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Showing papers in "International Journal of Systems Science in 1990"


Journal ArticleDOI
TL;DR: Employing the joint entropy, instead of the conditional entropy, to characterize the overhead, results in a symmetrical overhead and also permits the decomposition of the system capacity, or complexity, into components useful in following the response of the whole system to perturbations.
Abstract: Recent work by one of the authors has identified the average mutual information and the conditional entropy as two measures from information theory that are useful in quantifying the system organization and incoherence, respectively. While the scaled average mutual information, or network ascendency, is inherently symmetrical with respect to inputs and outputs, the scaled conditional entropy, or overhead, remains asymmetrical. Employing the joint entropy, instead of the conditional entropy, to characterize the overhead, results in a symmetrical overhead and also permits the decomposition of the system capacity, or complexity, into components useful in following the response of the whole system to perturbations.

262 citations


Journal ArticleDOI
TL;DR: In this article, the controllability and observability grammars in limited time and frequency intervals are used for model reduction in stable and unstable systems, and a near-optimal model reduction procedure is proposed.
Abstract: The controllability and observability gramians in limited time and frequency intervals are studied, and used for model reduction. In balanced and modal coordinates, a near – optimal reduction procedure is used, vielding the reduction error (norm of the different between the output of the orginal system and the reduced model) almost minimal. Several examples are given to illustrate the concept of model reduction in limited time or/and frequency intervals, for continuous- and discrete-time systems, as well as stable and unstable systems. In modal coordinates, the reduced model obtained from a stable system is always stable. In balanced coordinates it is not necessarily true, and stability conditions for the balanced reduced model are presented. Finally, model reduction is applied to advanced supersonic transport and a flexible truss structure.

237 citations


Journal ArticleDOI
TL;DR: In this article, a forward regression algorithm based on an orthogonal decomposition of the regression matrix is employed to select a suitable set of radial basis function centers from a large number of possible candidates.
Abstract: This paper investigates the identification of discrete-time non-linear systems using radial basis functions. A forward regression algorithm based on an orthogonal decomposition of the regression matrix is employed to select a suitable set of radial basis function centers from a large number of possible candidates and this provides, for the first time, fully automatic selection procedure for identifying parsimonious radial basis function models of structure-unknown non-linear systems. The relationship between neural networks and radial basis functions is discussed and the application of the algorithms to real data is included to demonstrate the effectiveness of this approach.

150 citations


Journal ArticleDOI
TL;DR: In this paper, the pole location of a perturbed matrix A+E is investigated and sufficient conditions for robust stability of a class of perturbed discrete systems are derived. But the case of a diagonalizable matrix A is not considered.
Abstract: This paper deals with the pole location of a perturbed matrix A + E. Two perturbation classes are discussed: one with structured perturbations |E| ≤ U (a given non-negative matrix) and one where only the spectral norm ||E|| is given. Sufficient conditions are derived for the eigenvalues of A + E to be located within a circle C(α, r). The case of a diagonalizable matrix A is also considered and a sufficient condition for robust stability of a class of perturbed discrete systems is derived. Numerical examples are presented for illustration.

49 citations


Journal ArticleDOI
TL;DR: In this paper, some useful theorems for the sensitivity analysis of priority that is playing an important role in the analytic hierarchy process are derived from the principle of hierarchical composition which is expressed in the form of a reachability matrix.
Abstract: The analytic hierarchy process (AHP) initialed by Saaty (1980) has recently been attracting attention as a useful support method for multi-objective decision making. This paper presents some useful theorems for the sensitivity analysis of priority that is playing an important role in the AHP. These theorems are derived from the principle of hierarchical composition which is expressed in the form of a reachability matrix. Using the theorems, we can easily calculate the degrees of effects caused by local or global changes in the priorities of some criteria, and also we can examine the possibility of rank reversal among alternatives. Furthermore, by applying these theorems to a dwelling selection problem, this paper verifies their effectiveness.

48 citations


Journal ArticleDOI
TL;DR: In this article, an inventory model with partial backlogging was developed, which defined the demand rate at a particular instant as a function of the amount of orders already backlogged at that instant of time.
Abstract: Very few researchers have considered inventory models with partial backlogging. The models developed earlier considered a fraction of demand to be backordered while the remaining fraction is lost during the stock out period. In this paper we have developed an inventory model with partial backlogging, redefining the demand rate at a particular instant as a function of the amount of orders already backlogged at that instant of time. Infinite replenishment rate and zero lead time are assumed. Expressions for optimum order quantity and optimuim value of maximum inventory are obtained by minimizing the total system costs. The model is illustrated with a numerical example, including sensitivity analysis with respect to the backlogging parameter.

