Analysis Of Large-scale Systems Research Articles

Large-scale systems analysis using approximate inverse models

Recent work by El-Attar and Vidyasagar for stabilizing a large-scale unstable multivariable system by stable decentralized feedback are reformulated in terms of approximations to the plant inverse. The approach has the advantage that the resulting stabilization conditions can very often be satisfied by the use of high-gain feedbacks.

A New Comparison Principle for the Stability Analysis of Complex Systems

A new comparison, extension of Matrozov's approach for the stability analysis of dynamical systems is established.To construct the comparison system vector valued functions whose maximum component is positive definite Instead of vector positive functions are used. In the proposed comparison principle the state vector of the studied system can appear explicitly as a variable in Wazewski's type inequality, thus increasing the flexibility of the approach. Algebraic criteria for uniform asymptotic and exponential stability of nonlinear comparison systems are also established. Finally, a decomposition scheme is proposed to facilitate the application of the method to the stability analysis of large-scale systems.

A Unified Approach for Load-Flow and Short-Circuit Analysis of Large-Scale Underground Distribution Systems

Large underground distribution networks have special features which can be used in developing efficient simplified methods for load-flow and short-circuit calculations. The paper presents a non-iterative method for load-flow and short-circuit analysis, equivalencing the AC system by two equivalent DC networks. When compared with the conventional Newton-Raphson method, the savings in storage requirements are around 75%. In addition, the same matrices used in load-flow calculations can be used for contingency analysis (primary feeder outage) and for symmetrical short-circuit calculations. The new method has been verified by simulation of five systems (9, 22, 63, 191 and 307 nodes). The last three form part of the Sao Paulo City underground distribution system. The results have been compared with the solutions obtained using the Newton-Raphson load-flow program and the impedance method for short-circuit calculations. No significant discrepancies have been observed. The method presented can be used, when necessary, in conjunction with a two-level approach to solve the complete circuit (primary and secondary). Sparse techniques make it possible to handle large networks, both for load-flow and short-circuit analysis. The sparse inverse matrix method used in the short-circuit calculations, when compared with the impedance matrix methods ordinarily used, requires less computer storage and is faster. Primary feeder outages have been simulated by compensation.

Subsystem simplification in large-scale systems analysis

A new procedure for stabilizing an unstable system by stable feedback is presented. The procedure is based on using lower order model for the given system. Stabilization conditions for the original system are given in terms of the error in the approximatipon. The procedure is extended to large-scale systems whereby stabilization conditions with decentralized feedback are presented.

An Evaluation Method for Environmental-Systems Planning: An Alternative Utility Approach

This paper is concerned with constructing a comprehensive standard for evaluating regional environmental systems. Because such systems are composed of complex natural, economic, and social systems, conventional engineering and economic methods are virtually ineffective for this purpose. Systems-analysis methods appear suited to providing proper evaluation as well as effective control of environmental systems. But, in applying systems analysis to environmental evaluation, we are faced with the problem of measuring numerically the level of satisfaction of the region's residents. Environmental systems are very large in scale, and the components (attributes) which contribute to quality of life are not only many and various but often conflict with each other. In addition they are not commensurable. Therefore new methodologies for evaluating environmental systems must be developed. In such complex large-scale systems analyses, it is necessary, whatever the method used, to structure objectives by means of decomposition and ordering, and the construction of a preference hierarchy is an effective way to perform this structuring. The utility approach to decision analysis is employed to choose the best solutions under this interactive procedure. However, environmental systems also permit, to some extent, the possibility of mathematical formulation in a more rigorous form. Shadow prices (dual optimal variables) are good criteria for evaluating a constrained system's performance. We provide some devices (1) to utilize dual variables obtained in mathematical programming, (2) to nest them into multiattribute utility functions in a hierarchical system, (3) to articulate value trade-offs, and (4) to clarify priorities among objectives. These four procedures constitute the nested Lagrangian-multiplier method.

