Showing papers in "IEEE Transactions on Automatic Control in 1978"

Survey of decentralized control methods for large scale systems

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

Computing integrals involving the matrix exponential

Abstract: A new algorithm for computing integrals involving the matrix exponential is given. The method employs diagonal Pade approximation with scaling and squaring. Rigorous truncation error bounds are given and incorporated in a Fortran subroutine. The computational aspects of this program are discussed and compared with existing techniques.

Feedback control of flexible systems

Abstract: Feedback control is developed for the class of flexible systents described by the generalized wave equation with damping. The control force distribution is provided by a number of point force actuators and the system displacements and/or their velocities are measured at various points. A feedback controller is developed for a finite number of modes of the flexible system and the controllability and observability conditions necessary for successful operation are displayed. The control and observation spillover due to the residual (uncontrolled) modes is examined and the combined effect of control and observation spillover is shown to lead to potential instabilities in the closed-loop system. Some remedies for spillover, including a straightforward phase-locked loop prefilter, are suggested to remove the instability mechanism. The concepts of this paper are illustrated by some numerical studies on the feedback control of a simply-supported Euler-Bernoulli beam with a single actuator and sensor.

Stable adaptive controller design--Direct control

Abstract: This paper deals with the design of stable adaptive controllers using a model reference approach. A systematic procedure is developed using the concept of positive realness and is generalized to arbitrarily located coutrol parameters. For plants with n poles and (\geq)(n-2) zeros, the uniform asymptotic stability in the large of the adaptive loop is demonstrated. For plants with (\leq)(n-3) zeros the stability problem is clawed and is stated as a conjecture. Simulation studies of the adaptive control of both stable and unstable plants are included towards the end of the paper.

Convergence analysis of parametric identification methods

Abstract: A certain class of methods to select suitable models of dynamical stochastic systems from measured input-output data is considered. The methods are based on a comparison between the measured outputs and the outputs of a candidate model. Depending on the set of models that is used, such methods are known under a variety of names, like output-error methods, equation-error methods, maximum-likelihood methods, etc. General results are proved concerning the models that are selected asymptotically as the number of observed data tends to infinity. For these results it is not assumed that the true system necessarily can be exactly represented within the chosen set of models. In the particular case when the model set contains the system, general consistency results are obtained and commented upon. Rather than to seek an exact description of the system, it is usually more realistic to be content with a suitable approximation of the true system with reasonable complexity properties. Here, the consequences of such a viewpoint are discussed.

Stability criteria for large-scale systems

Abstract: Recent research into large-scale system stability has proceeded via two apparently unrelated approaches. For Lyapunov stability, it is assumed that the system can be broken down into a number of subsystems, and that for each subsystem one can find a Lyapunov function (or something akin to a Lyapunov function). The alternative approach is an input-output approach; stability criteria are derived by assuming that each subsystem has finite gain. The input-output method has also been applied to interconnections of passive and of conic subsystems. This paper attempts to unify many of the previous results, by studying linear interconnections of so-called "dissipative" subsystems. A single matrix condition is given which ensures both input-output stability and Lyapunov stability. The result is then specialized to cover interconnections of some special types of dissipative systems, namely finite gain systems, passive systems, and conic systems.

Tracking methods in a multitarget environment

Abstract: The objective of this paper is to survey and put in perspective the existing methods of tracking in multitarget environment. In such an environment the origin of the measurements can be uncertain: they could have come from the target(s) of interest or clutter or false alarms or be due to the background. This compact and unified presentation of the state-of-art in multitarget tracking was motivated by the recent surge of interest in this problem. It is also hoped to be useful in view of the need to adapt and modify existing techniques before using them for specific problems. Particular attention is paid to the assumptions underlying each algorithm and its applicability to various situations.

Observer design for linear systems with unknown inputs

Abstract: Results from the geometric theory of linear systems are utilized to present a constructive solution to the problem of designing a Luenberger observer to evaluate a given set of linear functions of the state of a linear system subject to unknown or disturbance inputs

Stabilizability, detectability, and spectrum assignment for linear autonomous systems with general time delays

Abstract: A general linear autonomous system with both discrete and distributed delays in state and control variables is considered and an open-loop stabilizability problem is posed. It is proven that a simple algebraic rank condition, similar to the well-known Hautus condition, is necessary for open-loop stabilizability. This condition is also shown to be sufficient by constructing a proper stabilizing state feedback. The detectability problem for systems with general state and output delays is proven to be dual to state-feedback stabilizability of a transposed system with state and control delays. If the delays appear in control variables only the state-feedback spectrum assignability is equivalent to formal controllability of a certain pair of real matrices and, equivalently, to system state controllability.

