Showing papers on "Discrete time and continuous time published in 1980"
TL;DR: The basic ideas behind the parameter estimation methods are discussed in a general setting and an example is given which illustrates some properties of the methods and shows the usefulness of interactive computing.
372 citations
TL;DR: Two new algorithms for solution of the diserete-time algebraic Riccati equation are presented, related to Potter's and to Laub's methods, but based on the solution of a generalized rather than an ordinary eigenvalue problem.
Abstract: In this paper we shall present two new algorithms for solution of the diserete-time algebraic Riccati equation. These algorithms are related to Potter's and to Laub's methods, but are based on the solution of a generalized rather than an ordinary eigenvalue problem. The key feature of the new algorithms is that the system transition matrix need not be inverted. Thus, the numerical problems associated with an ill-conditioned transition matrix do not arise and, moreover, the algorithm is directly applicable to problems with a singular transition matrix. Such problems arise commonly in practice when a continuous-time system with time delays is sampled.
343 citations
TL;DR: In this article, the qualitative dynamics of a discrete time version of a deterministic, continuous time, nonlinear macro model formulated by Haavelmo are fully characterized, and several implications for dynamic economic modelling are discussed.
178 citations
TL;DR: It is shown that a search plan maximizes the overall probability of detection if and only if for each time interval i the search conducted at time i maximized the probability of detecting a stationary target with the probability that the stationary target occupies cell c.
Abstract: We consider optimal search for a moving target in discrete space. A limited amount of search effort is available at each of a fixed number of time intervals and we assume an exponential detection function. We show that a search plan maximizes the overall probability of detection if and only if for each time interval i the search conducted at time i maximizes the probability of detecting a stationary target with the probability that the stationary target occupies cell c equal to the probability that the moving target occupies cell c at time i and is not detected by the search at any time interval other than i. This characterization gives an iterative algorithm to compute optimal search plans. These plans are compared with incrementally optimal plans.
167 citations
TL;DR: In this article, a general class of linear, time-invariant multivariable systems that can be used in block implementations of discrete-time filters are described, including an explicit expression for the matrix transfer function of the block processor in terms of the single-input, single-output filter transfer function.
Abstract: This paper describes the general class of linear, time-invariant multivariable systems that can be used in block implementations of time-invariant discrete-time filters. Explicit relations between the properties of the block processor and the properties of the implemented filter are derived, including an explicit expression for the matrix transfer function of the block processor in terms of the single-input, single-output filter transfer function. These properties and relations are independent of the form of realization of the block processor. It is shown that all irreducible state-space realizations of the block processor can be derived by a simple procedure from a simple realization of the required filter transfer function.
102 citations
TL;DR: Several recurisve algorithms for parametric identification of discrete time systems derived from Model Reference Adaptive System (M.R.A.S.) techniques are analysed, belonging to the class of output error methods which have been very little discussed previously in the identification literature.
96 citations
01 Dec 1980
TL;DR: In this paper, it is shown that global convergence can be established for an adaptive control algorithm applied to the general class of stably invertible systems, where the adaptive control is applied to deterministic and stochastic deterministic systems.
Abstract: This paper shows that previous results on multi-input multi-output discrete time deterministic and stochastic adaptive control can be extended to a wider class of systems. It is shown that global convergence can be established for an adaptive control algorithm applied to the general class of stably invertible systems.
91 citations
01 Sep 1980
TL;DR: In this paper, hybrid self-tuning controllers are introduced which combine two sample rates to give both discrete time and continuous time features, and the limiting properties of such algorithms, as the sample rate increases, correspond to a continuous-time control law.
Abstract: Hybrid self-tuning controllers are introduced which combine two sample rates to give both discrete time and continuous-time features. The limiting properties of such algorithms, as the sample rate increases, are shown to correspond to a continuous-time control law. Undesirable intersample behaviour associated with the discrete-time control of continuous systems with high pole-zero excess is thus avoided. The results are illustrated by the control of a triple integrator.
81 citations
TL;DR: In this article, the stability problem of a first-order system with time- or state-variable time delay is investigated and the proposition that the time-varying system is not always stable (unstable) even if the frozen-time system is stable, is verified for a variable time delay system by several examples.
Abstract: In this paper the stability problem of a first-order system with time- or state-variable time delay is investigated and the proposition that the time-varying system is not always stable (unstable) even if the frozen-time system is stable (unstable) is verified for a variable time delay system by several examples.
74 citations
TL;DR: In this article, the stability properties of a fairly general diserete-time adaptive control scheme are analyzed and sufficient conditions for L ∞ stability in the presence of disturbances are given.
Abstract: The stability properties of a fairly general diserete-time adaptive control scheme are analyzed. Sufficient conditions for L^{\infty} stability in the presence of disturbances are given. The stability results are used to prove convergence of the process outputs in the disturbance-free case, without requiring any a priori stability assumption.
