Semistability theory for spatially distributed systems

The concepts of semistability and exponential semistability are well-developed for finite-dimensional systems with nonisolated equilibrium points, where asymptotic or exponential stability is not possible. Definitions of semistability and exponential semistability have recently been formulated for networks with time-delays. This paper further extends the semistability theory to continuous and discrete spatially distributed systems. This requires the definition of the notions of exact and approximate semicontrollability and semiobservability, and discrete approximate semicontrollability and semiobservability. Also introduced is the property of weak semistability. Necessary and sufficient conditions are given for exponential semistability and weak semistability, and sufficient conditions are given for semistability.     

Efficient computation of higher order frequency response functions for nonlinear systems with,and without,a constant term

The behaviour of a nonlinear system can be profoundly affected by the presence of a constant or dc term in the system governing equation. These changes are reflected in the nonlinear frequency response characteristics of the system which provide a powerful insight into the system's dynamics. In this article, a new and efficient algorithm is presented for computing the higher order Volterra frequency response functions from nonlinear time-domain models that may contain a constant term. A comparison with previous methods is included to demonstrate the significant gains in computational efficiency that are achieved using the new method. The algorithm is applicable to systems modelled by nonlinear differential, or difference, equations and is easily automated. Several examples are used to illustrate the method, and to highlight the importance of dc terms in nonlinear system analysis.     

Influence-based model decomposition for reasoning about spatially distributed physical systems

Many important science and engineering applications, such as regulating the temperature distribution over a semiconductor wafer and controlling the noise from a photocopy machine, require interpreting distributed data and designing decentralized controllers for spatially distributed systems. Developing effective computational techniques for representing and reasoning about these systems, which are usually modeled with partial differential equations (PDEs), is one of the major challenge problems for qualitative and spatial reasoning research.

This paper introduces a novel approach to decentralized control design, influence-based model decomposition, and applies it in the context of thermal regulation. Influence-based model decomposition uses a decentralized model, called an influence graph, as a key data abstraction representing influences of controls on distributed physical fields. It serves as the basis for novel algorithms for control placement and parameter design for distributed systems with large numbers of coupled variables. These algorithms exploit physical knowledge of locality, linear superposability, and continuity, encapsulated in influence graphs representing dependencies of field nodes on control nodes. The control placement design algorithms utilize influence graphs to decompose a problem domain so as to decouple the resulting regions. The decentralized control parameter optimization algorithms utilize influence graphs to efficiently evaluate thermal fields and to explicitly trade off computation, communication, and control quality. By leveraging the physical knowledge encapsulated in influence graphs, these control design algorithms are more efficient than standard techniques, and produce designs explainable in terms of problem structures.     

Fuzzy frequency response: Proposal and application for uncertain dynamic systems

Fuzzy frequency response: proposal and application for uncertain dynamic systems is proposed in this paper. The uncertain dynamic system is partitioned into several linear sub-models, in terms of transfer function, and organized into Takagi–Sugeno (TS) fuzzy structure. The main contribution of this approach is demonstrated, from a Theorem, that the fuzzy frequency response is a bound in the magnitude and phase Bode plots. The analysis, from the fuzzy dynamic model, at low and high frequencies, is obtained varying the frequency ω from zero to infinity.     

Fuzzy methodology for frequency response estimation of uncertain dynamic systems

Fuzzy frequency response: definition and analysis for uncertain dynamic systems is proposed in this paper. In terms of transfer function, the uncertain dynamic system is partitioned into several linear sub‐models and organized according to Takagi–Sugeno fuzzy representation. The main contribution of this paper is to demonstrate through the proposal of a Theorem that fuzzy frequency response is a boundary in the magnitude and phase Bode plots. Low‐ and high‐frequency analysis of fuzzy dynamic model is obtained by varying the frequency ω from zero to infinity. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust distributed MPC for load frequency control of uncertain power systems

Reliable Load frequency control (LFC) is crucial to the operation and design of modern electric power systems. However, the power systems are always subject to uncertainties and external disturbances. Considering the LFC problem of a multi-area interconnected power system, this paper presents a robust distributed model predictive control (RDMPC) based on linear matrix inequalities. The proposed algorithm solves a series of local convex optimization problems to minimize an attractive range for a robust performance objective by using a time-varying state-feedback controller for each control area. The scheme incorporates the two critical nonlinear constraints, e.g., the generation rate constraint (GRC) and the valve limit, into convex optimization problems. Furthermore, the algorithm explores the use of an expanded group of adjustable parameters in LMI to transform an upper bound into an attractive range for reducing conservativeness. Good performance and robustness are obtained in the presence of power system dynamic uncertainties.     

