Showing papers in "International Journal of Control in 1982"
TL;DR: Considering linear time-invariant distributed feedback systems, a necessary and sufficient condition for robust stability is derived with respect to plant perturbations belonging to a specified ball with design limitations imposed by plant uncertainties.
Abstract: Considering linear time-invariant distributed feedback systems, a necessary and sufficient condition for robust stability is derived with respect to plant perturbations belonging to a specified ball. The conclusion is shown to exhibit design limitations imposed by plant uncertainties.
287 citations
TL;DR: It is shown then that a non-singular linear transformation of the instruments gives a new and still consistent estimate.
Abstract: Consistency conditions for instrumental-variable methods applied to Hammerstein models are derived and analysed. It is necessary to have a model that is not over-parametrized and an input that is ‘ strongly persistently exciting ’, i.e. the inputs and their powers are jointly persistently exciting. Some specific choices of the instruments are proved to give consistency. Those instruments are formed as filtered inputs and powers of the input. Consistency can be guaranteed if either the input is white noise or if a certain transfer function is positive-real. The vector of instruments is, in general, of larger dimension than the parameter vector. It is shown then that a non-singular linear transformation of the instruments gives a new and still consistent estimate. Some simulations using the IV variants proposed in this paper are also included.
152 citations
TL;DR: An algorithm is suggested for the computation of a linear state feedback for a single input system such that the resultant closed-loop system has specified eigenvalues.
Abstract: An algorithm is suggested for the computation of a linear state feedback for a single input system such that the resultant closed-loop system has specified eigenvalues. The algorithm is more efficient than many comparable techniques, and has some desirable numerical properties. It is closely related to the QR algorithm for the eigenproblem, and extends to descriptor systems.
143 citations
TL;DR: In this article, the observability of autonomous discrete time systems is studied from a purely differential geometric point of view, and a proposal for the generalization of an invariant subspace is made.
Abstract: In this paper the observability of autonomous discrete time systems is studied from a purely differential geometric point of view. As with continuous time systems, this approach leads to a local canonical form for an observable system. A proposal for the generalization of an invariant subspace is made.
131 citations
TL;DR: In this article, it was shown that for a certain class of stable linear delay systems, one can estimate the decay rate of the solution of a linear delay system by a simple computation.
Abstract: In this paper it is shown that for a certain class of stable linear delay systems we can obtain an estimate of the decay rate of the solution by a simple computation.
119 citations
TL;DR: In this paper, the authors investigated the accuracy of the compensated least squares (CLS) method and proved that the estimates are asymptotically gaussian distributed. And they also showed that a commonly used instrumental variable method gives a better accuracy than the CLS method.
Abstract: The least-squares method in system identification leads generally to biased parameter estimates. A conceptually simple modification is to estimate the bias and to compute compensated parameter estimates. When white output noise is the only disturbance this principle (compensated least squares, CLS) can readily be used to obtain consistent estimates. The main purpose of the paper is to investigate the accuracy of the parameter estimates obtained when the CLS method is used. It is proved that the estimates are asymptotically gaussian distributed. An explicit expression for the covariance matrix is given. It is also shown that a commonly used instrumental variable method gives (asymptotically) better accuracy than the compensated least-squares method.
109 citations
TL;DR: In this paper, a method for designing an observer for the state of a linear time-invariant system with unknown inputs is presented, and the observer equation can be derived from the maximum uncontrollable subspace of the original system with the aid of a left inverse for a transposed linear system.
Abstract: A method is presented for designing an observer for the state of a linear time-invariant system with unknown inputs. The structure algorithm developed by Silverman is applied to obtain the observer which estimates the maximum estimable subspace of the state. It is shown that the observer equation can be derived from the maximum uncontrollable subspace of the original system with the aid of a left inverse for a transposed linear system. This leads us to the necessary and sufficient condition for the existence of a state observer. An application to the insensitivity observer synthesis is also included.
92 citations
TL;DR: In this article, the use of special row and column operations in the reduction of a rational matrix to its Smith-MacMillan form at infinity is investigated, and connections between this reduction procedure and the valuation approach are established.
Abstract: The use of special row and column operations in the reduction of a rational matrix to its Smith-MacMillan form at infinity is investigated. The connections between this reduction procedure and the valuation approach are established. A graphical method for finding the Smith-MacMillan form of a rational matrix at infinity from its Bode magnitude array, and some new results on realization theory for polynomial matrices are presented.
89 citations
TL;DR: In this article, a procedure for the construction of a reduced-order Luenberger observer for a linear time-invariant system subjected to immeasurable input disturbances is presented.
