Distributed model predictive control for consensus of nonlinear systems via parametric sensitivity

Tianyu Yu; Fei Zhao; Zuhua Xu; Jun Zhao; Xi Chen

doi:10.1016/j.isatra.2024.11.019

Distributed model predictive control for consensus of nonlinear systems via parametric sensitivity

ISA Trans. 2024 Nov 12:S0019-0578(24)00529-9. doi: 10.1016/j.isatra.2024.11.019. Online ahead of print.

Authors

Tianyu Yu¹, Fei Zhao², Zuhua Xu³, Jun Zhao⁴, Xi Chen⁵

Affiliations

¹ State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, China. Electronic address: yutianyu@zju.edu.cn.
² State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, China. Electronic address: zhaofeizju@zju.edu.cn.
³ State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, China. Electronic address: zhxu@zju.edu.cn.
⁴ State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, China. Electronic address: jzhao@zju.edu.cn.
⁵ State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, China. Electronic address: xi_chen@zju.edu.cn.

PMID: 39562226
DOI: 10.1016/j.isatra.2024.11.019

Abstract

To handle the nonlinear consensus problem, a distributed model predictive control (DMPC) scheme is developed via parametric sensitivity. A two-stage input computation strategy is adopted for enhancing optimization efficiency. In the background stage, each agent first establishes its next-step optimization problem based on communication topology, and then performs distributed optimization to calculate the future inputs. In the online stage, all the agents build their sensitivity equations based on new information. Three variants of sensitivity equation are developed based on the level of communication load capacity, and the corresponding computation strategies are proposed. After solution, the background inputs are corrected and implemented. The optimality and robustness of the proposed algorithm are rigorously derived. Finally, the superiority of this DMPC scheme is demonstrated in the multi-vehicle system with two different topologies.

Keywords: Consensus problem; Distributed model predictive control; Nonlinear programming; Parametric sensitivity.