Problems in Large-Scale Social Economic Systems

This paper attempts to show how complexity can defeat the analysis, prediction and control of large-scale dynamic systems. Some characteristics and facets of complexity are explored, and three research strategies are discussed which lead to a satisfactory treatment of complexity in dynamic systems. The research strategies relate to (i) the control-theoretic, hierarchical approach, (ii) the design-oriented, algebraic approach, (iii) models using catastrophe theory. The virtues of these approaches are compared, and some practical difficulties in dealing with complex systems are discussed.

Survey of decentralized control methods for large scale systems

This paper surveys the control theoretic literature on decentralized and hierarchical control, and methods of analysis of large scale systems.

Stability of large-scale nonlinear systems--Quadratic-order theory of composite-system method using M-matrices

The composite-system method for analyzing stability of large-scale system is studied focusing on the quadratic-order theorems using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -matrices. Here, by the term "composite-system method", we refer to the method to decompose a large-scale system into smaller subsystems and to make two-step analysis (i.e., first to analyze subsystems and second to combine the results to reduce the property of the whole). Theories about Lyapunov stability and about input-output stability are described from a unified standpoint and their mutual relation is clarified. As an application, multi-input multi-output systems. The contents are generally useful for stability analysis of large-scale nonlinear systems.

&amp;lt;tex&amp;gt;L_{2}&amp;lt;/tex&amp;gt;-stability of large-scale dynamical systems: Criteria via positive operator theory

A new approach to the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -stability analysis of large-scale dynamical systems, described as interconnections of several subsystems, is presented. By conducting this study within the framework of positive operator theory, stability criteria, which impose explicit and distinct conditions on the subsystems and the interconnections, are obtained. Some strong points of the main result of the paper are: 1) it is simpler to apply than the existing results and 2) it specializes to the classical "positivity theorem" for the case of single-loop negative feedback systems. Modifications of this result which permit the use of arbitrary multipliers are also outlined.

Evaluation and Control of Regional Environmental Systems in the Yodo River Basin: Socio-Economic Aspects

For analysis of large-scale environmental systems in the industrialized Yodo River basin area, a hierarchical multilevel system with many noncommensurable goals is formulated. A regional welfare function is derived in terms of the utility function in each region. For this purpose, a preference hierarchy corresponding to an objective hierarchy is constructed. In the process of deriving individual utility functions as components of the multiattribute utility functions, mathematical optimization technique is utilized. The shadow prices (Lagrangian multipliers), which combine with the constraints, will provide the relative measures for effectiveness of environmental control. The values should be transformed to the concept of utilities, which composes the basic terms for decision analysis. For derivation of the consistent “prices”, the mathematical models can be further decomposed in possible cases of modeling. Along with methodological discussion, some computational results are presented. Equity of income distribution is also taken into consideration. Priorities of problems to be confronted in making policies for the improvement of environmental quality are sought out in the preference-hierarchical system; further, a reformation plan of the industrial structure in these regions is proposed.

Multilevel stabilization of large-scale systems: A spinning flexible spacecraft

Multilevel stabilization schemes for high order linear systems are proposed in the framework of the decomposition-aggregation method used so far for stability analysis of large-scale systems by vector Liapunov functions. In one scheme, the output feedback is applied and the control parameters are determined for low order subsystems to produce a stable aggregate model for the overall system. When system inputs are decentralized such that each subsystem has a distinct input, and states are available for control, another scheme is proposed which has a multilevel structure with local and global controllers. Both stabilization schemes are aimed at the maximization of structural parameters which couple the subsystems. An 11th-order linear model of a spinning flexible spacecraft is stabilized by the proposed decomposition-aggregation method using both the passive and the active stabilization devices. The method can take advantage of the special structural features of the model to provide the best estimate of the stability region for a salient parameter which couples the wobble and the spin motion of the spacecraft.

Passivity Methods in the Input-Output Stability and Instability of Large-Scale Systems

A new approach to the L2-stability and L2-instability analysis of large-scale dynamical systems, described as an interconnection of several subsystems, is presented. Criteria which involve explicit and distinct passivity conditions on the subsystems and certain algebraic constraints on the interconnections are given. These are simpler and more general than the existing results for the stability and instability of large-scale systems and further have the following additional features: (i) they permit directly the use of arbitrary multipliers and (ii) they generalize some of the classical results for the stability and instability of single-loop negative feedback systems.

