Parameter identification and control of linear discrete-time systems

Saridis, George N.; Lobbia, R.

doi:10.1109/tac.1972.1099868

Cited by 67 publications

(9 citation statements)

References 7 publications

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“…In the single-input/single-output identification problem [ 1 ] , it was important to reduce the unknown matrices and vectors in (1) …”

Section: Canonical Forms For Multivariable Systemsmentioning

confidence: 99%

“…Recently, however we have developed [1] a stochastic approximation algorithm for identification of the unknown parameters of a single-input/single-output linear system with an arbitrary feedback controller. In this algorithm, the controller is capable of utilizing current information from the identifier and asymptotically approaches the "stochastic optimal controller" as the identifier estimates converge.…”

Section: Introductionmentioning

confidence: 99%

“…To achieve this goal, the matrices of the model must be presented in a special canonical form, similar to the phase-variable canonical form for single-input/single-output systems. It will be shown that identification algorithm [ 1 ] need not be extensively modified. However, the derivation of the transformations which recover estimates of system parameters from the identification estimates is slightly more involved than in the single-input/single-output case.…”

Section: Introductionmentioning

confidence: 99%

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Identification and Control of Multivariable Stochastic Feedback Systems

Lobbia¹,

Saridis²

1973

Journal of Cybernetics

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This paper considers the problem of simultaneous identification and control of stochastic processes characterized by linear dynamic models with unknown systems parameter coefficients. Stochastic approximation is used to derive consistent identification algorithms for the case in which arbitrary feedback controls are present. These identification methods can also be used for determining the order of the system, if the latter is unknown, as well as the exact canonical structure for the multivariable case.An approximation to the optimal control solution is obtained by explicitly separating the functions of identification and control, and asymptotic convergence to a stochastic optimal controller is attained without on-line structural modification. IntroductionThere is currently much interest in identification and control of stochastic systems where the mathematical model of the system is assumed unknown-the so-called "black box" problem, or where only partial information about the model is given. Such problems are typical of the real world, where most physical systems are perturbed by unwanted external disturbances, and accurate mathematical models for present-day complex systems are rarely attainable.Within this general framework, a frequently recurring problem is the simultaneous identification and feedback control of a stochastic system described by a linear, dynamic, discrete-time mathematical model with unknown system parameters. The identification part of the problem is in itself a formidable task. The difficulty arises from the fact that the presence of the feedback control signal produces additional correlations in existing identification algorithms that were intended for open-loop systems only.Recently, however we have developed [1] a stochastic approximation algorithm for identification of the unknown parameters of a single-input/single-output linear system with an arbitrary feedback controller. In this algorithm, the controller is capable of utilizing current information from the identifier and asymptotically approaches the "stochastic optimal controller" as the identifier estimates converge. However, the above identification scheme had not been generalized to handle other than single-input/single-output systems. But since models of most physical systems are of the multi-input/multi-output type, the purpose of this paper is to extend the scheme to the multivariable case. To achieve this goal, the matrices of the model must be presented in a special canonical form, similar to the phase-variable canonical form for single-input/single-output systems. It will be shown that

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“…In the single-input/single-output identification problem [ 1 ] , it was important to reduce the unknown matrices and vectors in (1) …”

Section: Canonical Forms For Multivariable Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Identification and Control of Multivariable Stochastic Feedback Systems

Lobbia¹,

Saridis²

1973

Journal of Cybernetics

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“…The application of stochastic approximation to the control of processes with uncertainty has been proposed by Saridis and Lobbia [ 1 ] in a recent paper. Their considerations are based on the classical approach to adaptive control, i.e., the characteristics of the plant to be controlled must be determined completely so that the parameters of the adjustable controller can be computed in order to optimize the performance for a given figure of merit.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Control Using Stochastic Approximation

Sinha¹,

Prasad²

1974

Journal of Cybernetics

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Adaptive control of systems with uncertainty can be implemented without complete identification of the plant if the cost function is measured continuously and the parameters of the controller are adjusted, using an efficient gradient method, to obtain optimum performance. As, in practice, only noisy measurements of the cost function are available, one has to use stochastic gradient methods. In this paper some efficient stochastic approximation algorithms are proposed for adaptive control.

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“…A multiple model filter bank has been used extensively in guidance, navigation, and control applications to detect parameter changes in the system in addition to its many other applications [9,16,18,34,35,36,41,52,65]. Willsky reported great success in arrhythmia detection and classification in electrocardiograms using both a multiple hypothesis model and the generalized likelihood ratio (GLR) [17,67].…”

Section: -12mentioning

confidence: 99%

Novel electrocardiogram segmentation algorithm using a multiple model adaptive estimator

Hoffman¹,

Miller²,

Kabrisky³

et al.

Proceedings of the 41st IEEE Conference on Decision and Control, 2002.

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This thesis presents a novel electrocardiogram (ECG) processing algorithm design based on a Multiple Model Adaptive Estimator (MMAE) for a physiological monitoring system. Twenty ECG signals from the MIT ECG database were used to develop system models for the MMAE. The P-wave, QRS complex, and T-wave segments from the characteristic ECG waveform were used to develop hypothesis filter banks. By adding a threshold filter-switching algorithm to the conventional MMAE implementation, the device mimics the way a human analyzer searches the complex ECG signal for a useable temporal landmark and then branches out to find the other key wave components and their timing. The twenty signals and an additional signal from an animal exsanuinaiton experiment were then used to test the algorithm. Using a conditional hypothesis-testing algorithm, the MMAE correctly identified the ECG signal segments corresponding to the hypothesis models with a 96.8% accuracy-rate for the 11539 possible segments tested. The robust MMAE algorithm also detected any misalignments in the filter hypotheses and automatically restarted filters within the MMAE to synchronize the hypotheses with the incoming signal. Finally, the MMAE selects the optimal filter bank based on incoming ECG measurements. The algorithm also provides critical heart-related information such as heart rate, QT, and PR intervals from the ECG signal. This analyzer could be easily added as a software update to the standard physiological monitors universally used in emergency vehicles and treatment facilities and potentially saving thousands of lives and reducing the pain and suffering of the injured. Subject Terms Physiological monitoring, vital-sign monitoring, MMAE, ECG, Electrocardiogram Report Classification unclassified Classification of this page unclassified Classification of Abstract unclassified Limitation of Abstract UU Number of Pages

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Parameter identification and control of linear discrete-time systems

Cited by 67 publications

References 7 publications

Identification and Control of Multivariable Stochastic Feedback Systems

Identification and Control of Multivariable Stochastic Feedback Systems

Adaptive Control Using Stochastic Approximation

Novel electrocardiogram segmentation algorithm using a multiple model adaptive estimator

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