Showing papers on "Discrete time and continuous time published in 1991"
TL;DR: In this paper, a Riccati equation approach is proposed to solve the estimation problem and it is shown that the solution is related to two algebraic Riemannian equations, and the estimation error dynamics is quadratically stable and the induced operator norm is kept within a prescribed bound for all admissible uncertainties.
Abstract: SUMMARY This paper is concerned with the problem of Hm estimation for linear discrete-time systems with timevarying norm-bounded parameter uncertainty in both the state and output matrices. We design an estimator such that the estimation error dynamics is quadratically stable and the induced operator norm of the mapping from noise to estimation error is kept within a prescribed bound for all admissible uncertainties. A Riccati equation approach is proposed to solve the estimation problem and it is shown that the solution is related to two algebraic Riccati equations.
240 citations
TL;DR: In this article, necessary and sufficient conditions for robust stability and performance of a system are provided for an interconnection of a nominal discrete-time plant and a stabilizing controller together with structured, norm-bounded, nonlinear/time-varying perturbations.
Abstract: Given an interconnection of a nominal discrete-time plant and a stabilizing controller together with structured, norm-bounded, nonlinear/time-varying perturbations, necessary and sufficient conditions for robust stability and performance of the system are provided. It is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem. The resulting stability robustness problem is shown to be equivalent to a simple algebraic one, the solution of which provides the desired necessary and sufficient conditions for performance/stability robustness. These conditions provide an effective tool for robustness analysis and can be applied to a large class of problems. In particular, it is shown that some known results can be obtained immediately as special cases of these conditions. >
235 citations
TL;DR: In this article, the authors considered the problem of estimating the parameters of a complex linear FM signal from a finite number of noisy discrete-time observations, and proposed an estimation algorithm consisting of two fast Fourier transforms (FFTs) accompanied by one-dimensional searches for maxima.
Abstract: The authors consider the problem of estimating the parameters of a complex linear FM signal from a finite number of noisy discrete-time observations An estimation algorithm is proposed, and its asymptotic (large sample) performance is analyzed The algorithm is computationally simple, consisting of two fast Fourier transforms (FFTs) accompanied by one-dimensional searches for maxima The variance of the estimates is shown to be close to the Cramer-Rao lower bound when the signal-to-noise ratio is 0 dB and above The authors applied the algorithm to the problem of estimating the kinematic parameters of an accelerating target by pulse-Doppler radar A representative test case was used to exhibit the usefulness of the algorithm for this problem, and to verify the analytical results by Monte Carlo simulations >
231 citations
TL;DR: It is shown that the one-way multigrid algorithm improves upon the complexity of its single-grid variant and is, in a certain sense, optimal.
Abstract: The numerical solution of discrete-time stationary infinite-horizon discounted stochastic control problems is considered for the case where the state space is continuous and the problem is to be solved approximately, within a desired accuracy. After a discussion of problem discretization, the authors introduce a multigrid version of the successive approximation algorithm that proceeds 'one way' from coarse to fine grids, and analyze its computational requirements as a function of the desired accuracy and of the discount factor. They also study the effects of a certain mixing (ergodicity) condition on the algorithm's performance. It is shown that the one-way multigrid algorithm improves upon the complexity of its single-grid variant and is, in a certain sense, optimal. >
187 citations
TL;DR: In this paper, state-space solutions to a discrete-time ℋ∞ problem are given. But the results are the direct analogues of those in the continuous time, the statespace derivation is considerably more difficult, and no unnecessary assumptions on the A matrix on the realization of the transfer function are needed.
Abstract: State-space solutions to a discrete-time ℋ∞ problem are given. For a given number γ>0we give a characterization of all controllers such that the ℋ ∞ norm of the closed-loop transfer function is less than γ The approach taken is based on the solution of two Riccati equations using the stable deflating subspace of a symplectic pencil. This ensures that no unnecessary assumptions on the ‘A’ matrix on the realization of the transfer function are needed. While the results are the direct analogues of those in the continuous time, the state-space derivation is considerably more difficult.