General Stability Analysis of Large-Scale Systems

Liapunov like conditions for asymptotic stability of singularly perturbed dynamic systems are established, which are used as a basis to link singular perturbation approach and vector Liapunov function approach to the stability analysis of singularly perturbed large-scale systems.New aggregation techniques are developed that essentially relax conditions on largescale systems, which can be singularly perturbed.The criteria are established for asymptotic stability of an invariant product set that can be time-invariant or time-varying. In a special case it can contain only the equilibrium state. The general results are illustrated by numerical examples and by an application to singularly perturbed large-scale systems.

Large Scale Control Problems in Electric Power Systems

The main large-scale control problems in electric power system operation, from optimal aliocation of generation and transmission resources to network state estimation, frequency and exchange power control, system stability and dynamic security, are illustrated and the methods presently used to solve them are recalled. Special attention is given to significant applications of decomposition by physical decoupling and relaxation or by time-division, of decentralized controls, of coordination and hierarchies, with a brief mention of large-scale system analysis areas open to further development.

On vector Lyapunov functions for stochastic dynamical systems

Vector Lyapunov functions are used in the stability analysis of large-scale stochastic systems described by Itô differential equations (with stochastic disturbances in the subsystems and in the interconnecting structure). Sufficient conditions for asymptotic stability and exponential stability with probability 1 and in probability are established, in all cases the objective is the same: to analyze large-scale systems in terms of their lower order (and simpler) subsystems and in terms of their interconnecting structure. Use of the method presented makes it often possible to circumvent difficulties usually encountered when the Lyapunov method is applied to high-dimensional systems and to systems with complicated interconnecting structure. In order to demonstrate the usefulness of the present approach, a specific example is considered.

The Use of Stochastic Models for Large-Scale System Research and Control

The use of stochastic models for solving problems of large-scale system control, operations research and system analysis is proposed. Special attention is paid to normal models the use of which extends known techniques of linear system theory to a wide class of large-scale systems. Basic principles of designing normal models for queueing systems are developed. The results of some queueing system study using normal models are discussed. The statement of the problem of identification of a complex system by a stochastic differential equation model is given.

Stabilization of Large-Scale Systems: A Spinning Flexible Spacecraft

Stabilization of high-order constant systems by multilevel control is proposed in the framework of the decomposition-aggregation method for stability analysis of large-scale systems. An 11-order linear model of a spinning flexible spacecraft is stabilized by the method using both the passive and the active stabilization devices. The method can take advantage of the special structural features of the model to provide the best estimate of the stability region for an important parameter which couples the wobble and the spin motion of the spacecraft.

Non-Lyapunov stability analysis of large-scale systems on time-varying sets

Non-Lyapunov stability analysis of time-dependent non-linear large-scale systems of arbitrary order and structure presented in the paper develops algebraic conditions for various types of practical and finite-time stability of the systems and provides information about trajectory bounds. The stability properties are studied on products of time-varying sets. The conditions guarantee the corresponding stability property of the overall system to be implied by practical stability or finite-time stability of all subsystems. Moreover, under the conditions the overall system possesses the smiw settling time as its subsystems. Application of the aggregation-decomposition approach to the stability analysis reduces the dimension of the overall system aggregate matrix to the number of subsystems. Examples are worked out to illustrate results.

Stability analysis of large-scale systems with stable and unstable subsystems

Sufficient conditions are given for both exponential and asymptotic stability of time-varying non-linear large-scale systems composed of stable and unstable subsystems. Sign-negative coupling among the subsystems, which can be of arbitrary order and interconnected in arbitrary fashion, is allowable. Under the conditions the required stability property of the overall system is implied by the stability properties of all its subsystems and global features of their interactions. The interactions can be expressed in terms of time-varying, sign-indefinite functions rather than only in terms of time-invariant positive definite functions. Three examples are worked out to illustrate application of- the results.

Asymptotic stability and instability of large-scale systems

The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations. With minor technical adjustments, the theory is broadened to include considerations of unstable subsystems as well as instability of composite systems.