Optimal fuzzy controller design: local concept approach

In this paper, we present a global optimal and stable fuzzy controller design method for both continuous- and discrete-time fuzzy systems under both finite and infinite horizons. First, a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers. Based on this sufficient condition, we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory. The stability of the entire closed-loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant feedback continuous fuzzy system possesses an infinite gain margin; that is, its stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties     

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.     

Decentralised sampled-data control for large-scale systems with nonlinear interconnections

This paper presents a decentralised sampled-data control technique for a class of large-scale systems, which are considered to consist of linear subsystems and nonlinear interconnections. The decentralised sampled-data controller design problem is established using a closed-loop subsystem. Based on the controller design problem, the stability condition is derived for a closed-loop large-scale system, and the maximum interconnection bound is guaranteed to satisfy the stability condition. Also, its sufficient condition is formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed technique is verified by using an example of the multi-machine power system.     

A double homotopy method for decentralised control design

An iterative algorithm that is based on the idea of two homotopy paths is proposed for output feedback decentralised ?_∞ control design. The approach follows a bilinear matrix inequality (BMI) formulation of the decentralised control problem. Along one homotopy path the BMI problem, which is non-convex, is locally linearised and solved. Along the second homotopy path the controller is deformed at each step so that in the end it attains a decentralised structure. The proposed computational algorithm can also be applied to obtain reduced-order decentralised controllers. Numerical examples are used to demonstrate the efficacy of the proposed algorithm.     

Decentralised controller design based on structured singular values

In this study, structured singular values are used in a different way from those commonly used in the robust control literature. It is shown that subject to conditions based on structured singular values, each local area controller can be designed independently. A MATLAB? program is developed to plot inverse structured singular values of multi input multi output (MIMO) system relative error matrix. This plot can be used to predict the stability of the global system with decentralised controller. Therefore decentralised controller design problem can be translated into an equivalent problem of decentralized controller design for a MIMO control system.     

Discrete-time optimal fuzzy controller design: global conceptapproach

Proposes a systematic and theoretically sound way to design a global optimal discrete-time fuzzy controller to control and stabilize a nonlinear discrete-time fuzzy system with finite or infinite horizon (time). A linear-like global system representation of a discrete-time fuzzy system is first proposed by viewing such a system in a global concept and unifying the individual matrices into synthetic matrices. Then, based on this kind of system representation, a discrete-time optimal fuzzy control law which can achieve a global minimum effect is developed theoretically. A nonlinear two-point boundary-value-problem (TPBVP) is derived as a necessary and sufficient condition for the nonlinear quadratic optimal control problem. To simplify the computation, a multi-stage decomposition of the optimization scheme is proposed, and then a segmental recursive Riccati-like equation is derived. Moreover, in the case of time-invariant fuzzy systems, we show that the optimal controller can be obtained by just solving discrete-time algebraic Riccati-like equations. Based on this, several fascinating characteristics of the resultant closed-loop fuzzy system can easily be elicited. The stability of the closed-loop fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal closed-loop fuzzy system can not only be guaranteed to be exponentially stable, but also stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant closed-loop fuzzy system possesses an infinite gain margin, i.e. its stability is guaranteed no matter how large the feedback gain becomes. An example is given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proven stability properties     

一类时滞大系统的分散弹性控制器设计:自适应方法

研究了一类时滞大系统的分散弹性自适应控制器的设计问题.当控制器增益摄动范数 有界但上界未知时,采用自适应方法,给出了系统一致有界稳定的条件和控制器的设计方案,且 该控制器具有在线调整的功能.并给出了特例情况下,即控制器增益摄动范数有界且上界已知 时,闭环系统可镇定的充分条件和相应弹性控制器的设计方案.数值算例说明了设计的可行性 和有效性.     

Decentralised disturbance-observer-based adaptive tracking in the presence of unmatched nonlinear time-delayed interactions and disturbances

This paper proposes an approximation-based nonlinear disturbance observer (NDO) approach for decentralised adaptive tracking of uncertain interconnected pure-feedback nonlinear systems with unmatched time-delayed nonlinear interactions and external disturbances. Compared with the existing approximation-based NDO approach for uncertain interconnected nonlinear systems where the centralised design framework was proposed, the main contribution of this paper is to develop a decentralised and memoryless NDO-based adaptive control scheme in the presence of unknown time-varying delayed interactions and disturbances unmatched in the control inputs. The recursive design methodology is derived to construct the decentralised NDO and controller where the function approximators used in the decentralised NDO are employed to design the decentralised adaptive controller. From the Lyapunov stability theorem using Lyapunov--Krasovskii functionals, it is shown that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors converge to an adjustable neighbourhood of the origin.     

Global decentralised stabilisation for a class of uncertain large-scale feedforward nonlinear systems

In this paper, the problem of global decentralised stabilisation for a class of uncertain large-scale feedforward nonlinear systems is investigated. The system under consideration is allowed to contain unknown non-Lipschitz continuous nonlinear terms. The design of the global decentralised controllers takes a two steps procedure. First of all, based on the adding a power integrator technique and the homogeneous domination approach a local homogeneous decentralised controller is proposed for each subsystem of the large-scale feedforward nonlinear system. Then, we integrate a series of nested saturation functions with the homogeneous decentralised controllers and adjust the saturation levels to ensure globally asymptotic stability of the closed-loop system. Simulation studies are conducted to illustrate the effectiveness of the proposed control method.     

