A new decentralised controller design method for a class of strongly interconnected systems

In this paper, two interconnected structures are first discussed, under which some closed-loop subsystems must be unstable to make the whole interconnected system stable, which can be viewed as a kind of strongly interconnected systems. Then, comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown. A new approach for the design of decentralised controllers is presented by determining the Lyapunov function structure previously, which allows the existence of unstable subsystems. By fully utilising the orthogonal space information of input matrix, some new understandings are presented for the construction of Lyapunov matrix. This new method can deal with decentralised state feedback, static output feedback and dynamic output feedback controllers in a unified framework. Furthermore, in order to reduce the design conservativeness and deal with robustness, a new robust decentralised controller design method is given by combining with the parameter-dependent Lyapunov function method. Some basic rules are provided for the choice of initial variables in Lyapunov matrix or new introduced slack matrices. As byproducts, some linear matrix inequality based sufficient conditions are established for centralised static output feedback stabilisation. Effects of unstable subsystems in nonlinear Lur'e systems are further discussed. The corresponding decentralised controller design method is presented for absolute stability. The examples illustrate that the new method is significantly effective.     

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 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.     

Robust decentralized control for a class of uncertain nonlinear interconnected systems with similar structures

This paper addresses the problem of the robust decentralized control for nonlinear interconnected systems with uncertainties. The similar structures of nonlinear interconnected systems are first defined. Then, controllers are designed for these systems to solve the problems of robust decentralized output tracking and robust decentralized stabilization via static output feedback. The results obtained in this paper show that the analysis and design of systems can be simplified by using the similar structures of systems. Simulation examples are given to show the effectiveness of the method.     

具有输入饱和的非线性关联大系统的分散控制

考虑了一类具有输入饱和的不确定非线性关联大系统的分散输出反馈鲁棒镇定问题,利用Riccati方程的方法和矩阵的Moore-Penrose逆给出了这类系统的一种分散输出反馈鲁棒镇定控制器的设计方法.同时,考虑了一类具有输入饱和的不确定非线性相似关联大系统,利用相似系统的结构特点,简化了分散输出反馈鲁棒镇定的条件.     

Decentralised adaptive robust control of uncertain large-scale interconnected systems with multiple time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. It is assumed that the upper bounds of the uncertainties, interconnection terms and external disturbances are unknown, and that the time-varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed decentralised local adaptive robust state feedback controllers are completely independent of time delays, the results obtained in this article may also be applicable to a class of large-scale interconnected dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.     

Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback

In this paper, a class of nonlinear interconnected systems with nonlinear nominal subsystems is considered. Matched and mismatched uncertainties are both dealt with. Based on sliding mode techniques, a decentralised robust control scheme, using only output information, is presented to stabilise the system locally, but under certain circumstances, global results can be obtained. The approach allows a more general structure for the interconnections and uncertainty bounds than other literature in this area. The conservatism in the results is reduced by fully using system output information and the uncertainty bounds. A numerical example is used to demonstrate the efficacy of the method.     

一类相似广义互联系统的导数-输出反馈鲁棒控制器设计

以广义系统中受限系统等价概念和导数反馈- 输出反馈为基础,定义了一类广义互联系统的相似结构,提出了相似性研究的新方向.这类系 统具有不满足匹配条件的非线性不确定互联项.设计了导数-输出反馈鲁棒分散控制器,使互 联系统在平衡点处渐近稳定.由于控制器本身也具有相似结构,因此易于工程实现.     

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.     

双线性系统的静态分散输出控制

研究了一类T-S双线关联系统的静态输出控制反馈问题。应用分散控制理论,得到了闭环关联大系统Lyapunov稳定的充分条件。相应的分散模糊控制器可由线性矩阵不等式(LMD的解得到。最后,由数例仿真验证了所提方法的有效性。     

Reduced-order control for a class of nonlinear similar interconnected systems with mismatched uncertainty

In this paper, a class of nonlinear interconnected systems with similar structure is considered. The interconnected system consists of matched and mismatched uncertainties. Based on constrained Lyapunov equations and by exploiting the structure of the interconnected system, a continuous output feedback reduced-order control scheme is presented to stabilize the system robustly. Our approach allows more general forms of known and uncertain interconnections than existing work. The effectiveness of the proposed reduced-order control scheme is illustrated through a numerical example.     

一类具有相似结构的组合大系统的鲁棒控制

本文考虑了一类非线性不确定组合大系统的鲁棒镇定问题，不确定性匹配条件。     

A gradient flow approach to decentralised output feedback optimal control

This paper visits the quadratic optimal control problem of decentralised control systems via static output feedback. A gradient flow approach is introduced as a tool to compute the optimal output feedback gain. Several nice properties are revealed concerning the convergence of the gain matrix along the trajectory of an ordinary differential equation obtained from the gradient of objective cost, i.e. the objective cost is decreasing along this trajectory. If the equilibrium points are isolated, the convergence can be guaranteed. A simulation example is given to illustrate the effectiveness of this approach.     

Near optimal decentralised control with a pre-specified degree of stability

In this paper we develop a method for computing near optimal decentralised control with a pre-specified degree of stability for large scale, linear, interconnected dynamical systems. All the calculations in the new method are performed off-line using a three level hierarchical structure. We provide a condition the satisfaction of which ensures that the system has a pre-specified degree of stability. We also show that the control developed using the new method is more stable than the optimal decentralised control obtained by neglecting all interactions between the subsystems.     

经状态反馈确保非线性不确定相似组合系统终极一致有界

提出关于非线性组合系统的相似概念，利用输入输出线性化方法讨论了不确定非线性相似组合系统经状态反馈确保终极一致有界的问题。     

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.     

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     

Decentralized sliding mode control for a class of nonlinear interconnected systems by static state feedback

In this paper, a class of interconnected systems is considered, where the nominal isolated systems are fully nonlinear. A robust decentralized sliding mode control based on static state feedback is developed. By local coordinate transformation and feedback linearization, the interconnected system is transformed to a new regular form. A composite sliding surface which is a function of the system state variables is proposed and the stability of the corresponding sliding mode dynamics is analyzed. A new reachability condition is proposed and a robust decentralized sliding mode control is then designed to drive the system states to the sliding surface in finite time and maintain a sliding motion thereafter. Both uncertainties and interconnections are allowed to be unmatched and are assumed to be bounded by nonlinear functions. The bounds on the uncertainties and interconnections have more general forms when compared with existing work. A MATLAB simulation example is used to demonstrate the effectiveness of the proposed method.     

Adaptive dynamical variable structure feedback regulation for nonlinear uncertain systems

In this article an adaptive discontinuous dynamical feedback strategy is presented for asymptotic output stabilization problems defined on nonlinear controlled systems exhibiting linear parametric uncertainty. A dynamical feedback controller, ideally achieving output stabilization via exact linearization, is obtained by means of output differentiation and sliding mode control ideas. The adaptive version of the dynamical variable structure controller is then obtainable via standard, direct, overparametrized adaptive control techniques available for linearizable systems through static state feedback. An illustrative example from the chemical process control area, including simulations, is provided.