170 citations
TL;DR: In this paper, error correction models (ECM's) and cointegrated systems that are formulated in continuous time are dealt with, and the long-run equilibrium coefficients in the continuous system are always identified in the discrete time reduced form, so that there is no aliasing problem for these parameters.
Abstract: This paper deals with error correction models (ECM's) and cointegrated systems that are formulated in continuous time. Long-run equilibrium coefficients in the continuous system are always identified in the discrete time reduced form, so that there is no aliasing problem for these parameters. The long-run relationships are also preserved under quite general data filtering. Frequency domain procedures are outlined for estimation and inference. These methods are asymptotically optimal under Gaussian assumptions and they have the advantages of simplicity of computation and generality of specification, thereby avoiding some methodological problems of dynamic specification. In addition, they facilitate the treatment of data irregularities such as mixed stock and flow data and temporally aggregated partial equilibrium formulations. Models with restricted cointegrating matrices are also considered.
145 citations
11 Dec 1991
TL;DR: The problem of the synthesis of a feedback control assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned speed of convergence is investigated and it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets.
Abstract: Linear discrete-time systems affected by both parameter and input uncertainties are considered. The problem of the synthesis of a feedback control assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned speed of convergence is investigated. It is shown that the problem has a solution if and only if there exists a certain Lyapunov function which does not belong to a pre-assigned class of functions (i.e. the quadratic ones) but it is determined by the target set in which ultimate boundedness is desired. One of the advantages of this approach is that one can handle systems with control constraints. No matching assumptions are made. For systems with linearly constrained uncertainties, it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets. An extension of the technique to continuous-time systems is presented. >
139 citations
TL;DR: In this paper, a solution to the problems of H/sub infinity /-optimal linear state regulation and filtering is derived based on a transfer function approach which applies standard spectral factorization.
Abstract: A solution is derived to the problems of H/sub infinity /-optimal linear state regulation and filtering. The solution method for both problems is based on a transfer function approach which applies standard spectral factorization. Return difference relations are given which are extensions of the relations associated with the linear quadratic problem. >
129 citations
Book•
01 Aug 1991
TL;DR: The relationship between discrete time and continuous time linear estimation and identification of continuous-time systems: a general framework is presented.
Abstract: 1 Continuous-time models and approaches.- 2 Discrete-time modeling and identification of continuous-time systems: a general framework.- 3 The relationship between discrete time and continuous time linear estimation.- 4 Transformation of discrete-time models.- 5 Methods using Walsh functions.- 6 Use of the block-pulse operator.- 7 Recursive block pulse function method.- 8 Continuous model identification via orthogonal polynomials.- 9 Use of numerical integration methods.- 10 Application of digital filtering techniques.- 11 The Poisson moment functional technique - Some New Results.- 12 Identification, estimation and control of continuous-time systems described by delta operator models.- 13 Identification of multivariable continuous- time systems.- 14 Use of pseudo-observability indices in identification of continuous-time multivariable models.- 15 SVD-based subspace methods for multivariable continuous-time systems identification.- 16 Identification of continuous-time systems using multiharmonic test signals.- 17 Adaptive model approaches.- 18 Nonparametric approaches to identification.- 19 From fine asymptotics to model selection.- 20 Real time issues in continuous system identification.
123 citations
TL;DR: In this article, a discrete-time H2 static output feedback design problem involving a constraint on H∞ disturbance attenuation is addressed and state space formulae are derived.
117 citations
TL;DR: An approach to combined discrete-continuous modelling which can be used to model and simulate an intelligent multi-layer control architecture as can be found in high autonomy systems is presented.
Abstract: In this paper we present an approach to combined discrete-continuous modelling which can be used to model and simulate an intelligent multi-layer control architecture as can be found in high autonomy systems. The modelling approach is based on system theoretical concepts; the three system specification formalisms-differential equation, discrete time, and the discrete event system specification formalism-have been combined to facilitate multi-formalisms modelling. Simulation concepts are based on the abstract simulator concept for discrete event simulation developed by Zeigler. Similar simulation methods have been developed to simulate modular, hierarchical discrete time and differential equation specified systems as well as multi-formalism models. Included in the paper are several examples of multi-formalism models together with the simulation results from the STIMS environment-an implementation of the modelling and simulation concepts in Interlisp-D/LOOPS.