TL;DR: The search algorithm represents the first use for asymmetric sources and distortion measures of a variation of a single stack algorithm proposed by Gallager, and establishes the existence of codes which attain almost any desired rate between the rate-distortion bound and the optimum entropy-coded quantizer.
Abstract: A rate-distortion theory is introduced for the optimal encoding of stationary memoryless continuous-amplitude sources with a single-letter distortion measure and reproduction alphabets of a given finite size. The theory arises from a judicious approximation of the original continuous-input discrete-output problem by one with discrete input and output. A size-constrained output alphabet rate-distortion function is defined, its coding significance is established by coding theorems, and a convergent algorithm is presented for its evaluation. The theory is applied to Gaussian sources with squared-error distortion measure. Using the algorithm for the calculation of the new rate-distortion function in this case establishes the existence of codes which attain almost any desired rate between the rate-distortion bound and the optimum entropy-coded quantizer. Furthermore, one can closely approach the rate-distortion limit with a surprisingly small number of output levels. The calculation furnishes optimal output levels, output level probabilities, and other parameters necessary for a trellis coding simulation. The search algorithm represents the first use for asymmetric sources and distortion measures of a variation of a single stack algorithm proposed by Gallager. Carrying out the simulation at a rate of 1 bit per source symbol, codes are found with 4 and 64 output levels which attain distortions smaller than that of an optimum quantizer and close to the rate-distortion bound. Furthermore, these codes attain comparable or better performance with far less search effort than previous attempts with a continuous output alphabet.
TL;DR: In this paper, it is shown that model reference adaptive systems (MRASs) can be derived from the self-tuning regulators (STR's) point of view, and that the positive real condition can be dispensed with in the deterministic case.
Abstract: Adaptive control can be approached from many different points of view. In recent years there has been much progress made both on model reference adaptive systems (MRAS's) and on self-tuning regulators (STR's). The two approaches are treated here in a general framework. It is shown that MRAS's can be derived from the STR point of view. Special attention is paid to the positive real condition, which appears in the analysis of both types of schemes. It is shown that this condition can be dispensed with in the deterministic case.
TL;DR: In this article, a simple error model for both discrete and continuous time adaptive systems is described for both bounded and unbounded inputs for the discrete case and extended to continuous time models.
Abstract: A simple error model is described for both discrete and continuous time adaptive systems. The stability of the model for both bounded and unbounded inputs is analyzed for the discrete case and extended to continuous time models. It is shown that \Delta\phi(k)\in I^{2} in the former case and \phi(t)\in L^{2} in the latter case due to the presence of a feedback signal and these in turn play an important role in the stability analysis of discrete and continuous time adaptive systems.
TL;DR: It is shown that a discrete time integrating regulator can be designed based on a strongly simplified model which has only two tuning parameters which are easy to choose from the step response of the open loop system.
TL;DR: The probability generating function for the queue length distribution for a multiplexer operating in a two state Markovian environment in which each state is characterized by its own Bernoulli arrival process and independent error process is derived.
Abstract: Most stochastic models for discrete time statistical multiplexers make the assumption that 1) arrivals are governed by a Bernoulli process and that 2) transmission errors or multiplexer failures are described by an independent error process. We study a multiplexer operating in a two state Markovian environment in which each state is characterized by its own Bernoulli arrival process and independent error process. We derive the probability generating function for the queue length distribution for such a system. We also consider two special cases of this model. One referred to as the saturated arrival model corresponds to a system in which during one of the two states, the saturated state, at least one arrival occurs during each discrete time unit. The other model, the breakdown model, corresponds to a system in which during one of the two states, the breakdown state, the multiplexer is inoperative. For both models, we generalize the analysis to cases in which the durations of the saturated state and breakdown state may take on values described by arbitrary distributions. Finally, we study the effects of different arrival processes and error processes on queue length behavior.
TL;DR: In this paper, an improved geometric-series method is presented for converting continuous time models to equivalent discrete time models, and a direct truncation method, a matrix continued fraction method and a geometric series method are presented.
TL;DR: In this paper, the authors consider the problem of searching for a target that moves in discrete time and space according to some Markovian process, and propose a myopic search strategy.
Abstract: We consider the problem of searching for a target that moves in discrete time and space according to some Markovian process. At each time, a searcher attempts to detect the target. If the searcher's action at each time is such as to maximize his chances of immediate detection, we call his strategy “myopic.” We provide a computationally useful necessary condition for optimality, and use it to provide an example wherein the myopic strategy is not optimal.
TL;DR: In this article, it was shown that necessary and sufficient (in some sense) conditions for the existence of positive definite solutions of this equation are directly connected with the stability of infinite dimensional linear systemsxk+1=Ax k.