42 citations


Journal ArticleDOI
Duan Li1
TL;DR: In this paper, a general separable class of stochastic multiobjective optimization problems with perfect state information is considered and a generating approach using a Stochastic Multiobjective Dynamic Programming method is developed to find the set of non-inferior solutions.
Abstract: A general separable class of stochastic multiobjective optimization problems with perfect state information is considered. A generating approach using a stochastic multiobjective dynamic programming method is developed to find the set of non-inferior solutions. The results reveal the variation of the optimal weighting coefficient vector along a non-inferior trajectory. Non-separability is not an inherent property of dynamic programming. A general class of non-separable dynamic problems can be transformed into corresponding separable multiobjective dynamic programming problems. Multiobjective dynamic programming is shown to be a separation strategy to solve non-separable dynamic programming.

36 citations


Journal ArticleDOI
TL;DR: A new class of observers for non-linear uncertain dynamical systems is proposed that is able to estimate the system's state regardless of the realization of the uncertainty.
Abstract: A new class of observers for non-linear uncertain dynamical systems is proposed. The non-linearity and uncertainty in the systems are assumed to be bounded. The bound is however unknown. Adaptive schemes are designed for the estimation of the bound. The observer, based on this estimation, is then able to estimate the system's state regardless of the realization of the uncertainty.

34 citations


Journal ArticleDOI
TL;DR: In this article, two new algorithms for identification and model reduction of stable linear continuous systems are proposed, based on the weighted impulse response gramians (Agathoklis and Sreeram 1988 b).
Abstract: Two new algorithms for identification and model reduction of stable linear continuous systems are proposed, based on the weighted impulse response gramians (Agathoklis and Sreeram 1988 b). In identification, the model parameters are obtained from the solution of a linear system of equations with coefficients obtained from the numerical evaluation of the weighted impulse response gramians. The reduction technique is based on retaining part of the original weighted impulse response gramians obtained as the solutions to the Lyapunov equation for the original system in controllability canonical form. This yields different stable models for different values of the weighting factor. The model corresponding to zero weighting factor matches the impulse response norm of the original system and its derivatives exactly. Finally, the method is illustrated by a numerical example and is compared with well-known balanced realization techniques.

34 citations


Journal ArticleDOI
TL;DR: The effectiveness of systems dynamics as a methodology for modelling, simulating and analysing real-life systems can be significantly increased if it is extended to deal with imprecise and vague variables or events.
Abstract: Systems dynamics has been used to model and simulate a variety of environments, e.g. economic, social and political, which require quantification or some types of human behaviour. The lack of empirical verification of the relationships in the systems dynamics models has often been criticised. Nevertheless, the methodology is effective in dealing with time-varying (dynamic) interactions among components of the analysed system. The effectiveness of systems dynamics as a methodology for modelling, simulating and analysing real-life systems can be significantly increased if it is extended to deal with imprecise and vague variables or events. Such an extension requires: (1) treatment of imprecise and vague input variables as fuzzy variables: (2) use of fuzzy arithmetic in the level, rate and auxiliary equations when fuzzy numbers are involved; and (3) replacement of some of the relationships in the systems dynamics models either with conditional statements including fuzzy variables, or with fuzzy algorithms.

29 citations


Journal ArticleDOI
TL;DR: In this article, the structure at infinity of non-linear closed-loop systems locally undergoing sliding regimes about a smooth surface defined in state space is examined, and the stability properties of this internal behaviour model are studied.
Abstract: In this article we examine the structure at infinity of non-linear closed-loop systems locally undergoing sliding regimes about a smooth surface defined in state space. By using a locally diffeomorphic state coordinate transformation, associated with the relative degree of the system, one obtains a normal form exhibiting the basic internal dynamic structure of the controlled system. It is found that the local existence of sliding motions demands a considerably simple local structure at infinity of the original non-linear system. The ideal sliding dynamics in local sliding surface coordinates is shown to coincide precisely with the zero dynamics. The stability properties of this internal behaviour model are studied. Several illustrative examples are presented.

Journal ArticleDOI
A. S. C. Sinha1
TL;DR: In this article, it is shown that exponential stability can be achieved by a suitable choice of state feedback controls of large-scale systems with infinite delay, and that a Lyapunov functional can be constructed by using certain results from J. K. Hale's Theory of Functional Differential Equations.
Abstract: The problem of stabilizing a class of large-scale non-linear infinite delay systems is considered. It is shown that exponential stability can be achieved by a suitable choice of state feedback controls of large-scale systems with infinite delay, and that a Lyapunov functional can be constructed by using certain results from J. K. Hale's Theory of Functional Differential Equations (1977).