TL;DR: This chapter studies the problem of estimating a given function of a vector of unknowns by using measurements depending non-linearly on the problem element and affected by unknown but bounded noise by using a method to compute the axis-aligned box of minimal volume containing the feasible solution set.
TL;DR: A learning algorithm is employed, the genetic algorithm, to search efficiently through a space of probabilistic CA rules for a local rule that best reproduces the observed behavior of the data.
TL;DR: In this article, the conditions under which the original DDP algorithm can be expected to converge are investigated and modifications in the algorithm to improve convergence properties are proposed, and three procedures for modifying the stagewise Hessian matrices to guarantee convergence are proposed.
Abstract: The conditions under which the original differential dynamic programming (DDP) algorithm can be expected to converge are investigated and modifications in the algorithm to improve convergence properties are proposed. Quadratic convergence of DDP requires that the stagewise Hessian matrices computed in the algorithm be positive definite. Three procedures for modifying the stagewise Hessian matrices to guarantee convergence for situations in which the stagewise Hessian matrices are not positive definite are proposed. One of the procedures (an active shift) converges quadratically. The computational requirements for DDP with and without the shift procedures are presented, and the impact of the ratio of state variable dimension to control variable dimension on the relative efficiency of the different shift procedures is discussed. Numerical results for a series of problems, including one with 16 state variables and 200 time steps, are presented. The most robust shift procedure is an adaptive shift that utilizes a constant shift followed by an active shift. >
TL;DR: In this article, a discrete-time method for structural system identification using linear filters is presented, which is well known in electrical and systems engineering fields, and therefore is not new.
Abstract: Most of the previous studies considered structural system identification in the continuous‐time domain. The discrete‐time approach to the problem is more natural since all the recordings are in the discrete‐time form. This study presents a discrete‐time method for system identification by using discrete‐time linear filters. The method itself is well known in electrical and systems engineering fields, and therefore is not new. The objective in the paper is to present the method by emphasising its relation to the more familiar continuous‐domain modal analysis approach that is widely used in structural engineering. In addition to the method, some practical but important problems are also discussed in the paper, such as the processing of data, the selection and validation of models in the identification, and the detection of soil‐structure interaction. As an example, a 12‐story building was identified by using recordings from the magnitude 6.4, San Fernando, California earthquake of February 9, 1971.
TL;DR: It is shown that Laguerre networks are best suited to realized systems whose exponential unit-sample responses die down rapidly.
Abstract: An analytical approach is introduced that directly yields the optimum value of the Laguerre parameter b. This is achieved by minimizing the mean-square error between the unit-sample response of the given discrete system and that of its Laguerre counterpart. It is shown that Laguerre networks are best suited to realized systems whose exponential unit-sample responses die down rapidly. >
TL;DR: In this article, a discrete-time modeling of transition-noise dominant channels is considered, which facilitates performance analysis of various sample-data detection schemes, based on the proposed channel description method in the presence of transition noise, expressions for signal-to-total noise power ratios associated with a few selected detection schemes are derived.
Abstract: Discrete-time modeling of transition-noise-dominant channels is considered which facilitates performance analysis of various sample-data detection schemes. Based on the proposed channel description method in the presence of transition noise, expressions for signal-to-total-noise-power ratios associated with a few selected detection schemes are derived. Under the assumption of a Lorentzian step response and perfect equalization, a comparison is made among different detectors based on the signal-to-noise ratio figure-of-merit evaluated as a function of linear density. >
TL;DR: In this article, it was shown that the discrete-time disturbance rejection problem can be solved by making direct use of some results on linear-quadratic zero-sum dynamic games.