Model reduction using the Routh stability criterion

Abstract: A new method of model reduction is introduced based on the Routh stability criterion. The reduced order transfer function is determined directly from elements in the Routh stability arrays of the high-order denominator and numerator. An eighth order example illustrates the accuracy of the method, the preservation of the frequency response and computational simplicity. The method is equally applicable to unstable systems.

On feedback stabilization of time-varying discrete linear systems

Abstract: Results are given for stabilizing time-varying discrete linear systems by means of a feedback control stemming from a receding-horizon concept and a minimum quadratic cost with a fixed terminal constraint. The results parallel those recently obtained for continuous-time systems [8] and extend a well-known method of Kleinman for stabilizing discrete fixed linear systems [7].

Singular optimal control problems

Abstract: For the last 30 years the optimization of nonsingular control problems has been an Important part of control engineering, and its mathematical theory is well developed and widely known. On the other hand, singular control problems prove more difficult to analyse and—although necessary conditions for optimality of singular controls have been established over the past decade—It is only recently that sufficient, and necessary and sufficient, conditions have been formulated. The purpose of this book Is to collect together all known results in optimal control theory (as well as appropriate computational methods) which can be applied to the singular problems In optimal control and which up to now have been scattered In numerous journals. Complete and self-contained, the volume begins with an historical survey of singular control problems and leads to the presentation of important, recent results in the field. There are specific real-world applications and the authors discuss those avenues of research which require further Investigation. All those involved In the optimization of dynamical systems will welcome the publication of this book. In addition to advanced students, lecturers and research workers in universities, this will include practising mechanical, chemical and electrical engineers, builders, textile technologists, paper scientists and chemists, and many concerned with non-technical fields such as economics and business management Contents An historical survey of singular control problems Introduction. Singular control in space navigation. Method of Mlele via Green's theorem. Linear systems—quadratic cost Necessary conditions for singular optimal control. Sufficient conditions and necessary and sufficient conditions for optimality. References. Fundamental concepts Introduction. The general optimal control problem. The first variation of J. The second variation of J. A singular control problem. References. Necessary conditions for singular optimal control Introduction. The generalized Legendre-Clebsch condition. Jacobson's necessary condition. References. Sufficient conditions and necessary and sufficient conditions tor non-negativity of nonsingular and singular second variations Introduction. Preliminaries. The nonsingular case. Strong positivlty and the totally singular second variation. A general sufficiency theorem for the second variation. Necessary and sufficient conditions for non-negativity of the totally singular second variation. Necessary conditions for optimality. Other necessary and sufficient conditions. Sufficient conditions for a weak local minimum. Existence conditions for the matrix Rlccati differential equation. Conclusion. References. Computational methods for singular control problems Introduction. Computational application of the sufficiency conditions of theorems in the previous chapter. Computation of optimal singular controls. Joining of optimal singular and non-singular sub-arcs. Conclusion. References. Conclusion The Importance of singular optimal control problems. Necessary conditions. Necessary and sufficient conditions. Computational methods. Switching conditions. Outlook for the future Author index. Sublect index.

Greatest common divisor via generalized Sylvester and Bezout matrices

Abstract: We present new methods for computing the greatest common right divisor of polynomial matrices. These methods involve the recently studied generalized Sylvester and generalized Bezoutian resultant matrices, which require no polynomial operations. They can provide a row proper greatest common right divisor, test for coprimeness and calculate dual dynamical indices. The generalized resultant matrices are developments of the scalar Sylvester and Bezoutian resultants and many of the familiar properties of these latter matrices are demonstrated to have analogs with the properties of the generalized resultant matrices for matrix polynomials.

Eigenvalue/eigenvector assignment using output feedback

Abstract: The problem of pole-assignment in a linear time-invariant multivariable system using output feedback is considered. New sufficient conditions are derived to assign an almost arbitrary set of min (n,m+r- 1) distinct eigenvalues, where n, m , and r are the number of states, inputs, and outputs, respectively. The analysis also highlights the freedom in selection of closed-loop eigenvectors which can be used for response shaping.

