A new computational method for sparse optimal control of cyber-physical systems with varying delay

Sida Lin; Dongyao Yang; Jinlong Yuan; Changzhi Wu; Tao Zhou; An Li; Chuanye Gu; Jun Xie; Kuikui Gao; Sida Lin; Dongyao Yang; Jinlong Yuan; Changzhi Wu; Tao Zhou; An Li; Chuanye Gu; Jun Xie; Kuikui Gao

doi:10.3934/era.2024306

Electronic Research Archive

2024, Volume 32, Issue 12: 6553-6577. doi: 10.3934/era.2024306

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A new computational method for sparse optimal control of cyber-physical systems with varying delay

1.
School of Science, Dalian Maritime University, Dalian 116026, China
2.
Chongqing National Center for Applied Mathematics, Chongqing Normal University, Chongqing 404087, China
3.
Institute for Intelligent Systems Research and Innovation (IISRI), Deakin University, Geelong 3217, Australia
4.
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
5.
School of Management, Guangzhou University, Guangzhou 510006, China
6.
Department of Basics, PLA Dalian Naval Academy, Dalian 116018, China
7.
Ayata Incorporation, 2700 Post Oak Blvd, 21st Floor, Houston, TX 77056, USA

Received: 20 September 2024 Revised: 10 November 2024 Accepted: 19 November 2024 Published: 04 December 2024

In practice, network operators tend to choose sparse communication topologies to cut costs, and the concurrent use of a communication network by multiple users commonly results in feedback delays. Our goal was to obtain the optimal sparse feedback control matrix $ K $. For this, we proposed a sparse optimal control (SOC) problem governed by the cyber-physical system with varying delay, to minimize $ ||K||_0 $ subject to a maximum allowable compromise in system cost. A penalty method was utilized to transform the SOC problem into a form that was constrained solely by box constraints. A smoothing technique was used to approximate the nonsmooth element in the resulting problem, and an analysis of the errors introduced by this technique was subsequently conducted. The gradients of the objective function concerning the feedback control matrix were obtained by solving the state system and a variational system simultaneously forward in time. An optimization algorithm was devised to tackle the resulting problem, building on the piecewise quadratic approximation. Finally, we have presented of simulations.
- cyber-physical system,
- $ l_0 $-norm of a matrix,
- sparse feedback matrix,
- varying delay,
- smoothing technique
Citation: Sida Lin, Dongyao Yang, Jinlong Yuan, Changzhi Wu, Tao Zhou, An Li, Chuanye Gu, Jun Xie, Kuikui Gao. A new computational method for sparse optimal control of cyber-physical systems with varying delay[J]. Electronic Research Archive, 2024, 32(12): 6553-6577. doi: 10.3934/era.2024306

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Abstract

In practice, network operators tend to choose sparse communication topologies to cut costs, and the concurrent use of a communication network by multiple users commonly results in feedback delays. Our goal was to obtain the optimal sparse feedback control matrix $ K $. For this, we proposed a sparse optimal control (SOC) problem governed by the cyber-physical system with varying delay, to minimize $ ||K||_0 $ subject to a maximum allowable compromise in system cost. A penalty method was utilized to transform the SOC problem into a form that was constrained solely by box constraints. A smoothing technique was used to approximate the nonsmooth element in the resulting problem, and an analysis of the errors introduced by this technique was subsequently conducted. The gradients of the objective function concerning the feedback control matrix were obtained by solving the state system and a variational system simultaneously forward in time. An optimization algorithm was devised to tackle the resulting problem, building on the piecewise quadratic approximation. Finally, we have presented of simulations.

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