Journal ArticleDOI
TL;DR: A frequency-domain approach to derive stable reduced-order models for a stable linear discrete-invariant system is presented based on combining the Schwarz approximation with the bilinear transformation.
Abstract: A frequency-domain approach to derive stable reduced-order models for a stable linear discrete-invariant system is presented. The method is based on combining the Schwarz approximation with the bilinear transformation. An efficient algorithm that avoids the bilinear transformation is derived by which the bilinear Schwarz discrete models are derived directly in the z-domain. The state-space bilinear Schwarz approximation is also presented by which the lower-order time-domain model matrices are derived by suitable truncation of the original system matrices in the bilinear Schwarz canonical form. The aggregation matrix relating the original system and reduced model state vectors is also derived. A numerical example is included to illustrate the method.

Journal ArticleDOI
TL;DR: In this paper, an especially simple parity vector method is denned; in this method, the redundant measurement relations are derived using a prediction of the state and the output of the system.
Abstract: An especially simple parity vector method is denned; in this method, the redundant measurement relations are derived using a prediction of the state and the output of the system. The parity vector is a linear combination of the redundant measurement; in the absence of failure, it is only a function of redundant measurement noise, but in the presence of failure, it deviates from the normal value. The generalized likelihood ratio test is used to detect the character of the parity vector and to declare the failure component.

Journal ArticleDOI
TL;DR: In this paper, an adaptive controller for multi-input multi-output (MIMO) systems is presented, which is able to modify repeatedly the control variables between successive output measurements, making the proposed approach particularly appealing for the control of composition products of distillation columns when expensive and slow chromatographs are used.
Abstract: An adaptive controller for multi-input multi-output (MIMO) systems is presented, which is able to modify repeatedly the control variables between successive output measurements. This feature makes the proposed approach particularly appealing for the control of composition products of distillation columns when expensive and slow chromatographs are used. The control algorithm is derived by minimizing the predicted error signal, as well as the control increments, over a future control horizon which is suitably selected. Applications to a simulated non-linear model of a binary distillation column demonstrate the effectiveness of the proposed method.

Journal ArticleDOI
TL;DR: A class of large-scale non-separable problems is considered, where the overall objective function is not of an additive form with respect to subsystems and a three-level methodology is developed, which decomposes the overall large- scale problem into smaller subproblems and reaches the optimal solution in an iterative way.
Abstract: A class of large-scale non-separable problems is considered, where the overall objective function is not of an additive form with respect to subsystems. The non-separable optimization problem is embedded in a corresponding multiobjective separable optimization problem. A theoretical grounding is established for the original problem's optimal solution, which is attained by a non-inferior solution of the corresponding multiobjective separable optimization problem. A three-level methodology, which decomposes the overall large-scale problem into smaller subproblems and reaches the optimal solution in an iterative way, is also developed.

Journal ArticleDOI
TL;DR: In this article, a sliding mode attitude control law is derived for slewing of the space vehicle and a stabilizer is designed based on the asymptotically decoupled system describing the elastic deflections in two orthogonal planes.
Abstract: A control system design is presented for large angle rotational manoeuvres of a spacecraft-beam-tip body (an antenna or a reflector) configuration. Although this approach is applicable to three-axis manoeuvres, for simplicity only single-axis control is treated here. It is assumed that an unknown but bounded disturbance torque acts on the spacecraft. A sliding mode attitude control law is derived for slewing of the space vehicle. This slewing control law requires only the attitude error and its derivative for feedback. It does not need any information on the elastic motion of the system. For the damping of the elastic motion, a stabilizer is seperately designed based on the asymptotically decoupled system describing the elastic deflections in two orthogonal planes. Simulation results are presented to show that precise large rotational manoeuvres can be performed using an attitude controller and elastic mode stabilizer in spite of the uncertainty in the system.

