Cooperative game-oriented optimal design in constraint-following control of mechanical systems
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ORIGINAL PAPER
Cooperative game-oriented optimal design in constraint-following control of mechanical systems Qinqin Sun · Guolai Yang Ye-Hwa Chen
· Xiuye Wang ·
Received: 12 November 2019 / Accepted: 2 July 2020 © Springer Nature B.V. 2020
Abstract This paper proposes a cooperative gameoriented optimal design problem of robust control for uncertain mechanical systems. State of the concerned system is affected by (possibly fast) time-varying but bounded uncertainty. The task is to drive the system to obey a set of prescribed constraints. A β-measure is defined to gauge the constraint-following error; based on which, a robust control with two tunable parameters is then proposed to render the system to be uniform boundedness and uniform ultimate boundedness. For the seeking of the optimal design parameters, two cost functions, each of which is dominated by one tunable
parameter, are developed, and thereout a two-player cooperative game is formulated. Finally, the optimal design problem is successfully solved: with the existence, uniqueness, and analytical expression of the Pareto-optimality. This paper is the first ever endeavor to cast both constraint following and cooperative game into control framework for uncertain mechanical systems. Keywords Mechanical system · Constraint following · Cooperative game · Robust control · Optimal design
1 Introduction Q. Sun · G. Yang (B)· X. Wang The School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, People’s Republic of China e-mail: [email protected] Q. Sun e-mail: [email protected] X. Wang e-mail: [email protected] Y.-H. Chen The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA Y.-H. Chen The Key Laboratory of Road Construction Technology and Equipment of MOE, Chang’an University, Xi’an 710064, People’s Republic of China e-mail: [email protected]
Many efforts have been done in the robust control design for mechanical systems in the past. Cheng and Chen [1] designed a robust control for Euler– Lagrange mechanical systems with decentralized adaptive scheme. Yang et al. [2] proposed a robust control for under-actuated mechanical systems with model uncertainty. Rascon ´ et al. [3,4] explored a robust tracking control scheme for mechanical systems. However, the past works usually apply a generic control theory that is not solely intended for mechanical systems, that is control theory oriented. This paper falls into a physical system oriented framework [5] that starts with the characteristics of the problem, which only exist for mechanical systems, while along the way, the knowledge of control theory will help to pave the way for a concrete control design. As there is no need to satisfy the perfor-
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mance requirement too strictly in real life, it is practical to design an optimal control to let the control cost and the system performance render an acceptable balance. In recent years, many important results of optimal control des
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