Showing papers on "Discrete time and continuous time published in 1983"
TL;DR: In this article, a general existence and uniqueness theorem for the solution of such a system is proved and used in the rigorous derivation of exact discrete models satisfied by the various types of data.
Abstract: This paper is concerned with the efficient estimation of structural parameters in closed linear systems of higher order stochastic differential equations when the data are in discrete form and the model generally includes both stock and flow variables. A general existence and uniqueness theorem for the solution of such a system is proved and used in the rigorous derivation of exact discrete models satisfied by the various types of data. It is shown how these models can be used in the computation of various asymptotically efficient estimates obtained by the maximization of the Gaussian likelihood or approximations to it.
157 citations
TL;DR: In this paper, the authors consider the aliasing problem of identifying the parameters of a continuous time stochastic process from discrete time data and analyze the extent to which restricting attention to processes with rational spectral density matrices reduces the number of observationally equivalent models.
Abstract: This paper reconsiders the aliasing problem of identifying the parameters of a continuous time stochastic process from discrete time data. It analyzes the extent to which restricting attention to processes with rational spectral density matrices reduces the number of observationally equivalent models. It focuses on rational specifications of spectral density matrices since rational parameterizations are commonly employed in the analysis of the time series data.
111 citations
TL;DR: In this paper, the authors compare different definitions of the Wigner distribution with respect to aliasing and computational complexity and conclude that no definition leads to a function that is optimum in all respects.
Abstract: There is no straightforward way to proceed from the continuous-time Wigner distribution to a discrete-time version of this time-frequency signal representation. A previously given definition of such a function turned out to yield a distribution that was periodic with period π instead of 2π and this caused aliasing to occur. Various alternative definitions are considered and compared with respect to aliasing and computational complexity. From this comparison it appears that no definition leads to a function that is optimum in all respects. This is illustrated by an example.
103 citations
Abstract: The problem of studying lifelength distributions in discrete time is considered for certain forms of hazard functions. A class of life distributions that consists of the geometric, the Waring and the negative hypergeometric distributions is shown to result when the hazard function is inversely proportional to some linear function of time.
76 citations
TL;DR: The problem of modifying the system by feedback in order for it to enjoy such a property is solved and the problem of finding conditions which ensure the reproducibility of the input-output behaviour is solved.
Abstract: This paper deals with the problem of finding conditions which ensure the reproducibility of the input-output behaviour of a linear analytic discrete-time system by means of a linear discrete-time system. On this basis the problem of modifying the system by feedback in order for it to enjoy such a property is posed and solved,
71 citations
TL;DR: The problem of designing finite-length discrete-time matched filters is considered for situations in which exact knowledge of the input signal and/or noise characteristics is not available, and for a wide generality of norm-deviation models for the noise covariance matrix.
Abstract: The problem of designing finite-length discrete-time matched filters is considered for situations in which exact knowledge of the input signal and/or noise characteristics is not available. Such situations arise in many applications due to channel distortion, incoherencies, nonlinear effects, and other modeling uncertainties. In such cases it is often of interest to design a minimax robust matched filter, i.e., a nonadaptive filter with an optimum level of worst-case performance for the expected uncertainty class. This problem is investigated here for three types of uncertainty models for the input signal, namely, the mean-absolute, mean-square, and maximum-absolute distortion classes, and for a wide generality of norm-deviation models for the noise covariance matrix. Some numerical examples illustrate the robustness properties of the proposed designs.
56 citations
22 Jun 1983
TL;DR: An `asymptotic recovery' design procedure is proposed for square discrete-time, linear, time-invariant multivariable systems and indications are given of conditions under which the procedure can be expected to work well.
Abstract: An `asymptotic recovery' design procedure is proposed for square discrete-time, linear,-time-invariant multivariable systems Both the cases of negligible processing time (compared with the sampling interval) and of significant processing time are discussed Indications are given of conditions under which the procedure can be expected to work well, although a complete theoretical justification is not yet available An example of the use of the procedure is given
51 citations
TL;DR: In this paper, a zero-order singular perturbational type approximation for model reduction of discrete-time linear systems is developed for system which have fast subsystems and which are represented in the internally balanced format.