Abstract: This paper is devoted to a study of the properties of the equationA*FA−F=−G, where F∈L(ℌ) is unknown, A∈L(ℌ), G∈L(ℌ) is positive andℌ is a Hilbert space. It is shown that necessary and sufficient (in some sense) conditions for the existence of positive definite solutions of this equation are directly connected with the stability of infinite dimensional linear systemxk+1=Ax k . The relationships between stability of such a system and stability of a continuous-time system generated by a strongly continuous semigroup are given also. As an example the case of the delayed system in Rn\(R^n \dot x\left( t \right) = A_0 x\left( t \right) + A_1 x\left( {t - 1} \right)\) is considered.
Patent•
20 Oct 1980
TL;DR: In this paper, a P-I-D controller in a process control system is self tuned in response to discrete time model identification parameters which are converted to P-II-D form.
Abstract: A P-I-D controller in a process control system is self tuned in response to discrete time model identification parameters which are converted to P-I-D form. Additionally, the P-I-D parameters are limited to prevent them from exceeding the controller's specified range.
TL;DR: Spectral analysis and analysis of variance of simulation data demonstrate that many of the details of the dynamics of deterministic models do not appear in a stochastic context, even in large populations, and are therefore biologically irrelevant.
TL;DR: In this article, the Schwarz canonical form description of a linear discrete-time system is used to derive reduced-order models which are stable if the original system is stable, and the steady-state response of the models to a step input is equal to that of the system.
Abstract: The Schwarz canonical form description of a linear discrete-time system will be used to derive reduced-order models which are stable if the original system is stable. Further, the steady-state response of the models to a step input is equal to that of the system.
TL;DR: It is shown that the generated morphemes depend more heavily on the timing regime than on the particular state transition function of the cells, and local synchronisation is sufficient to reestablish the seeming complexity and the fo...
Abstract: In this paper we study different timing regimes for a class of morpheme generating systems. These systems were previously analysed in their classical discrete time form:1 in that form they are of the type of developmental systems proposed by Lindenmayer.1,2,3By timing regime we mean rules governing activation of local transitions. The fixed limeslep, globally synchronous regime underlying L-systems are one example and the basis of our previous study. In this paper some other possibilities are considered, naturally expressable in discrete event form. Each of them involves some measure of local synchronisation and variable timing. These various timing regimes are compared with respect to the variability of the morphemes generated by them. This is done by cluster analysis.|It is shown that: (I) the generated morphemes depend more heavily on the timing regime than on the particular state transition function of the cells; (ii) local synchronisation is sufficient to reestablish the seeming complexity and the fo...
TL;DR: In this article, a set of optimal stand densities over one rotation of an even-aged stand is derived mathematically using a discrete time, continuous state dynamic programming model for forestry.
Abstract: A set of optimal stand densities over one rotation of an even-aged stand is derived mathematically using a discrete time, continuous state dynamic programming model. The use of the calculus approach to search for optimal solutions stage by stage is new for forestry. The criterion for optimization used is the maximum physical harvest over one rotation. When the stand growth model has the biologically reasonable form suggested here, it is easy to determine the optimal stand density over any number of growth periods. This, in turn, makes it easy to determine the optimal rotation age by sensitivity analysis of total return on the number of stages in the decision process.
TL;DR: There exist several essential differences between continuous-time and discrete-time systems with respect to state observer theory, and full-order and reduced-order state reconstructors are derived.
Abstract: In this paper the design of state reconstruction algorithms for linear discrete-time systems is analysed. It is shown that there exist several essential differences between continuous-time and discrete-time systems with respect to state observer theory. Full-order and reduced-order state reconstructors are derived and the relationship between the different algorithms is discussed.
TL;DR: The proposed detectors are seen to be robust over a class of possible noise statistics, based on a Huber-Tukey mixture model, which contains noises characterized by heavy-tailed probability density functions.
Abstract: The problem of designing robust systems for the detection of stochastic signals in noise is considered for the large-sample-size, small-signal case. By applying two previously-established models for the detection of stochastic signals, known results for the robust detection of deterministic signals are extended on a limited basis to the stochastic- signal case. The proposed detectors are seen to be robust over a class of possible noise statistics, based on a Huber-Tukey mixture model, which contains noises characterized by heavy-tailed probability density functions. In addition, numerical results are presented which verify the robustness property of the proposed detectors over wider classes of noise mixtures.
TL;DR: In this paper, discrete time linear quadratic-optimal control is investigated on a fixed-bed catalytic fixed-body reactor with stochastic upstream disturbances. But the simulation results show that the control system behaviour is similar to the one described in this paper.
TL;DR: It is shown that the performance of this detector can be made arbitrarily close to that of the optimal memoryless detector for a large class of noises.
Abstract: In this paper the problem of memoryless discrete time detection of a constant signal in additive φ-mixing noise is considered. The fidelity criterion is taken to be the asymptotic relative efficiency. The optimal detector nonlinearity is approximated by a polynomial, and the statistical knowledge required for the design of the detector is the family of joint moments of the noise, resulting in a very simple design procedure for the detector. It is shown that the performance of this detector can be made arbitrarily close to that of the optimal memoryless detector for a large class of noises.