Abstract: Using the simplest matrix generalized inverse, the {l}-inverse, a procedure is developed for the construction of a reduced-order Luenberger observer for a linear time-invariant system subjected to immeasurable input disturbances. Illustrative examples are included.
83 citations
TL;DR: An adaptive control scheme, based on the LQ control solution, is proposed, and the stability of the resulting adaptively controlled system and conditions for a good tracking are studied.
Abstract: The paper studied the problem of the adaptive tracking of a reference signal by the output of any deterministic discrete SISO linear system with unknown parameters. An adaptive control scheme, based on the LQ control solution, is proposed. The stability of the resulting adaptively controlled system and conditions for a good tracking are studied. Several simulations illustrate the proposal.
81 citations
TL;DR: In this article, it was shown that a sufficiently large class of incentive games with perfect or partial dynamic information admits an optimal incentive scheme that is affine in the available information, and explicit expressions for these affine incentive schemes are obtained.
Abstract: Through a geometric approach, it is shown that a sufficiently large class of incentive (Stackelberg) problems with perfect or partial dynamic information admits optimal incentive schemes that are affine in the available information. As a byproduct of the analysis, explicit expressions for these affine incentive schemes are obtained, and the general results are applied to two different classes of Stackelberg game problems with partial dynamic information.
TL;DR: In this article, the most commonly used modal reduction techniques are represented by means of signal flow diagrams connecting inputs and state variables, and each method is then analyzed to determine key characteristics, i.e. steady-state agreement, initial-value agreement, independence of the reduced model on the choice of retained state variables and inputs.
Abstract: Six of the most commonly-used modal reduction techniques are represented by means of signal flow diagrams connecting inputs and state variables. In this representation, the derivation and the cross-comparison of the various methods are greatly facilitated. Each method is then analysed to determine key characteristics, i.e. (i) steady-state agreement, (ii) initial-value agreement, (iii) independence of the reduced model on the choice of retained state variables and inputs, and (iv) eigen vector orientation. Realistic, large-scale systems are used to evaluate the static and dynamic characteristics of each model reduction method numerically. These studies reveal some important, and often unrecognized, weaknesses of several traditional techniques and confirm the strength of the newly-developed technique of Litz.
TL;DR: In this paper, it was shown that the well-known diagonal dominance condition associated with Rosenbrock's stability theorems is unnecessary and can be replaced by a less restrictive generalized diagonal dominance conditions.
Abstract: This paper shows that the well-known diagonal dominance condition associated with Rosenbrock's stability theorems is unnecessary and can be replaced by a less restrictive generalized diagonal dominance condition. Similar results are derived for generalized block diagonally dominant systems. Whenever possible graphical interpretations are given to facilitate the implementation of these ideas in computer aided design packages.
TL;DR: This paper presents a synthesis technique for linear time invariant n×n multiple-input-multiple-output (MIMO) feedback systems with constrained ‘ plant’ P, and output feedback, whose solutions are guaranteed to solve the original MIMO problem.
Abstract: This paper presents a synthesis technique for linear time invariant n×n multiple-input-multiple-output (MIMO) feedback systems with constrained ‘ plant’ P, and output feedback. Due to uncertainty, P is known only to be a member of a set &𝒫 = {P}. It is required for all Pep, the n2 system transfer functions tuv be members of specified sets of acceptable outputs a uv;; u. v+ 1, [tdot] n. The problem is rigorously converted into a number of single-input-single output (SISO) uncertainty problems, whose solutions are guaranteed to solve the original MIMO problem. The technique has several advantages over previous ones : (1) fixed point theory is not needed to rigorously justify the theory—the justification is very simple ; (2) there is significantly less overdesign inherent in the method ; and (3) if arbitrary small sensitivity is desired over arbitrary large bandwidth, then the set p must satisfy certain constraints as 8→∞. It is shown that these constraints are inherent in all linear time invariant compensat...
TL;DR: In this method, any positive integer can be chosen as the number of sub-intervals and much computing time and storage can be saved, and the recursive algorithms developed also make it possible to identify on-line the parameters of bilinear systems.
Abstract: Problems of analysis and parameter estimation of bilinear systems via block-pulse functions are discussed, and recursive algorithms convenient for computers are presented. Compared with Walsh function approaches, the results are much simpler in form. In this method, any positive integer can be chosen as the number of sub-intervals. Consequently, much computing time and storage can be saved, and the recursive algorithms developed also make it possible to identify on-line the parameters of bilinear systems.
TL;DR: The conditions given in this paper guarantee the stability of the error between the plant output and the reference sequence and the validity of the theoretical results is demonstrated by numerical examples.