具有扰动的多时滞线性系统的鲁棒控制器

本文讨论了多时滞多扰动线性系统的鲁棒控制器设计问题，证明了在一定条件下时滞扰动系统能稳的充分条件为其标称系统二次型能稳，给出了按标称系统的给定稳定裕度设计系统鲁棒控制器的方法。     

Sliding mode observer–controller design for uncertain Markovian jump systems with time delays

This paper proposes a sliding mode observer–controller design method for uncertain Markovian jump systems with time delays and uncertain switching probabilities. Both the structures of a sliding mode observer and a sliding mode controller are given. By the mode‐dependent Lyapunov functional approach, a sufficient condition for the stochastic stability of the closed‐loop system is given, which can be converted into a convex optimization problem. The reachability of the sliding surfaces in both the estimation error space and the state estimate space can be ensured by the presented control scheme. Finally, the effectiveness of the proposed design method is demonstrated by a simulation example. Copyright © 2011 John Wiley & Sons, Ltd.     

Decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems

Under the weaker conditions on the drift and diffusion terms, this paper focuses on the global decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems. By introducing an appropriate coordinate transformation, the original system is transformed into an equivalent one with tunable gain. After that, by reasonably combing the homogeneous domination approach with stochastic nonlinear systems stability criterion, and skillfully choosing the low gain scale, the decentralised output-feedback controller is constructed for each subsystem to ensure that the closed-loop system is globally asymptotically stable in probability. The simulation example is given to demonstrate the effectiveness of the proposed design scheme.     

Stabilising agent design for the control of interconnected systems

This article presents a new control design strategy for stabilising large-scale interconnected systems operating in semi-automatic control modes. The large-scale system is modelled by subsystems connected to each other in an arbitrary configuration. Each subsystem is regulated by a dedicated multivariable controller that also allows for a manual control mode. The notion of asymptotically positive realness constraint (APRC) is introduced and applied for deriving the interconnection stabilisability condition in the time domain. The interactions between subsystems are taken into consideration in the stability condition. The APRC is subsequently employed in the so-called stabilising agent to accommodate the closed-loop control and man-in-the-loop coexistence. The multipliers of the APRC quadratic supply rate are updated on-the-fly to ensure that the constraint satisfaction of stabilising agents is recursively feasible. The stabilising agents are developed independently from the control law under the same auspice controller. Due to this independence, operational errors from the manual control adjustments, that may destabilise the control systems, can be avoided. The decentralised agents render stabilising bounds for the manipulated variables in the automatic control mode, and at the same time, provide warning signals and manipulation guidance for the operators to prevent possible plant-wide destabilisation in the manual control mode. Our main results are illustrated through numerical simulations for an industrial modular system.     

Robust wedge-stability analysis and design of continuous constrained systems with stability radii

In this paper, based on stability radii, a sufficient condition is first proposed to ensure the robust wedge stability of continuous-time constrained systems with state feedback. The saturated actuator is reformulated as a conditioned linear actuator subject to structured uncertainties and then an auxiliary matrix is introduced so that the closed-loop system can be characterized into a scheme of stability radius approach. We also investigate the issue of maximizing complex stability radius subject to a wedge region by state feedback. Through iteratively solving a parametrized Riccati equation, a desired maximizing state feedback controller corresponding to the prescribed wedge subregion can be obtained. An example is given to illustrate the design algorithm and to reveal the feasibility of stability radius approach for continuous-time constrained systems.     

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.     

Performance improvement using time delays in multivariable controller design

A new controller for linear multivariable ordinary systems is suggested in which distributed delays are included in the feedback loop. A general design approach to obtain this type of controller is suggested. It is shown that the resulting closed-loop system is asymptotically stable under some sufficient conditions. Sufficient conditions are derived under which the disturbance attenuation, the robustness against parameter variations, and the time-delay stability margins are improved by the proposed controller. The state feedback tracking controller and the dual-state observer are obtained by modification of the proposed controller.     

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.     

Decentralised output-feedback control design for switched fuzzy large-scale systems

This paper investigates the output-feedback control design problem for a class of switched Takagi–Sugeno fuzzy large-scale systems with non-measurable premise variables. The considered fuzzy large-scale systems consist of several interconnected subsystems with different switching modes and there exists the asynchronous switching between the system switching modes and the controller switching modes. A decentralised state observer is proposed to estimate the unmeasured states, and a new output-feedback decentralised control scheme is developed by using the state observers and the switching functions. Based on the theory of Lyapunov stability and average dwell-time methods, the sufficient conditions of ensuring the switched control system stability are proposed and proved, which are formulated in the form of linear matrix inequalities. An applicable example is provided to show the effectiveness of the obtained theoretical results.     

Global decentralised stabilisation for a class of uncertain large-scale high-order upper-triangular nonlinear systems

This paper considers the global decentralised stabilisation problem for a class of uncertain large-scale high-order upper-triangular nonlinear systems. First, a local linear decentralised controller is recursively constructed based on the generalised homogeneous system theory and the adding a power integrator method. Second, aiming for global stabilisation, a series of nested saturation functions are integrated with the proposed local linear decentralised controller. Then, it is proved that the obtained decentralised saturated controller will render the whole closed-loop system globally asymptotically stable. Due to the flexibility of the generalised homogeneous method, the proposed control approach not only weakens the existing restrictions imposed on the interconnected nonlinearities, but also can be applied to a more general class of upper-triangular nonlinear systems. Furthermore, two simulations examples are conducted to show the effectiveness of the proposed control scheme.