Abstract: A new zero-order singular perturbational type approximation is developed for model reduction of discrete-time linear systems. This approximation is also suitable for model reduction of systems which have fast subsystems and which are represented in the internally balanced format. Subsystem elimination as suggested by Moore for continuous-time systems does not generalize for the discrete-time case, and the singular perturbational approximation gives a particular solution to the discrete-time internally balanced model reduction problem.
49 citations
Book•
01 Oct 1983
TL;DR: The objective is to introduce some basic tools needed for signal and system analysis and design applicable to dynamic controls through mathematical derivations and computer simulations.
Abstract: Objectives: To introduce some basic tools needed for signal and system analysis and design applicable to dynamic controls through mathematical derivations and computer simulations. The topics include • signals and systems representation • Laplace transform • solving differential equations • z transform • solving difference equations • modeling of electrical systems • modeling of mechanical systems • time-domain analysis • frequency-domain analysis • state space model and its solution
01 Dec 1983
TL;DR: A stationary law of product form for the Markov process describing the state of the network is computed and the conditional expected travel time of a job given the job's requested processing times at particular nodes along its route is obtained.
Abstract: We study a new class of networks of queues whose nodes operate in round-robin fashion and other ways of interest to computer science. We compute a stationary law of product form for the Markov process describing the state of the network. Moreover, we obtain the conditional expected travel time of a job given the job's requested processing times at particular nodes along its route.
TL;DR: A new Doppler frequency estimator operating in the discrete time domain is derived from an analysis of the Dopplers signal statistics and it is shown that the estimator gives a nearly unbiased estimate of the mean frequency of the signal spectrum, regardless of the spectrum shape.
Abstract: A new Doppler frequency estimator operating in the discrete time domain is derived from an analysis of the Doppler signal statistics. It is shown that the estimator gives a nearly unbiased estimate of the mean frequency of the signal spectrum, regardless of the spectrum shape. The discrete time implementation gives the advantage that, under specified conditions, the range-velocity product of a pulsed Doppler velocity meter can be increased.
TL;DR: Two new algorithms for the efficient computation of the optimum lag Wiener filter as well as the optimum prediction distance predictor are introduced, featuring a coupled step-down step-up recursion which takes full advantage of both the Toeplitz nature of the matrix and the shifted structure of the right-hand side vectors.
Abstract: In many applications, including geophysical signal processing and system identification, the computation of a FIR Wiener filter, corresponding to the optimum lag between the input signal and the desired response, or of an optimum prediction distance predictor are often required. These problems lead to the solution of a family of Toeplitz systems of equations having the same associated matrix but right-hand side vectors which are shifted versions of each other. A very efficient method for the solution of the optimum lag problem is the well known Simpson's sideways recursions. The purpose of this paper is to introduce two new algorithms for the efficient computation of the optimum lag Wiener filter as well as the optimum prediction distance predictor. Their main characteristic is a coupled step-down step-up recursion which takes full advantage of both the Toeplitz nature of the matrix and the shifted structure of the right-hand side vectors. The proposed algorithms are featured by increased speed (they are about twice as fast as Simpson's scheme) and computational simplicity. In addition, they provide recursive error computation capability and give further insight into the problem.
TL;DR: The Rauch-Tung-Streibel smoother recursion is used to derive a new smoother algorithm based upon a decomposition of the linear model dynamical equation and maximizing use of rank-1 matrix modification that parallels Bierman's forward recursive square-root information filter/ backward recursive U-D factorized covariance algorithm.
TL;DR: In this article, the authors study Markov jump decision processes with both continuously and instantaneously acting decisions and with deterministic drift between jumps, and obtain necessary and sufficient optimality conditions for these decision processes in terms of equations and inequalities of quasi-variational type.
Abstract: We study Markov jump decision processes with both continuously and instantaneouslyacting decisions and with deterministic drift between jumps. Such decision processes were recentlyintroduced and studied from discrete time approximations point of view by Van der Duyn Schouten.Weobtain necessary and sufficient optimality conditions for these decision processes in terms of equations and inequalities of quasi-variational type. By means of the latter we find simple necessaryand sufficient conditions for the existence of stationary optimal policies in such processes with finite state and action spaces, both in the discounted and average per unit time reward cases.