Implementation of the local reference node concept for spatially distributed circuits

Large spatially distributed microwave and millimeter‐wave systems involve the interaction of linear and nonlinear circuits with their electromagnetic environment. Here a circuit‐level approach to the modeling of circuit‐field interactions is developed. ©1999 John Wiley & Sons, Inc. Int J RF and Microwave CAE 9: 376–384, 1999     

互联电力系统鲁棒分布式模型预测负荷频率控制

负荷频率控制是现代互联电力系统运行的重要保障.本文针对含有不确定因素和负荷扰动的多区域互联电力系统提出了一种基于线性矩阵不等式参数可调节的鲁棒分布式预测控制算法.设计各个区域控制器目标函数引入相邻区域的状态变量和输入变量,同时考虑发电机变化速率约束和阀门位置约束,将求解一组凸优化问题转化成线性矩阵不等式求解,得到各个区域的控制律,在线性矩阵不等式中引入一组可调参数,将优化一个上限值转化成优化吸引区,降低算法的保守性.仿真结果验证了该算法在负荷扰动、系统参数不确定和结构不确定性情况下具有鲁棒性.     

Learning-based frequency response function estimation for nonlinear systems

In this paper, we perform the nonlinear frequency response function (FRF) estimation for a class of nonlinear systems. Two non-parametric estimation techniques are considered: radial basis function neural network (RBF-NN)-based estimation and support vector machine (SVM)-based estimation. Based on the system's available observations, the proposed estimation models are used to predict its frequency response. Simulation results are provided to demonstrate the model implementation. Finally, a comparative study is carried out to evaluate the effectiveness of the RBF-NN and SVM schemes, which has demonstrated that the SVM outperformed RBF-NN in the FRF estimation.     

Multi‐layer distributed protocols for robust cooperative tracking in interconnected nonlinear multiagent systems

We develop a mixed graph and optimal control theoretic formulation to design a robust cooperative control protocol for a large‐scale multiagent system with partially known interconnected first‐, second‐, or mixed first‐ and second‐order dynamics. In each case, we transform the control protocol design task to a robust communication graph design problem, which, from a cyber‐physical perspective, is interpreted as the control layer design problem for an interconnected system with unknown agent layer dynamics. According to this viewpoint, each state variable has its own control layer communication topology separate from the other state variable's communication topology and the unknown agent layer interconnection topologies. We prove that all cooperative, decentralized, and centralized tracking protocols can be treated as a single design problem and, by deriving closed‐form solutions for the robust control layer topologies, we further provide a simpler design procedure, which is only based on the matrix manipulations. Aside from the linear implementation of the protocol and the connection of the proposed formulation to the well known rules‐of‐thumb in optimal control theory, this creates a higher potential to transfer ideas to industry. Modeling uncertainties tolerable by a given control layer topology is analyzed, and a preliminary performance‐oriented analysis and design approach for large‐scale interconnected systems is discussed. We show that exactly the same steps can be followed to design appropriate control layers for both tracking and stabilization.     

A parametric frequency response method for non-linear time-varying systems

A new parametric frequency response algorithm is introduced to investigate linear and non-linear dynamic systems with time-varying parameters. In the new algorithm the time-varying parameters are regarded as additional inputs of the systems and the non-linear generalised frequency response functions for multi-input-single-output systems are then employed to obtain Zadeh's system functions from a differential equation representation. The parametric frequency response method reveals how the time-varying parameters affect the behaviour of the systems through a time-varying term. The new method can be applied to both linear and non-linear time-varying systems.     

开放分布系统中局部信任度计算方法研究*

针对现有的局部信任度计算方法忽视了交互经验的时效性及充分性等问题, 提出一种证据理论框架下的局部信任度计算方法, 该方法采用了时效因子计算函数来区分不同时间内的交互经验在局部信任度计算中的重要性;同时,采用了半梯形函数来区分基于不同交互经验计算得到的局部信任度的有效性。实验分析表明,该方法对实体行为改变有较强的敏感性,能有效地降低对各种恶意实体的局部信任度。     

Adaptive open loop control for a class of distributed parameter systems

The real time implementation of closed loop control laws obtained by the minimization of a quadratic criterion with finite time intervals is a difficult problem, if we consider computing time and the eventual determination of the state variables. It would seem useful therefore to define, for complex systems such as distributed parameter systems, a control type which unites the advantages of open loop control, with its relative simplicity of implementation, and those of closed loop control, with its ability to reduce perturbations. It is for this reason that we use the principle of adaptive open loop control. In this paper, we describe the principles of such a method and results obtained from one example studied by numerical computation or hybrid simulation in real time.     

