Discrete‐Time Indefinite Stochastic LQ Control via SDP and LMI Methods

Zhou, Shijie; Zhang, Weihai

doi:10.1155/2012/638762

Cited by 8 publications

(10 citation statements)

References 22 publications

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“…On the other hand, the following result corresponding to semidefinite programming (SDP) is known [10].…”

Section: Preliminary Resultsmentioning

confidence: 99%

Stackelberg strategy for discrete-time stochastic system and its application to weakly coupled systems

Mukaidani

2014

2014 American Control Conference

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In this paper, infinite-horizon Stackelberg strategy for discrete-time stochastic system is investigated. A necessary condition for the existence of the strategy set is established via a set of cross-coupled stochastic algebraic Lyapunov and Riccati equations (CSALREs). As another important contribution, weakly coupled large-scale stochastic discrete-time systems are considered. After establishing an asymptotic structure with positive definiteness for CSALREs solutions, parameter independent strategy set is established. Moreover, degradation of cost via the proposed strategy set is also derived. Finally, the equivalence between the parameter independent linear quadratic (LQ) controls and the proposed approximate reduced-order Stackelberg strategy set is proved for ε = 0. A numerical example is provided to demonstrate the efficiency of the obtained results.

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“…On the other hand, the following result corresponding to semidefinite programming (SDP) is known [10].…”

Section: Preliminary Resultsmentioning

confidence: 99%

Stackelberg strategy for discrete-time stochastic system and its application to weakly coupled systems

Mukaidani

2014

2014 American Control Conference

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“…It has been an important work to study nonlinear PDE [1] due to their rich mathematical structures and features [2][3][4][5] as well as important applications in fluid dynamics and plasma physics [6][7][8][9][10][11][12]. Although many theories and methods were proposed to discuss the PDE [13][14][15][16][17][18][19][20], however, most nonlinear PDE have no analytic solutions; numerical methods are necessary to study hydrodynamic characteristics of PDEs [21][22][23][24]. For the discretization of time derivative in time-dependent PDEs for numerical methods, the well-known ways is the ODE solver, such as multi-step method and Runge-Kutta method.…”

Section: Formulation Of the Problem Of Interest For This Investigationmentioning

confidence: 99%

The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

Dong

Yang

2018

Mathematics

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We develop a Lax–Wendroff scheme on time discretization procedure for finite volume weighted essentially non-oscillatory schemes, which is used to simulate hyperbolic conservation law. We put more focus on the implementation of one-dimensional and two-dimensional nonlinear systems of Euler functions. The scheme can keep avoiding the local characteristic decompositions for higher derivative terms in Taylor expansion, even omit partly procedure of the nonlinear weights. Extensive simulations are performed, which show that the fifth order finite volume WENO (Weighted Essentially Non-oscillatory) schemes based on Lax–Wendroff-type time discretization provide a higher accuracy order, non-oscillatory properties and more cost efficiency than WENO scheme based on Runge–Kutta time discretization for certain problems. Those conclusions almost agree with that of finite difference WENO schemes based on Lax–Wendroff time discretization for Euler system, while finite volume scheme has more flexible mesh structure, especially for unstructured meshes.

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“…In recent years, there is an increasing interest in mean-field control theory in mathematics and the control communities. Especially, the linear-quadratic (LQ) optimal control problems [20][21][22][23] of classical stochastic systems have been generalized to mean-field stochastic systems [24][25][26][27][28][29][30][31]. Finite and infinite horizon LQ problems of continuous-time mean-field stochastic systems were discussed in [24] and [25] respectively.…”

Section: Introductionmentioning

confidence: 99%

Characterization of Stochastic Mean‐Field Type Index

Zhang

2017

Asian Journal of Control

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scriptH− index of mean‐field stochastic differential equations (SDE) is investigated in this paper. For systems with state‐ and input‐dependent noise, we obtain a sufficient condition of scriptH− index larger than some λ>0 via the solvability of differential Riccati equations (DRE). Especially, a necessary and sufficient condition is given for mean‐field SDE with state‐dependent noise, which generalize the corresponding results of classical stochastic systems to the mean‐field stochastic models.

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Discrete‐Time Indefinite Stochastic LQ Control via SDP and LMI Methods

Cited by 8 publications

References 22 publications

Stackelberg strategy for discrete-time stochastic system and its application to weakly coupled systems

Stackelberg strategy for discrete-time stochastic system and its application to weakly coupled systems

The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

Characterization of Stochastic Mean‐Field Type Index

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