Journal ArticleDOI
TL;DR: In this paper, sufficient conditions are obtained for the asymptotic stability of the trivial solution of the competition system and this result is used for the derivation of sufficient conditions for the global asymPT stability.
Abstract: Sufficient conditions are obtained for the asymptotic stability of the trivial solution of and this result is used for the derivation of sufficient conditions for the global asymptotic stability of the positive equilibrium of the competition system

Journal ArticleDOI
TL;DR: In this paper, a generalization of the vector-matrix is introduced, and the array algebra is constructed, which generalizes the various concepts in the conventional vectormatrix theory.
Abstract: In order to develop a new analysis technique for distributed parameter systems (DPS), the array that is a generalization of the vector-matrix is introduced, and the array algebra is constructed, which generalizes the various concepts in the conventional vector-matrix theory. A wide class of DPS is approximately transformed into array dynamical systems by use of the finite element method or the finite difference method. In the array system formulation, the spatial structure of the DPS is preserved, and the formulation is accordingly suitable for the utilization of the spatial-state-distribution pattern (SSDP), which is in a sense the essence of the DPS, to the control. An array optimization problem for an array dynamical system is formulated, and the necessary optimality condiiion is derived by use of the array algebra. The linear quadratic (LQ) problem for a linear array dynamical system is investigated, and the resultant optimal control is the array version of the well-known LQ optimal control a...

Journal ArticleDOI
Li D. Xu1
TL;DR: In this paper, the problem of employing linguistic variables to rank alternatives across a set of criteria is investigated, with emphasis placed on modelling the decision-maker's reasoning process, and a fuzzy mathematical model is employed to represent this sort of linguistic evaluation and synthesis, which can be employed in expert systems for making inferences on multi-criteria problems.
Abstract: The problem of employing linguistic variables to rank alternatives across a set of criteria is investigated, with emphasis placed on modelling the decision-maker's reasoning process. Given a set of alternatives, decision-makers often do not make conclusions immediately, instead evaluating them in the light of a given set of criteria and then synthesizing the knowledge obtained from the evaluation. Both evaluation and synthesis are usually expressed linguistically rather than numerically. A fuzzy mathematical model is employed to represent this sort of linguistic evaluation and synthesis. An example is presented to illustrate the basic idea and technique. This example is also used to compare the proposed technique with another existing technique. The model can be employed in expert systems for making inferences on multi-criteria problems.

Journal ArticleDOI
TL;DR: In this paper, a necessary and sufficient condition for the observability or detectability of a continuous-time time-invariant linear system (CILS) to be preserved after discretization is presented.
Abstract: On assuming that a continuous-time time-invariant linear system (CFLS) is reachable or stabilizable, a necessary and sufficient condition is presented that the discrete-time time-invariant linear system resulting from the hold equivalence approximation to the CILS is also reachable or stabilizable. The studies are based on the eigenvalues and eigenspaces of the adjoint A∗ of the system matrix A and the kernel of the adjoint B∗ of the input matrix B appearing in the CILS. A necessary and sufficient condition for the observability or detectability of a CILS to be preserved after discretization is also sought.

Journal ArticleDOI
TL;DR: In this paper, the authors considered linear discrete-time dynamical systems x k+1 =Ax k +c k with constrained inputs c k ∈ Ω, for which the matrix A possesses the property of leaving a proper cone K + positively invariant.
Abstract: Linear discrete-time dynamical systems x k+1 =Ax k +c k with constrained inputs c k ∈Ω, for which the matrix A possesses the property of leaving a proper cone K + positively invariant, i.e. AK + ⊂K + . Necessary and sufficient conditions guarantee that a non-empty set D(K; a, b)⊂R n , obtained from the intersection of translated proper cones, is positively invariant for motions of the system. Both the homogeneous and inhomogeous cases are considered. It is shown how the results presented can be used to solve the saturated state feedback regulator problem

Journal ArticleDOI
TL;DR: A technique is presented for estimating the reachable set from the asymptotically-stable origin of a class of n-dimensional linear systems under bounded control, an optimal version of a Lyapunov method and provides an (over-)estimate of the full Reachable set.
Abstract: The reachable set from a given point of a controlled dynamical system is the set of all states to which the system can be driven from that point in a finite time by the allowed controls. A technique is presented Tor estimating the reachable set from the asymptotically-stable origin of a class of n-dimensional linear systems under bounded control. The technique is an optimal version of a Lyapunov method, and provides an (over-)estimate of the full reachable set; it involves the minimization of a quadratic constraint, followed by the maximization of a quadratic form subject to this constraint. The non-linear optimization problems can be routinely solved by means of computer algebra and commonly available computer software. In general, the technique produces a much-improved estimate of the reachable set compared to that given by the standard Lyapunov method. Another advantage of the technique is that it is truly applicable to higher-dimensional systems (n ≥ 3). Since the estimate produced is in the convenien...

