Stochastic linear quadratic regulation for discrete-time linear systems with input delay

Song, X.; Zhang, Huanshui; Xie, Lihua

doi:10.1016/j.automatica.2009.04.024

Cited by 26 publications

(19 citation statements)

References 13 publications

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“…This case has a practical importance. There are studies where the cost matrices are allowed to be indefinite (see [3,16] and reference there in). In this paper we will investigate this special case to considered general discrete-time Riccati equations (1).…”

Section: The Lmi Approachmentioning

confidence: 99%

“…Thus, X + ≥ X and trX + (1)+...+ trX + (N) ≥ trX(1)+...+ trX(N) for any solution X of (3)- (4), i.e. for any matrix X satisfies restrictions of (16) and then X + is the solution of optimization problem (16).…”

Section: R(i Z)=−s(i Z) and F(i Y) T R(i Y)=−s(i Y)mentioning

confidence: 99%

“…Further on, suppose thatX is a solution of optimization problem (16). The inequalities (17) are fulfilled forX, i.e.X ∈ dom P † and assumptions for theorem 4.1 hold forX =X.…”

Section: R(i Z)=−s(i Z) and F(i Y) T R(i Y)=−s(i Y)mentioning

confidence: 99%

“…..,N. We investigate the numerical behavior of the LMI approach applied to the described optimization problems LMI: (16) and LMI(Y): (18) for finding the maximal solution to set of discrete-time generalized Riccati equations (3) - (4). In addition, we compare these LMI solvers with derived recurrence equations (12) for the maximal solution to the same set of equations.…”

Section: R(i Z)=−s(i Z) and F(i Y) T R(i Y)=−s(i Y)mentioning

confidence: 99%

“…In addition, the CPU time in seconds is included. The optimization problems (16) and (18) need the equals iteration steps (the column avIt) for finding the maximal solution to set of equations (3) We introduce an additional example where the above optimization problems are compared. This choice of the matrices B 0 (i), B 1 (i), i = 1, 2, 3 guaranteed that the matrices R(i, X) are positive semidefinite, i.e.…”

Section: R(i Z)=−s(i Z) and F(i Y) T R(i Y)=−s(i Y)mentioning

confidence: 99%

See 4 more Smart Citations

Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison

Ivanov¹

2012

Stochastic Modeling and Control

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Section: The Lmi Approachmentioning

confidence: 99%

Section: R(i Z)=−s(i Z) and F(i Y) T R(i Y)=−s(i Y)mentioning

confidence: 99%

“…Further on, suppose thatX is a solution of optimization problem (16). The inequalities (17) are fulfilled forX, i.e.X ∈ dom P † and assumptions for theorem 4.1 hold forX =X.…”

Section: R(i Z)=−s(i Z) and F(i Y) T R(i Y)=−s(i Y)mentioning

confidence: 99%

Section: R(i Z)=−s(i Z) and F(i Y) T R(i Y)=−s(i Y)mentioning

confidence: 99%

Section: R(i Z)=−s(i Z) and F(i Y) T R(i Y)=−s(i Y)mentioning

confidence: 99%

See 3 more Smart Citations

Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison

Ivanov¹

2012

Stochastic Modeling and Control

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Optimal control for discrete-time singular stochastic systems with input delay

Fan

Liang

Wang

2016

Optim. Control Appl. Meth.

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SUMMARYThe finite-horizon linear quadratic regulation problem is considered in this paper for the discrete-time singular systems with multiplicative noises and time delay in the input. Firstly, the extremum principle is discussed, and a stationary condition is derived for the singular stochastic system. Then, based on the relationships established between the state and the costate variables, the stationary condition is also shown to be a sufficient criterion assuring the existence of the solution for the stochastic control problem. The optimal controller is designed as a linear function of the current state and the past inputs information, which can be recursively calculated by effective algorithms. With the designed optimal controllers, the explicit expression is also derived for the minimal value of the performance index. One numerical example is provided in the end of the paper to illustrate the effectiveness of the obtained results.

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Linear quadratic regulation for discrete‐time systems with multiplicative noise and multiple input delays

Zhang

2016

Optim Control Appl Methods

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SUMMARYThis paper is concerned with the optimal linear quadratic regulation problem for discrete-time systems with state and control dependent noises and multiple delays in the input. We show that the problem admits a unique solution if and only if a sequence of matrices, which are determined by coupled difference equations developed in this paper, are positive definite. Under this condition, the optimal feedback controller and the optimal cost are presented via some coupled difference equations. Our approach is based on the stochastic maximum principle. The key technique is to establish relations between the costate and the state. Copyright

show abstract

Stochastic linear quadratic regulation for discrete-time linear systems with input delay

Cited by 26 publications

References 13 publications

Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison

Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison

Optimal control for discrete-time singular stochastic systems with input delay

Linear quadratic regulation for discrete‐time systems with multiplicative noise and multiple input delays

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