TL;DR: In this paper, the authors consider deterministic and stochastic versions of discrete time analogs of optimization problems of the Bolza type and obtain optimality conditions that are always sufficient and which are also necessary if the given problem satisfies a strict feasibility condition and a bounded recourse condition.
Abstract: In this paper we consider deterministic and stochastic versions of discrete time analogs of optimization problems of the Bolza type. The functionals are assumed to be convex, but we make no differentiability assumptions and allow for the explicit or implicit presence of constraints both on the state xt and the increments△x t. The deterministic theory serves to set the stage for the stochastic problem. We obtain optimality conditions that are always sufficient and which are also necessary if the given problem satisfies a strict feasibility condition and, in the stochastic case, a bounded recourse condition. This is a new condition that bypasses the uniform boundedness restrictions encountered in earlier work on related problems.
TL;DR: In this article, the authors extended the development of empirically tractable mixed continuous time stochastic models for analysis of intra-urban residential histories and identified the effect of tenure type, age of household head, size of household and duration of stay on movement probabilities.
22 Jun 1983
TL;DR: It is shown by simulation that for certain geometries and loading the proposed nonlinear adaptive scheme can produce considerable improvement in performance over the linear scheme proposed in earlier investigations.
Abstract: This paper considers the problem of adaptively controlling the nonlinear dynamics associated with connected mechanical links such as those which form robotic manipulators. By first considering a single link, linear and nonlinear adaptive control methodologies are compared. It is shown by simulation that for certain geometries and loading the proposed nonlinear adaptive scheme can produce considerable improvement in performance over the linear scheme proposed in earlier investigations. The case of a two degree of freedom, two link, planar arm is then considered in detail. A discrete time model matching adaptive controller is then derived using a specific descretization of the continuous time nonlinear dynamics. Conditions which guarantee global stability of the control scheme are derived for the case of controlling the descretized model, and simulations are presented for the case of controlling the actual continuous time dynamics.
TL;DR: In this paper, a relationship between forward shift and backward shift representations is established and conditions for causality in either representation are presented, as well as algorithms for obtaining state-space representations of a large class of causal, discrete time systems.
Abstract: The primary purpose of this paper is to codify a number of independent but interrelated results in linear, multivariable, discrete time systems. In particular, a relationship between forward shift and backward shift representations is established. Conditions for causality in either representation are presented, as are algorithms for obtaining state-space representations of a large class of causal, discrete time systems. The effect on the transfer matrix of non-zero initial conditions is explicitly shown. The finite and infinite poles and zeros of square, invertible systems are defined and related to the lack of row or column ‘ properness ’ of particular representations. The role of the interactor and ‘ inverse interactor ’ in zero determination is also discussed.
TL;DR: In this article, the problem of determining the various classes of state-feed back dead-beat controllers for linear multivariable discrete-time systems is considered and the solution is based on an approach of closed-loop eigenstructure assignment.
Abstract: The paper considers the problem of determining the various classes of state-feed back dead-beat controllers for linear multivariable discrete-time systems. Unlike earlier work, attention is not restricted to the special case of minimum-time dead-beat controllers. A general dead-beat control problem is posed and solved. The solution is based principally on an approach of closed-loop eigenstructure assignment. The minimum of free parameters in each class are specified and used in an explicit parametric form for the feedback gain matrix. The concept of the greatest minimum of free parameters is introduced. Finally, the method is illustrated by a numerical example
TL;DR: In this article, the authors describe the continuous time stochastic process for money and inflation under which Cagan?s adaptive expectations model is optimal and analyzes how data formed by sampling money and prices at discrete points in time would behave.
Abstract: This paper describes the continuous time stochastic process for money and inflation under which Cagan?s adaptive expectations model is optimal. It then analyzes how data formed by sampling money and prices at discrete points in time would behave.
01 Jan 1983
TL;DR: In this article, the authors discuss the general theory of optimal stopping for Brownian motion and explain why many sequential decision problems in discrete time lead to stopping problems when they are formulated in continuous time.