Journal ArticleDOI
TL;DR: In this paper, the stabilization of large structural systems (LSS) under (i) mode truncation and linear parametric perturbations, or (ii) mode-traction and actuator saturations is considered.
Abstract: The stabilization of large structural systems (LSS) under (i) mode truncation and linear parametric perturbations, or (ii) mode truncation and actuator saturations is considered. A new robust stability condition for the perturbed LSS controlled by observer-based compensators is derived. A stability criterion is also given for the stabilization of LSS by observer-based constrained controls. Finally, a simply supported beam problem is provided for illustration.

Journal ArticleDOI
TL;DR: In this article, reachability conditions are developed for discrete single-input-single-output variable structure control systems described by linear mathematical models in general state-space form to reach a switching function from anywhere in state space.
Abstract: Reachability conditions are developed for discrete single-input-single-output variable structure control systems described by linear mathematical models in general state-space form to reach a switching function from anywhere in state space. Stability conditions of a sliding mode are investigated. A modified algorithm is proposed to simplify the design procedure. Practical application to a thermal process has been achieved by using the modified algorithm to show the potential for development and practical results are compared with those using the classical PID controller design.

Journal ArticleDOI
TL;DR: In this paper, a non-linear inversion and pole assignment is used to control an elastic robotic arm of two links based on nonlinear inverses and poles assignment for stabilization.
Abstract: This paper considers control of an elastic robotic arm of two links based on non–linear inversion and pole assignment for stabilization. The design is performed in two steps. First, based on non-linear inversion, a non–linear controller is designed for the trajectory control of the joint angles using joint torquers. The inverse controller accomplishes trajectory control of the joint angles, this excites the elastic modes of the arm. In order to damp the elastic oscillations, a stabilizer is designed for a linearized system about the terminal state using the pole assignment technique. In the closed–loop system, first the inverse controller acts when a command is given, and the stabilizer automatically switches when the joint angle trajectory enters a specified neighbourhood of the final commanded position. Simulation results are presented to show that in the closed–loop system accurate joint angle trajectory tracking and elastic mode stabilization can be accomplished in spite of payload uncertainty in the ...

Journal ArticleDOI
TL;DR: In this article, the authors derived the Cayley-Hamilton theorem to show that Ackermann's formula for the pole-placement problem of SISO systems can be extended to the case of a class of MIMO systems.
Abstract: The matrix Cayley-Hamilton theorem is first derived to show that Ackermann's formula for the pole-placement problem of SISO systems can be extended to the case of a class of MIMO systems. Moreover, the extended Ackermann formula newly developed by the authors is employed for fast determination of the desired feedback gain matrix for a general MIMO system with an appropriate artificial input. The proposed method will enhance the application of state-space pole-placement concepts to a general class of multivariable control systems.

Journal ArticleDOI
TL;DR: In this article, a perturbation measure is found which guarantees that all the poles of a perturbed continuous system will stay inside a circle with radius r and center at α, α> r < 0, on the real axis.
Abstract: A perturbation measure is found which guarantees that all the poles of a perturbed continuous system will stay inside a circle with radius r and centre at — α, α > r > 0, on the real axis. Bounds are then formulated for different subregions in the complex plane. The bounds are obtained by using the general Lyapunov matrix equation.

Journal ArticleDOI
TL;DR: This paper presents one of the very important applications of the multimodel con-trot technique, which enables the use of linear control theory to applications in non-linear complex processes.
Abstract: This paper presents one of the very important applications of the multimodel con-trot technique. This type of control enables us to extend the use of linear control theory to applications in non-linear complex processes. The process under control is modelled by several linear models around different points and modes of operation. During the application, the right model is selected among the available set of models and is used to generate suitable control signals which enable the process to track certain desired trajectories. This controller is built by the use of a microcomputer interfaced with a non-linear thermal process where the inside temperature and humidity are the controlled variables. The results of a real-time application to this process are given.

Journal ArticleDOI
TL;DR: In this article, a technique to design stabilizing state feedback controllers for linear discrete-time systems subject to possibly time-varying parametric uncertainties is presented, where stability considerations rely on the second method of Lyapunov, and an upper bound is derived for the cost of the controlled uncertain system with respect to a designer chosen quadratic cost function.
Abstract: A technique to design stabilizing state feedback controllers is presented for linear discrete-time systems subject to possibly time-varying parametric uncertainties. Conditions imposed on the uncertainties are less stringent than those found in the cited literature. The controller design procedure is based on the solution of a Riccati-like algebraic matrix equation. Stability considerations rely on the second method of Lyapunov, To evaluate the system's performance degradation due to uncertainty, an upper bound (guaranteed cost) is derived for the cost of the controlled uncertain system with respect to a designer chosen quadratic cost function. Two examples are given.