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A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

Fragoso, Marcelo D ; Costa, Oswaldo L V

IEEE transactions on automatic control, 2010-12, Vol.55 (12), p.2692-2707 [Periódico revisado por pares]

New York, NY: IEEE

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Título:
A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters
Autor: Fragoso, Marcelo D ; Costa, Oswaldo L V
Assuntos: Algorithms ; Applied sciences ; Closed loop systems ; Computer science; control theory; systems ; Continuous-time ; Control systems ; Control theory. Systems ; Cost function ; Differential algebraic equations ; Differential equations ; Dynamical systems ; Dynamics ; Exact sciences and technology ; Filtering ; Horizon ; jump Markov linear systems ; Linear systems ; Mathematical analysis ; Modelling and identification ; Operations research ; Optimal control ; Postal services ; Riccati equations ; Separation ; separation principle ; Studies
É parte de: IEEE transactions on automatic control, 2010-12, Vol.55 (12), p.2692-2707
Notas: ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
Descrição: In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.
Editor: New York, NY: IEEE
Idioma: Inglês

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A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

Fragoso, Marcelo D ; Costa, Oswaldo L V

New York, NY: IEEE

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