Abstract: This paper considers the stability of a model reference adaptive control system with input amplitude constraints. The conditions given in this paper guarantee the stability of the error between the plant output and the reference sequence. The validity of the theoretical results is demonstrated by numerical examples.
TL;DR: In this article, a rational transfer function model of the plant is proposed for feedback systems with high plant uncertainty, where only plan input and output data are available over finite, sometimes incomplete, time intervals.
Abstract: A rational transfer function model of the plant is generally desirable in feedback system design, when only plan input and output data are available over finite, sometimes incomplete, time intervals. This is especially so in a recent exact design technique for highly uncertain time-varying and non-linear plants. Here, the plants are replaced rigorously by an equivalent linear time-invariant plant set. Existing numerical techniques were found inadequate, especially in the high-frequency range, which is important in the design of feedback systems with large plant uncertainty. A technique was developed with excellent results, even for noisy data, unstable and non-minimum phase plants and severely truncated time intervals. The transfer function is calculated directly, without derivation of the input, output signal transforms. The operations involve repeated integrations of the data. Numerous examples are included.
TL;DR: In this paper, structural controllability results for matrix pairs [A, B] where A = A 0 + Σ μ iAi, B = B 0 + σ μ i, Bi, with the Ai, Bi, fixed, and the μ i, free scalar parameters were established.
Abstract: We establish structural controllability results for matrix pairs [A, B] where A = A 0 + Σ μ iAi , B = B 0 + σ μ i, Bi , with the Ai , Bi , fixed, and the μ i , free scalar parameters The results characterize structural controllability in several ways, via tests involving the checking of the rank or the evaluation of the determinant of various constant matrices formed from the Ai , Bi A number of the results used as intermediate results tests for a full rank property of matrix nets, ie tests that check if M = M0+ ΣμiMi prescribed, μ i variable, has full rank for almost all μ i
TL;DR: In this paper, a modification of the classical interpolation procedure was proposed for the stabilization of a single input-output plant, with uncertainly in the gain factor by means of an asymptotically stable control and feedback sensor.
Abstract: This paper is a sequel to an earlier work in which we applied classical Novnnlinna-Pick interpolation to the stabilization of a single input-output plant, with uncertainly in the gain factor by means of an asymptotically stable control and feedback sensor. In this present work, we show that for the proper design we need a modification of the classical interpolation procedure, a point not clearly brought out in our previous paper.
TL;DR: In this paper, several approaches to estimating the parameters of a continuous-time model of a multivariable system from samples of input and output observations arc discussed, including indirect methods where a discrete time model is first obtained from the input-output data and then transformed into a continuous time model, as well as direct methods where the continuous time models are obtained straight from the samples of the observations.
Abstract: Several approaches to estimating the parameters of a continuous-time model of a multivariable system from samples of input and output observations arc discussed. These include indirect methods where a discrete-time model is first obtained from the input-output data and then transformed into a continuous-time model, as well as direct methods where the continuous-time model is obtained straight from the samples of the observations. An example is used to compare the methods.
TL;DR: In this paper, a Lyapunov-e direct method is used to find stabilizing state feedback laws for systems with uncertain state or control matrices, where the uncertainties are modelled as sector bounded non-linearities, and feedback laws ensuring global asymptotic closed loop stability are obtained using LyAPunov'e direct methods.
Abstract: Existence criteria and computational methods are presented for finding stabilizing state feedback laws for systems with uncertain state or control matrices. The uncertainties are modelled as sector bounded non-linearities, and feedback laws ensuring global asymptotic closed loop stability are obtained using Lyapunov'e direct method. The algorithms essentially amount to repeatedly solving a parameter dependent Riccati equation until the maximal solution becomes positive definite.
TL;DR: Simulation results obtained for a realistic traffic situation on a 30 km long motorway are discussed both from an algorithmical and a traffic control engineering viewpoint.
Abstract: Optimal motorway traffic control strategies are derived on the basis of a highly accurate, non-linear, discrete dynamical traffic flow model. By application of these strategies, traffic can be driven back to its nominal state condition in a prescribed optimal manner after occurrence of a severe disturbance. Because of the high order of the optimal traffic control problem, four known decomposition methods arc applied, in order to reduce the computational effort needed for its solution. Simulation results obtained for a realistic traffic situation on a 30 km long motorway are discussed both from an algorithmical and a traffic control engineering viewpoint.
TL;DR: In this paper, a method for approximating high order stable systems via lower order stable models is presented, which is an improvement over previous Routh-Pade methods since the denominator polynomial of the model transfer function, even if based on the elements of a Routh array, contains two free parameters.