Stabilization of interconnected dynamical systems by online convex optimization

The problem of stabilizing networks of interconnected dynamical systems (NDS) in a scalable fashion is considered. As the first contribution, a generalized lemma and example network are provided to demonstrate that state‐of‐the‐art, tractable dissipation‐based NDS stabilization methods can fail even for simple unconstrained, linear, and time‐invariant dynamics. Then, a solution to this issue is proposed, in which controller synthesis is decentralized via a set of parameterized storage functions. The corresponding stability conditions allow for max‐type construction of a trajectory‐specific Lyapunov function for the full closed‐loop network, whereas neither of the local storage functions is required to be monotonically converging. The provided approach is indicated to be nonconservative in the sense that it can generate converging closed‐loop trajectories for the motivating example network and a prescribed set of initial conditions. For input‐affine NDS and quadratic parameterized storage functions, the synthesis scheme can be formulated as a set of low‐complexity semidefinite programs that are solved online, in a receding horizon fashion. Moreover, for linear and time‐invariant networks, an even simpler, explicit control scheme is derived by interpolating a collection of a priori generated converging state and control trajectories in a distributed fashion. Copyright © 2012 John Wiley & Sons, Ltd.     

Output frequency response function of nonlinear Volterra systems

An expression for the output frequency response function (OFRF), which defines the explicit analytical relationship between the output spectrum and the system parameters, is derived for nonlinear systems which can be described by a polynomial form differential equation model. An effective algorithm is developed to determine the OFRF directly from system simulation or experimental data. Simulation studies demonstrate the significance of the OFRF concept, and verify the effectiveness of the algorithm which evaluates the OFRF numerically. These new results provide an important basis for the analytical study and design of a wide class of nonlinear systems in the frequency domain.     

Optimisation and adaptation of synchronisation controllers for networked second-order infinite-dimensional systems

ABSTRACT

The adaptation and optimisation of synchronisation control for networked second-order distributed parameter systems are considered. The objective is to design output feedback controllers guaranteeing agreement between the states of the N systems that individually track a reference model. The controller structure involves feedback terms consisting of the pairwise difference of the measurements of the second-order systems as well as coupling terms that enforce consensus. Placing the closed-loop networked systems in aggregate form allows for further optimisation of the synchronisation gains. Using the aggregate systems ‘closed-loop energy’ as a suitable optimisation measure, the search for the synchronisation gains reduces to the minimisation of the optimisation index, which eventually is described by the trace of the solution to a parameterised Lyapunov operator equation. Considering the adaptation of the synchronisation gains offers an alternative to optimisation. The adaptation is based on Lyapunov redesign-methods and utilises a parameter-dependent Lyapunov functional to extract them. Due to its structure, all network topology information is handled at the local level, thereby relaxing the graph topology conditions in the adaptive case. Numerical studies are included to provide an insight on the effects of synchronisation control of networked second-order distributed parameter systems.     

Dual-rate sampled-data systems. Some interesting consequences from its frequency response analysis

The main goal of this contribution is to introduce a new procedure in order to analyse properly SISO dual-rate systems (DRS) and to provide straightforward answers to some common general questions about this kind of systems. Frequency response analysis based on DRS lifting modelling can lead to interesting results about stability margins or performance prediction. As a novelty, it is explained how to understand DRS frequency response and how to handle it for an easy computation of magnitude and phase margins keeping classical frequency domain methods. There are also some repetitive questions about DRS that can be analysed and answered properly using the results from this contribution: what the optimum relation between sampling periods is or what effects does delay have in a DRS. Every step is illustrated with examples that should clarify the understanding of the text.     

Optimal control of switched distributed parameter systems with spatially scheduled actuators

In many areas of control there are gaps between the existing theory and applications. This is more so in hybrid infinite dimensional systems and in particular hybrid systems in which both the actuator and the controller are switched. The main objective of this paper is to start filling in one of these gaps. We present a theoretical formulation and provide methodologies for implementing optimal and switching policies of spatially scheduled actuators for a class of distributed parameter systems (DPS). The optimization method employed is based on finite horizon LQR optimal control. Well posedness and optimality, pertaining to the switching policies of spatially scheduled actuators, are presented and proven. Tutorial examples motivated by thermal manufacturing applications along with extensive simulation results of the proposed actuator-plus-controller switching scheme are presented.     

Verification of distributed control systems in intelligent manufacturing

This paper presents an application of formal methods for validation of flexible manufacturing systems controlled by distributed controllers. A software tool verification environment for distributed applications (VEDA) is developed for modeling and verification of distributed control systems. The tool provides an integrated environment for formal, model-based verification of the execution control of function blocks following the new international standard IEC61499. The modeling is performed in a closed-loop way using manually developed models of plants and automatically generated models of controllers.     

Fault detection for discrete spatially interconnected systems with time-delay over finite frequency domains

This paper investigates the problem of fault detection observer design for discrete spatially interconnected time-delay systems (SITSs) in finite frequency range. Firstly, a delay-dependent generalised Kalman–Yakubivich–Popov (GKYP) lemma for SITSs is proposed. Then, by the giving GKYP lemma, a distributed fault detection observer design method can be derived by solving a set of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.