadratic constraints. A novel decentralised dynamic output feedback control strategy involving local projection operator-based reduced-order observers is proposed. This decentralised controller is characterised by the separation property. Two easily verifiable conditions that guarantee the asymptotic stability of the closed-loop system driven by the proposed decentralised controller are given. The effectiveness of the developed decentralised control strategy is illustrated with a numerical example and simulations.     

一类具有不确定性的相似组合系统的鲁棒输出反馈镇定

讨论受非线性扰动的线性相似子系统经非线性互联而形成的组合大系统（相似组合系统）的鲁棒输出反馈镇定问题,这类相似组合系统可以用结构类似于“砰砰”控制的分散输出反馈控制器鲁棒渐近镇定。     

Decentralized overlapping control of a formation of unmanned aerial vehicles

Decentralized overlapping feedback laws are designed for a formation of unmanned aerial vehicles. The dynamic model of the formation with an information structure constraint in which each vehicle, except the leader, only detects the vehicle directly in front of it, is treated as an interconnected system with overlapping subsystems. Using the mathematical framework of the inclusion principle, the interconnected system is expanded into a higher dimensional space in which the subsystems appear to be disjoint. Then, at each subsystem, a static state feedback controller is designed to robustly stabilize the perturbed nominal dynamics of the subsystem. The design procedure is based on the application of convex optimization tools involving linear matrix inequalities. As a final step, the decentralized controllers are contracted back to the original interconnected system for implementation.     

A constructive method to static output stabilisation of Markov jump systems

This paper is concerned with the static output feedback stabilisation of Markov jump systems. Transition probabilities are assumed to be incomplete, namely, they may be known, uncertain with known lower and upper bounds and unknown. To linearise the nonlinearities induced by unknown transition probabilities, a linearisation is developed. To solve the static output feedback problem by means of linear matrix inequalities, a constructive method is proposed to separate the controller gain matrices from Lyapunov variables. Based on the linearisation and the separation, sufficient conditions are established to guarantee that the closed-loop system is stochastically stable by the designed static output feedback controller. The obtained results are further extended to deal with norm-bounded or polytopic uncertainties on system matrices. Numerical examples are given to demonstrate the effectiveness of the proposed method.     

稳定降阶控制器设计的新方法

这篇文章首先提出了稳定降阶控制器的一个特殊结构, 然后给出了两种控制器设计方法. 一种是基于新的松弛变量的特殊构造, 另一种是基于分离李雅普诺夫矩阵和控制器矩阵的两步法. 新的方法可以处理具有不同阶数和不同数目不稳定极点的几个系统的同时镇定问题, 而这个问题是很难用一般的鲁棒控制方法处理的. 本文提出的新方法还可以拓展到处理H无穷, 严格正实以及分散控制问题. 最后, 我们讨论了控制器的范数约束问题. 在该方法中, 甚至每一个控制器参数都可以被施加绝对值约束. 本文还讨论了相关的NP难问题, 给出了相应的控制器设计算法. 最后, 给出了几个例子验证了所提出的设计方法的有效性, 并且对这两种设计方法进行了对比.     

State Feedback Control for a Class of Fractional Order Nonlinear Systems

Using the Lyapunov function method, this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form, and presents a number of new results. First, some new properties of Caputo fractional derivative are presented, and a sufficient condition of asymptotical stability for fractional order nonlinear systems is obtained based on the new properties. Then, by introducing appropriate transformations of coordinates, the problem of controller design is converted into the problem of finding some parameters, which can be certainly obtained by solving the Lyapunov equation and relevant matrix inequalities. Finally, based on the Lyapunov function method, state feedback stabilization controllers making the closed-loop system asymptotically stable are explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.      

Observer-based H-infinity output feedback control with feedback gain and observer gain variations for Delta operator system

Considering that the controller feedback gain and the observer gain are of additive norm-bounded variations, a design method of observer-based H-infinity output feedback controller for uncertain Delta operator systems is proposed in this paper. A sufficient condition of such controllers is presented in linear matrix inequality （LMI） forms. A numerical example is then given to illustrate the effectiveness of this method, that is, the obtained controller guarantees the closed-loop system asymptotically stable and the expected H-infinity performance even if the controller feedback gain and the observer gain are varied.     

Feedback stabilization of fuzzy systems via linear matrix inequalities

This paper considers the problem of designing robust feedback stabilization controller for a class of fuzzy systems. Based on piecewise Lyapunov functions, new design techniques for state feedback and output feedback controllers are proposed. The resultant controller is robust against measurement and modelling perturbations. The design conditions are non-conservative, and the design process is easy to construct by using commercially supported linear matrix inequalities software packages.     

Decentralized output feedback robust stabilization for a class ofnonlinear interconnected systems with similarity

In this paper, the problem of decentralized output feedback stabilization for a class of nonlinear uncertain interconnected systems with similar subsystems is considered, and a type of controller with holographic structure is developed. It is shown that both the analyses of systems and the design of controllers are simplified by a similar structure. Finally, an example is presented to illustrate the results given in this paper and an estimation of the associated stabilized domain. Simulation shows that our method is very effective     

Special decentralized control problems in discrete-time interconnected systems composed of two subsystems

In this paper, some special decentralized control problems are addressed for discrete-time interconnected systems. First it is pointed out that some subsystems must be unstable to ensure stability of the overall system in some special cases. Then a special kind of decentralized control problem is studied. This kind of problem can be viewed as harmonic control among independent subsystems. Research results show that two unstable systems can generate a stable system through some effective cooperations. In addition, a decentralized controller design method based on linear matrix inequality is also given by using parameter-dependent Lyapunov function method developed for the study of robust stability. A special linear star coupled dynamical network is also considered. The central subsystem must be unstable to stabilize the whole network under a special coupling. Several examples are given to illustrate the results.     

Design of structured dynamic output-feedback controllers for interconnected systems

We address the design of structured controllers for networks of interconnected multivariable discrete-time subsystems. Different from existing approaches, where the structure of the controller is fixed a priori, we aim to design decentralised controllers such that each subsystem has a controller, which may not only use the output of its own associated subsystem, but also selected outputs of other subsystems. The total number of all those additional outputs used is to be minimised, while satisfying a guaranteed level of ?_∞-performance. For the resulting non-convex optimisation problem, we first present a novel characterisation of the ?_∞-performance of the closed-loop system by means of a system augmentation approach. Then, stimulated from compressive sensing theory, we propose a weighted ?₁-minimisation to relax the ?₀ objective function for structure optimisation. We develop an algorithm to deal with the relaxed decentralisation control problem, where the controller is obtained by iteratively solving convex optimisation problems. In addition, an iterative algorithm is developed to optimise the initial values such that the solvability of the decentralised control problem is further improved. Finally, an example is given to show the effectiveness of the proposed approaches.