Abstract: A method for approximating high order stable systems via lower order stable models is presented. It is an improvement over previous Routh-Pade methods since the denominator polynomial of the model transfer function, even if based on the elements of a Routh array, contains two free parameters. A systematic procedure is illustrated for evaluating, besides the numerator coefficients, such denominator parameters in order to ensure a good fit, in the Pade sense, and a suitable stability margin.
TL;DR: In this paper, a simple procedure for obtaining stabilization of a class of continuous and discrete linear systems subjected to control structure constraints is presented, giving more attention to the so-called decentralized control.
Abstract: In this paper we present a simple procedure for obtaining stabilization of a class of continuous and discrete linear systems subjected to control structure constraints, giving more attention to the so-called decentralized control. Contrary to the continuous case where much work has been done, the solution presented here for the discrete case is one of the first to be presented. Some examples are treated and, for the continuous case, some comparisons are made with other methods found in the literature.
TL;DR: In this article, necessary and sufficient conditions of asymptotic stability independent of delay of a certain class of both the retarded and neutral types of delay differential systems are obtained and the stability conditions reduce to positivity of a quartic equation.
Abstract: In this paper necessary and sufficient conditions of asymptotic stability independent of delay of a certain class of both the retarded and neutral types of delay differential systems are obtained. The stability conditions reduce to positivity of a quartic equation. Conditions for the latter in explicit form are given by the authors in an earlier publication. In addition, sufficient conditions for stability for a general order delay differential system independent of delay are also obtained. Such conditions are ascertained from the fact that a sufficient condition for any algebraic equation to have no positive real roots, is that all its coefficients be positive.
TL;DR: It will be shown by means of some counterexamples that these assumptions cannot be relaxed unless additional restrictions are introduced and how the parsimony principle should be used when estimating the parameters of regression models by the least squares method is presented.
Abstract: The parsimony principle is frequently used in system identification on more or less heuristical grounds. Recently, a formal proof of this principle has been given. Here the assumptions used in that proof are examined to some extent. It will be shown by means of some counterexamples that these assumptions cannot be relaxed unless additional restrictions are introduced. A result showing how the parsimony principle should be used when estimating the parameters of regression models by the least squares method is also presented.
TL;DR: In this article, the conditions for existence and characterization of fixed modes in decentralized multivariable control systems employing local controllers are investigated and the necessary and sufficient conditions for a system polo at s = λ to be a fixed mode are investigated.
Abstract: This paper investigates the conditions for existence and the characterization of fixed modes in decentralized multivariable control systems employing local controllers. It is shown that for scalar local controllers in the diagonal control structure, the necessary and sufficient condition for a system polo at s= λ to be a fixed mode is that s= λ be a transmission zero of all subsystems formed by selecting the same inputs and outputs of the system. The results are applied to scalar controllers in any arbitrary control structure and also to non-scalar local controllers and similar conditions are obtained. Examples are discussed for illustration.
TL;DR: In this paper, the design of both analogue and digital set-point tracking controllers can be readily effected on the basis only of structural plant properties which are directly derivable from the plant transfer function matrices.
Abstract: It is shown that, for a large class of multivariable plants, the design of both analogue and digital set-point tracking controllers can be readily effected on the basis only of structural plant properties which are directly derivable from the plant transfer function matrices. This general design methodology is illustrated by designing both an analogue and a digital set-point tracking controller for a boiler furnace
TL;DR: A unified description of several so-called fast, algorithms used to derive least-squares ladder algorithms in the filter and the predictor forms and an easy derivation of the ‘ exact ’ instrumental variable ladder algorithm which, to the authors' knowledge, has not previously been described in the literature.
Abstract: We propose a unified description of several so-called fast, algorithms. The projection operator technique is used to derive least-squares ladder (or lattice) algorithms in the filter and the predictor forms. This technique, usually associated with orthogonal projection operations, is extended to oblique projections. The first application is an easy derivation of the ‘ exact ’ instrumental variable ladder algorithm which, to our knowledge, has not previously been described in the literature. A second application is a new derivation, based on the operator technique, of an algorithm for the fast calculation of gain matrices for recursive estimation schemes.
TL;DR: In this paper, a new geometric method of calculating multivariable system zeros and zero directions is presented by considering a particular choice of state feedback control law, motivated by the study of variable structure systems in the sliding mode.
Abstract: A new geometric method of calculating multivariable system zeros and zero directions is presented by considering a particular choice of state feedback control law. This control law has been motivated by the study of variable structure systems in the sliding mode. The cases of singular and non-singular CB have been treated separately.