Abstract: Publisher Summary This chapter discusses the general theory of optimal stopping for Brownian motion. It explains why many sequential decision problems in discrete time lead to stopping problem when they are formulated in continuous time. The solution of the limiting form of the problem can be constructed, in principle, by taking the union of certain open sets and this approach is closely related to the comparison technique. The chapter describes several Markov processes, each of which is capable of producing a sequence of rewards, and the problem of choosing just one of them at each stage so as to maximize the total discounted expectation. Each separate process has an index, depending on its state, and the optimal allocation policy is then defined by choosing the process with highest index at every stage. There is a strong connection between multi-armed bandits and stopping problems because the index for a single Markov process must be determined by solving a family of stopping problems.
21 Feb 1983
TL;DR: This work gives a discrete-time model for a central server computer system, and shows that the equilibrium distribution is of product-form given the requests for workload at the different stations of a cycle.
Abstract: We give a discrete-time model for a central server computer system, and show that the equilibrium distribution is of product-form Given the requests for workload at the different stations of a cycle, we compute the conditional cycle time distribution, which is linear in that requests.
TL;DR: The results show that the suboptimal strategy may give near-optimal control performance.
Abstract: Optimal control of linear discrete time stochastic systems with an amplitude constraint on the input is considered. A suboptimal controller is obtained by considering linear feedback laws with saturation. The variances of the closed-loop system are evaluated by approximating the stationary probability distribution of the state with a gaussian distribution. The gradient of the loss with respect to the feedback gain is evaluated, and an iterative algorithm to optimize the regulator parameters is given. Numerical examples are used to evaluate the control performance of the suboptimal strategy. The obtained loss is compared with a lower bound on the minimum of the loss which is achievable in amplitude constrained control. The results show that the suboptimal strategy may give near-optimal control performance
TL;DR: In this paper, a subsystem controller design method is proposed depending on the separability of the slow and fast controls, and conditions for a complete separation of slow-and fast subsystems are given.
Abstract: Linear shift-invariant discrete-time systems satisfying the two time scale property-are considered. Conditions for a complete separation of slow and fast subsystems are given. Subsystem regulator problems are investigated and the controllability property of the system is established based on the subsystem controllability properties. A subsystem controller design method is proposed depending on the separability of the slow and fast controls.
TL;DR: In this paper, a geometric approach to the stabilizability of linear systems by output feedback is presented and analyzed for both discrete time and continuous time single-input-single-output systems.
Abstract: In this paper we present a geometric approach to the stabilizability of linear systems by output feedback. The geometric approach is completely analysed for both discrete time and continuous time single-input-single-output systems. Two examples are worked out in detail to illustrate the theoretical development. We also show how our approach can be extended to dyadic systems. The simplicity of the geometric approach in the special case when the number of inputs or outputs is one less than the order of the system is illustrated with the help of examples. ‡Present address : Bell Laboratories, South Plainfield, New Jersey 07080, U.S.A
22 Jun 1983
TL;DR: An algebraic theory for analysis and design of linear multivariable feedback systems, which is sufficiently general to apply to lumped and distributed systems as well as continuous or discrete time is presented.
Abstract: This paper presents an algebraic theory for analysis and design of linear multivariable feedback systems, which is sufficiently general to apply to lumped and distributed systems as well as continuous or discrete time. By use of a controller with two vector inputs, results are obtained which give global parametrizations of all I/O and D/O maps achievable for a given plant by a stabilizing compensator. Also given are conditions sufficient for the asymptotic tracking of a class of inputs. Sufficient conditions for the robustness of the above results are also presented. In the special case of lumped systems it is shown that the design theory can be simplified to involve manipulations of polynomial matrices only.
01 Dec 1983
TL;DR: A tutorial account is given of H∞ theory for the design of controllers which optimize the weighted sensitivity matrix for linear multi-input, multi-output discrete time systems.
Abstract: A tutorial account is given of H∞ theory for the design of controllers which optimize the weighted sensitivity matrix. Linear multi-input, multi-output discrete time systems are considered.
Posted Content•
TL;DR: The cross-equation restrictions implied by dynamic rational expectations models can be used to resolve the aliasing identification problem when it is known that the true continuous time process has a rational spectral density matrix.
Abstract: This paper shows how the cross-equation restrictions implied by dynamic rational expectations models can be used to resolve the aliasing identification problem. Using a continuous time, linear-quadratic optimization environment, this paper describes how the resulting restrictions are sufficient to identify the parameters of the underlying continuous time process when it is known that the true continuous time process has a rational spectral density matrix.