Leader-follower strategies for multilevel systems

Abstract: Sequential strategies for dynamic systems with multiple decision makers and multiple performance indices are surveyed and reviewed. These strategies are generalizations of Stackelberg or leader-follower strategies for two-person games. The review includes structures with one coordinator and several second-level decision makers, and linear hierarchical structures with only one decision maker at each level Several information structures are considered.

Optimization by decomposition and coordination: A unified approach

Abstract: In the general framework of inifinite-dimensional convex programming, two fundamental principles are demonstrated and used to derive several basic algorithms to solve a so-called "master" (constrained optimization) problem. These algorithms consist in solving an infinite sequence of "auxiliary" problems whose solutions converge to the master's optimal one. By making particular choices for the auxiliary problems, one can recover either classical algorithms (gradient, Newton-Raphson, Uzawa) or decomposition-coordination (two-level) algorithms. The advantages of the theory are that it clearly sets the connection between classical and two-level algorithms, It provides a framework for classifying the two-level algorithms, and it gives a systematic way of deriving new algorithms.

Design of variable structure model-following control systems

Abstract: A new design concept for adaptive model-following control systems capable of shaping the error transient responses is developed using the theory of variable structure systems and sliding mode. It is shown that the resulting model-following control system exhibits adaptive properties inherent in adaptive model-following systems designed by existing methods. An aircraft control problem which has been approached using various model-following techniques is considered and a performance comparison with the present design is made.

Control strategies for decision makers using different models of the same system

Abstract: Situations in which strategies of various decision makers are designed using different models of the same system are a characteristic of large-scale system practice. For interconnected systems with slow and fast dynamics we develop a design algorithm which takes into account such multimodel situations. Conditions for the validity of this approximate design are formulated and illustrated by a power system example.

A microprocessor system for multifunctional control of upper-limb prostheses via myoelectric signal identification

Abstract: The paper deals with the problem of controlling artificial limbs in cases where several limb functions require control. These situations are of importance, especially to above-elbow upper-extremity amputees. Here, classical EMG (myoelectric) controllers have failed in the past, since they were based on only determining existence or nonexistence of an EMG signal. Recent work by Lyman et al. at UCLA has approached this multifunctional (MF) control problem via using a large number of electrodes, though still considering only a limited part of the EMG spectrum. The present approach is based on earlier work by Graupe et al. [4], considering the whole spectrum of the EMG signal via identifying its time series model such that several limb functions can be controlled from a single signal site. However, the present work subsequently employs parallel filtering to discriminate between the various limb functions of interest to achieve fast discrimination and control as required for practical applications, since this allows the identification itself to be performed off line. Real-time on-line results are presented in the paper, as recently obtained from tests carried out on a 1969 Vietnam above-elbow amputee who had most severe (90 percent) nerve and muscle loss at his stump, and could therefore not use more than one or two electrode pairs. The results, where complete discrimination was achieved within 0.15 to 0.2 seconds using 8-bit Intel 8080 microprocessors at double precision (incorporating hardware multipliers), have yielded an 85 percent success rate in discrimination between four to five limb functions using a single electrode pair. It is noted that the amputee mentioned had no previous EMG actuation training whatsoever.

Realization and stabilization of 2-d systems

Abstract: During recent years several state-space models concerning discrete 2-D systems (systems with two time parameters) have appeared in the literature. These are used, for example, in image processing. To these models are attached the names of Attasi [1], Fornasini-Marchesini [2], Givone-Roesser [3]. In this paper it is shown that all these models are special cases of a new model which is a straightforward generalization of the 1-D case. Under certain conditions the existence of a stabilizing feedback is shown. In the last part connections with [4] are made.

A canonical parameter space for linear systems design

Abstract: A canonical parameter space is introduced for linear time-invariant, discrete-time systems design. All observable and controllable linear systems of a given order are shown to share one stability domain in this space. This invariance of the stability domain is shown to be fundamental to the solution of the gain output-feedback stabilizability problem and other significant linear systems design problems. The geometric properties of the stability domain are investigated. Its convex hull is shown to be a simplex. Our approach is compared to the D -decomposition, the root-locus, and other methods. Its advantages over these methods in attacking the problem of stabilizability by gain output-feedback and other important problems are discussed.

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

Abstract: The composite-system method for analyzing stability of large-scale system is studied focusing on the quadratic-order theorems using M -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.

