Stochastic control of linear sigularly perturbed systems

Haddad, A.; Kokotović, P.V.

doi:10.1109/tac.1977.1101603

Cited by 45 publications

(11 citation statements)

References 8 publications

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“…To formally introduce these two subproblems, one can assume that the short-term (weekly, daily, or hourly) decisions are made each week ½W, day ½D, and hour ½H, and investment decisions are made each season ½T S . The problem defined in (3)-(10) can then be restated as an optimization problem subject to multirate discrete-time processes using techniques introduced in [22], [89]. Even with this temporal decomposition, both short-term generation scheduling and planning problems remain truly stochastic optimization problems, and as such are computationally very challenging.…”

Section: Temporal Decomposition Of Planning and Scheduling Functionsmentioning

confidence: 99%

“…These properties are essential for supporting the validity of often practiced spatial decomposition methods in very large-scale electric power networks, and conditions for localized response [34], [35]. The complex-valued power flow constraint (22) can be further written as two sets of realvalued nonlinear equations representing real power and reactive power balance equations…”

Section: General Dae Model Of Today's Electric Power Systemsmentioning

confidence: 99%

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From Hierarchical to Open Access Electric Power Systems

Ilić

2007

Proc. IEEE

123

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Section: Temporal Decomposition Of Planning and Scheduling Functionsmentioning

confidence: 99%

Section: General Dae Model Of Today's Electric Power Systemsmentioning

confidence: 99%

From Hierarchical to Open Access Electric Power Systems

Ilić

2007

Proc. IEEE

123

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“…it was demonstrated by Teneketzis and Sandell (1977) and Haddad and Kokotovic (1977) that the optimal solution may be approximated by the solutions of two reduced order stochastic control problems in the slow and fast time scale.…”

Section: Stochastic Filtering and Controlmentioning

confidence: 99%

Applications of Singular Perturbation Techniques to Control Problems

Kokotović¹

1984

SIAM Rev.

386

126

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This paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years. The first three sections are devoted to the standard model and its time-scale, stability and controllability properties. The next two sections deal with linear-quadratic optimal control and one with cheap (near-singular) control. Then the composite control and trajectory optimization are considered in two sections, and stochastic control in one section. The last section returns to the problem of modeling, this time in the context of large scale systems. The bibliography contains more then 250 titles. D IS T R I B U T I O N / A V A I L A B I L I T Y O F A B S T R A C T U N C L A S S I F I E D / U N L I M I T E D S S A M E A S R PT. □ O T I C U S E R S □ 21. A B S T R A C T S E C U R I T Y C L A S S I F I C A T I O NUnclassified S E C U R I T Y C L A S S I F I C A T I O N O F T H IS P A G E S E C U R IT Y C L A S S IF IC A T IO N O F TH IS P A G E S E C U R I T Y C L A S S I F I C A T I O N O F T H I S P A G E APPLICATIONS OF SINGULAR PERTURBATION TECHNIQUES

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“…Stochastic Perturbations. Linear quadratic optimal control problems for singularly perturbed systems with random perturbations have been considered in [177,179,191,240]. We mention here the paper of Haddad and Kokotovic [179], devoted to the construction of a suboptimal regulator.…”

Section: Numerical Computation S Variousproblems and Applicationsmentioning

confidence: 99%

Singular perturbations in optimal control problems

Vasil’eva¹,

Dmitriev²

1986

J Math Sci

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One presents a survey of the works on the theory of optimal control by deterministic objects, described by systems of ordinary differential or difference equations, where the investigation is carried out with the aid of the methods of the theory of singular perturbations. One analyzes the possibility of the application of the theory of singular perturbations to the investigation of control problems with large amplification coefficient in the feedback circuit, to the description of sliding regimes in systems with variable structure, and to the construction of effective numerical algorithms for the solution of optimization problems. INTRODUCTIONIn the last decades the mathematical theory of optimal processes has been intensively developed. Considerable attention has been given to problems with small perturbations. The application of the methods of perturbation theory (asymptotic methods) in problems of optimal control is useful because of the following reasons.i. In mathematical modeling one neglects frequently various small quantities and as a result one operates with idealized models~ The theory of perturbations allows us to establish a correspondence between the exact (perturbed) and the simplified (unperturbed, degenerate) models. This correspondence is established by the investigation of a limiting process from the solution of the perturbed problem to the solution of the unperturbed one. The theory of perturbations allows us to obtain corrections to the solution of the simplified problem (asymptotic expansion) and allows us to study the sensitivity of the solution of the exact problem with respect to small perturbations.2. The asymptotic theory gives us the possibility to obtain a qualitative picture of the solution~ 3. The knowledge of the as~cmptotics allows us to offer economical computational procedures for the approximate solution of the initial problems of optimal control, the solution of which is difficult or practically impossible because of nonlinearity, computational instability (as a consequence of the "rigidity"), high dimensionality, etco 4. Small perturbations in optimal control problems can be introduced artifically and then the theory of perturbations emerges as a method of investigation of the initial, in a certain sense "bad" (for example, ill-posed) problem.The investigation of optimal control problems by the methods of perturbation theory presents interest also for perturbation theory itself since its development is stimulated by the various new problems which emerge. The survey of F. L. Chernous'ko and V. B. Kolmanovskii The present survey is devoted to deterministic objects described by systems of ordinary differential or difference equations. Stochastic objects and objects described by partial differential equations are virtually not considered in this survey. The given bibliography does not have the pretention of absolute completeness. Additional references can be found in the works cited in the survey. We give some definitions and notations which will be used in the survey. The symbol ...

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Stochastic control of linear sigularly perturbed systems

Cited by 45 publications

References 8 publications

From Hierarchical to Open Access Electric Power Systems

From Hierarchical to Open Access Electric Power Systems

Applications of Singular Perturbation Techniques to Control Problems

Singular perturbations in optimal control problems

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