Abstract: It is shown that the discrete-time disturbance rejection problem, formulated in finite and infinite horizons, and under perfect state measurements, can be solved by making direct use of some results on linear-quadratic zero-sum dynamic games. For the finite-horizon problem an optimal (minimax) controller exists, and can be expressed in terms of a generalized (time-varying) discrete-time Riccati equation. The existence of an optimum also holds in the infinite-horizon case, under an appropriate observability condition, with the optimal control, given in terms of a generalized algebraic Riccati equation, also being stabilizing. In both cases, the corresponding worst-case disturbances turn out to be correlated random sequences with discrete distributions, which means that the problem (viewed as a dynamic game between the controller and the disturbance) does not admit a pure-strategy saddle point. Results for the delayed state measurement and the nonzero initial state cases are presented. >
01 Mar 1991
TL;DR: In this paper, an iterative learning control algorithm is presented for a class of linear discrete-time dynamic systems with unknown but periodic parameters, and a sufficient condition for convergency of the iterative algorithm is provided.
Abstract: An iterative learning control algorithm is presented for a class of linear discrete-time dynamic systems with unknown but periodic parameters. Then a sufficient condition for convergency of the iterative algorithm is provided. It is also shown that the result can be extended to a class of nonlinear unknown systems. To show the effectiveness of the algorithms, two examples are given.
TL;DR: In this article, strong approximation results concerning discrete-time nonlinear input-output maps are presented, which can be used as a basis for adaptive filtering or for the adaptive identification of G's.
Abstract: Some strong approximation results concerning discrete-time nonlinear input-output maps are presented. The results concern maps G that are causal, time invariant, and satisfy certain continuity and approximately finite-memory conditions. It is shown that such G's can be uniformly approximated arbitrarily well by finite sums. This can be used, for example, as a basis for adaptive filtering or for the adaptive identification of G's. Similar propositions hold also for G's that are not necessarily causal. >
Book•
01 Dec 1991
TL;DR: Introduction to Control Systems, Modelling of Dynamic Systems, System Time Response,frequency Response, Frequency Domain Compensator Design, Root Locus, Process Control, Discrete Time Systems, Nonlinearities in Control Systems.
Abstract: Introduction to Control Systems, Modelling of Dynamic Systems, System Time Response, Frequency Response, Frequency Domain Compensator Design, Root Locus, Process Control, Discrete Time Systems, Computer Control Systems, Nonlinearities in Control Systems. Appendices.
IBM1
TL;DR: The analysis of a rate-based access control scheme in high speed environments that is based on a buffered leaky bucket algorithm is presented and the detailed analysis of the binary Markov source throttled by such rate- based access control schemes is presented.
Abstract: The analysis of a rate-based access control scheme in high speed environments that is based on a buffered leaky bucket algorithm is presented. The analysis is carried out in discrete time, which is representative of asynchronous transfer mode environments. For the cell arrivals to the leaky bucket, a general discrete Markovian arrival process is considered which models bursty and correlated sources. The introduction of the deficit function allows the reduction of the original problem to a more standard discrete time queuing system with the same arrival process. As an important special case, the detailed analysis of the binary Markov source throttled by such rate-based access control schemes is presented. Along with explicit recursions for computation of state probabilities and simple characterization of the asymptotic behavior of the queue buildup, some guidelines for the parameter selection of these schemes is provided. >
01 Jan 1991
TL;DR: The main theme of as discussed by the authors is the connections between various Riccati equations and the closed loop stability of control schemes based on Linear Quadratic (LQ) optimal methods for control and estimation.
Abstract: The main theme of this Chapter will be the connections between various Riccati equations and the closed loop stability of control schemes based on Linear Quadratic (LQ) optimal methods for control and estimation. Our presentation will encompass methods applicable both for discrete time and continuous time, and so we discuss concurrently the difference equations (discrete time) and the differential equations (continuous time) — the intellectual machinery necessary for the one suffices for the other and so it makes sense to dispense with both cases in one fell swoop.