Partial differential equations and finite difference methods in image processing--Part II: Image restoration

Abstract: Application of Partial Differential Equation (PDE) models for restoration of noisy images is considered. The hyperbolic, parabolic, and elliptic classes of PDE's yield recursive, semirecursive, and nonrecursive filtering algorithms. The two-dimensional recursive filter is equivalent to solving two sets of filtering equations, one along the horizontal direction and other along the vertical direction. The semirecursive filter can be implemented by first transforming the image data along one of its dimensions, say Column, and then recursive filtering along each row independently. The nonrecursive filter leads to Fourier domain Wiener filtering type transform domain algorithm. Comparisons of the different PDE model filters are made by implementing them on actual image data. Performances of these filters are also compared with Fourier Wiener filtering and spatial averaging methods. Performance bounds based on PDE model theory are calculated and implementation tradeoffs of different algorithms are discussed.

On delayed sharing patterns

Abstract: A counterexample is given to a conjectured separation result for delayed sharing patterns when the delay is at least two units. The conjecture is proved to be true for a unit delay.

Extended Levinson and Chandrasekhar equations for general discrete-time linear estimation problems

Abstract: Recursive algorithrms for the solution of linear least-squares estimation problems have been based mainly on state-space models. It has been known, however, that recursive Levinson-Whittle-Wiggins-Robinson (LWR) algorithms exist for stationary time-series, using only input-output information (i.e, covariance matrices). By introducing a way of classifying stochastic processes in terms of an "index of nonstationarity" we derive extended LWR algorithms for nonstationary processes We show also how adding state-space structure to the covariance matrix allows us to specialize these general results to state-space type estimation algorithms. In particular, the Chandrasekhar equations are shown to be natural descendants of the extended LWR algorithm.

Optimal location of measurements for distributed parameter estimation

Abstract: The problem of optimal measurement locations for state estimation in linear distributed parameter systems is considered. It has previously been shown that the optimal sensor location problem for distributed systems can be posed as an optimal control problem for a system described by the infinite-dimensional matrix Riccati equation for the filter covariance. A more efficient approach based on an upper bound of the filter covariance is developed in the present study. The relationship between the present approach and that of minimizing a measure of the filter covariance is studied. A detailed example is considered, and the results of the two approaches are compared.

Bilinear system identification by Walsh functions

Abstract: A new technique, which uses a finite orthonormal expansion to approximate input and output functions, is proposed for file identification of a class of nonlinear systems. Walsh functions form the basis of the expansions as a consequence of their useful properties here. That is, the parameter estimation problem is reduced to algebraic form by Fine's relationship for the integral of Walsh functions [1], by the operational matrix concept of Chen and Hsiao [2], and by the very desirable group properties of Walsh functions [3]. Computational examples are presented to illustrate the utility of this method. The availability of Walsh-function programs makes the method particularly amenable to practice.

On norm bounds for algebraic Riccati and Lyapunov equations

Abstract: New lower bounds on the spectral norms of the positive definite solutions to the continuos and discrete algebraic matrix Riccati and Lyapunov equations are derived. These bounds are much easier to compute than previously available bounds and appear to be considerably tighter in many cases.

Theory and error analysis of vibrating-member gyroscope

Abstract: There is a general class of gyroscopic instruments that use a vibrating member as the sensitive element. Instruments in this class are governed by the differential equations \ddot{x} + \Omega^{2}x - c\omega\dot{y} = 0 \ddot{y} + \Omega^{2}y - c\omega\dot{x} = 0 which describe the position of a reference point on the vibrating member relative to a coordinate system fixed in the instrument case. The point (x,y) moves in an elliptical orbit with poriod 2\pi/\Omega . The orbit precesses at a rate -c\omega/2 (with c \leq 2 ) relative to the coordinate system and, hence, tends to remain fixed in inertial space. The differential equations for the orbital elements ( a =semimajor axis b =semiminor axis, φ=inclination, and \theta =orbital angle) are derived for a nonideal gyroscope with damping and anisoelasticity present. The difforential equations for the long-term effects are obtained by averaging the coefficients over the approximate period of oscillation. These equations can he transformed into a fourth-order system of linear differential equations with constant coefficients in the average energy and angular momentum, and their derivatives. These equations are solved explicitly for several cases of practical interest and the results are interpreted physically.