Optimal Stabilization Control for Discrete-Time Mean-Field Stochastic Systems

Zhang, Huanshui; Qi, Qingyuan; Fu, Minyue

doi:10.1109/tac.2018.2813006

Cited by 44 publications

(28 citation statements)

References 28 publications

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“…These results have possible applications in areas such as irregular measurement feedback control, robust control, H ∞ control, and stochastic control. We would also like to emphasize that the proposed technique used in this paper, namely the solving of an associated FBDEs, is a very general strategy, with which we have successfully solved other complicated control problems such as stochastic LQ control with time delay [15,18], Stackerberge game control [37], mean field stochastic control [38], stabilization of NCSs with simultaneous transmission delay and packet dropout [39].…”

Section: Discussionmentioning

confidence: 99%

Optimal control with irregular performance

Zhang¹,

Jin²

2019

Sci. China Inf. Sci.

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In this paper, we solve the long-standing fundamental problem of irregular linear-quadratic (LQ) optimal control, which has received significant attention since the 1960s. We derive the optimal controllers via the key technique of finding the analytical solutions to two different forward and backward differential equations (FBDEs). We give a complete solution to the finite-horizon irregular LQ control problem using a new 'two-layer optimization' approach. We also obtain the necessary and sufficient condition for the existence of optimal and stabilizing solutions in the infinite-horizon case in terms of solutions to two Riccati equations and the stabilization of one specific system. For the first time, we explore the essential differences between irregular and standard LQ control, making a fundamental contribution to classical LQ control theory. We show that irregular LQ control is totally different from regular control as the irregular controller must guarantee the terminal state constraint of P 1 (T )x(T ) = 0.

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Section: Discussionmentioning

confidence: 99%

Optimal control with irregular performance

Zhang¹,

Jin²

2019

Sci. China Inf. Sci.

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“…This time-invariant characteristic is well-suited to the representation of manufacturing variations in physical parameters. Various control methods have also been proposed for time-varying stochastic parameters (e.g., [29]- [34]). Parameters that vary over time are applicable to cases in which noise has an effect on the parameters, in contrast to static manufacturing variations.…”

Section: Literature Reviewmentioning

confidence: 99%

Stochastic Optimal Control to Minimize the Impact of Manufacturing Variations on Nanomechanical Systems

et al. 2019

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This paper presents a control method intended to suppress the effects of manufacturing variations on nanomechanical systems. Often, the resonance characteristics of nanoscale devices are inconsistent, due to unavoidable variations in the fabrication process. This is important because resonant vibrations enhance the sensitivities of the devices. As such, the sensitivities of these systems can be degraded if the device characteristics are not identified. To address this fundamental problem, this paper presents a multidisciplinary method based on control theory, nanotechnology, and communication technology. A stochastic optimal feedback controller is employed to enhance an average sensitivity by regarding the variations as stochastic parameters. This method is applied to nanoscale receivers that detect transmitted binary data based on binary phase-shift keying in communication systems. The proposed method controls the vibrations of carbon nanotubes (CNTs) that serve as the antennas of the receiver. The proposed method is demonstrated via a numerical simulation using nanoscale receivers with the manufacturing variation. The simulation based on experimental data obtained from CNTs shows that the average performance of the devices is enhanced. INDEX TERMS Nanoelectromechanical systems, optimal control, stochastic systems.

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“…Relevant developments for mean‐field control problems can be found in [9–16] and references therein. The continuous‐time finite‐horizon mean‐field Linear Quadratic (LQ)control problem studied in [15], where a sufficient and necessary solvability condition to the problem was presented in terms of an operator criterion and by using a decoupling technique, the optimal control was designed via two Riccati equations.…”

Section: Introductionmentioning

confidence: 99%

“…For the finite discrete‐time mean‐field LQ control problems, a necessary and sufficient solvability condition was presented in [12] alongside with an explicit optimal control using a matrix dynamical optimisation method. The infinite case of the same type of problem was analysed in [14, 16], whereas, in [14], a stabilising condition and the equivalence of

L^{2}

open‐loop stabilisability and

L^{2}

closed‐loop stabilisability were established. In [16], the authors proved that, under the exact detectability (exact observability) assumption, the mean‐field system is stabilisable in the mean‐square sense with the optimal controller if and only if a set of coupled algebraic Riccati equations have a unique positive semi‐definite (positive definite) solution.…”

Section: Introductionmentioning

confidence: 99%