01 Jan 1991
26 Jun 1991
TL;DR: In this article, the authors define stability in the sense of Lyapunov for logical discrete event systems (DES) and show that a more conventional analysis of stability which employs appropriate LyAPunov functions can be used for logical DES, which is illustrated on a manufacturing system that processes batches of N different types of parts according to a priority scheme.
Abstract: Discrete event systems (DES) are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals. "Logical" DES are a class of discrete time DES with equations of motion that are most often non-linear and discontinuous with respect to event occurrences. Recently, there has been much interest in studying the stability properties of logical DES and several definitions for stability, and methods for stability analysis have been proposed. Here we introduce a logical DES model and define stability in the sense of Lyapunov for logical DES. Then we show that a more conventional analysis of stability which employs appropriate Lyapunov functions can be used for logical DES. This standard approach has the advantage of not requiring high computational complexity (as some of the others) but the difficulty lies in specifying the Lyapunov functions. The approach is illustrated on a manufacturing system that processes batches of N different types of parts according to a priority scheme, one of Dijkstra's "self-stabilizing" distributed Systems, and a load balancing problem in computer networks.
26 Jun 1991
TL;DR: This paper analyzes worst case identification of linear shift invariant systems with an l1 error criterion and a characterization of optimal algorithms and intrinsic errors of identification is given.
Abstract: This paper analyzes worst case identification of linear shift invariant systems with an l 1 error criterion A characterization of optimal algorithms and intrinsic errors of identification is given The application of this characterization is made to identification in l 1 The assumed apriori information on the plant are bounds on the system gain and decay rate of the impulse response of the unknown system and the experimental data is assumed to be a finite set of corrupted impulse or step response samples of the systems Comparisons are made with the H ? system identification problem Comments on the l 1 identification of small signal models of smooth nonlinear discrete time systems are made
TL;DR: In this paper, the authors use martingale theory and a method-of-moments technique to derive a class of estimators for the size of a closed population in a capture-recapture experiment in discrete time.
Abstract: We use martingale theory and a method-of-moments technique to derive a class of estimators for the size of a closed population in a capture-recapture experiment in discrete time where the capture probabilities on the successive capture occasions are allowed to be different. The same capture probability is assumed to apply to all animals in the population on the same occasion. Explicit expressions are given for these estimators and their associated standard errors which involve only simple computation. An optimal estimator for the population size is found. Asymptotic results are readily obtained by an application of a martingale central limit theorem. Two examples are given to compare the results.
TL;DR: The motivation of this paper is to provide a new solution to the problem of the estimated model admissibility using an ad-hoc modification of the control law, and to propose a general framework for robustly designing the adaptive linear controllers, irrespective of the underlying control law.
TL;DR: In this paper, the identification and maximum likelihood estimation of systems of linear stochastic differential equations using panel data is discussed. But the approach in the social sciences advocates the estimation of the "exact discrete model" after a reparameterization with LISREL or similar programs for structural equations models.
Abstract: The present paper deals with the identification and maximum likelihood estimation of systems of linear stochastic differential equations using panel data. So we only have a sample of discrete observations over time of the relevant variables for each individual. A popular approach in the social sciences advocates the estimation of the “exact discrete model” after a reparameterization with LISREL or similar programs for structural equations models. The “exact discrete model” corresponds to the continuous time model in the sense that observations at equidistant points in time that are generated by the latter system also satisfy the former. In the LISREL approach the reparameterized discrete time model is estimated first without taking into account the nonlinear mapping from the continuous to the discrete time parameters. In a second step, using the inverse mapping, the fundamental system parameters of the continuous time system in which we are interested, are inferred. However, some severe problems arise wit...
TL;DR: In this article, the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete-time systems, and for general classes of disturbance functions and reference signals, consisting in free responses of periodic processes.
Abstract: In this paper the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete-time systems, and for general classes of disturbance functions and reference signals, consisting in free responses of periodic processes. The necessary and sufficient conditions for the existence of a solution, which involve the periodic notion of invariant zero, are found. A constructive design procedure of the periodic compensator is given; it is based on the internal model principle.