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Constraint-following control for uncertain mechanical systems: an intelligent multi-agent game-theoretic approach

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Abstract

Practically all performance requirement of systems can be formulated as constraints. In engineering, systems are tasked, via proper control design, to follow the constraints. There are however two major challenges. The first is that systems possess uncertainty, which may be (possibly fast) time-varying. The second is that systems are mostly nonlinear, due to effects such as nonlinear elasticity, etc. To resolve the challenges, a novel performance measure \({\hat{\beta }}\) is introduced as a dynamic depiction of the constraint-following error. A new control design is proposed based on this measure. The control design procedure includes two phases. The first phase is to design a control scheme, based on a feasible parameter (meaning the parameter only needs to be selected within a certain range), which renders guaranteed performance regardless of the uncertainty. After that, the second phase is to seek an optimal design for the control parameters. This task is resolved by an intelligent multi-agent game-theoretic approach. We consider there are multi-agents in the design process, each addresses a design consideration. However these considerations are opposite: with one’s decreases (or increases) will increase (or decrease) the other. Agents are to cooperate with each other intelligently to reach the optimal choice of the design parameters. The design is applied to an active suspension system, and its performance is verified by comparing with linear-quadratic regulator control and sliding mode control methods.

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Acknowledgements

The research is supported by the National Natural Science Foundation of China (No. 52005302). This research is also supported by the Shandong Postdoctoral Science Foundation (No. SDCX-ZG-202202029), the Taishan Scholar Foundation of Shandong Province (No. tsqn201909113), the National Natural Science Foundation of China (No. 52174120), and the Elite Plan (No. 0104060540418).

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Authors and Affiliations

  1. College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao, 266590, Shandong, People’s Republic of China

    Rongrong Yu, Guofeng Wang, Jindong Bai & Qiang Zhang

  2. The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Ye-Hwa Chen

  3. National Engineering Laboratory for Highway Maintenance Equipment, Chang’an University, Xi’an, 710065, Shaanxi, People’s Republic of China

    Ye-Hwa Chen

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  1. Rongrong Yu
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Correspondence to Qiang Zhang.

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Yu, R., Wang, G., Bai, J. et al. Constraint-following control for uncertain mechanical systems: an intelligent multi-agent game-theoretic approach. Nonlinear Dyn 111, 13653–13668 (2023). https://doi.org/10.1007/s11071-023-08483-x

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