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Chao Sun1,Guoqiang Hu1,2.[en_title][J].Control Theory and Technology,2023,21(3):437~447.[Copy]
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Nash equilibrium seeking with prescribed performance
ChaoSun1,GuoqiangHu1,2
0
(1 Continental-NTU Corporate Lab, Nanyang Technological University, 639798 Nanyang, Singapore;2 School of Electrical and Electronic Engineering, Nanyang Technological University, 639798 Nanyang, Singapore)
摘要:
In thiswork,we study aNash equilibrium (NE) seeking problem for stronglymonotone non-cooperative games with prescribed performance. Unlike general NE seeking algorithms, the proposed prescribed-performance NE seeking laws ensure that the convergence error evolves within a predefined region. Thus, the settling time, convergence rate, and maximum overshoot of the algorithm can be guaranteed. First, we develop a second-order Newton-like algorithm that can guarantee prescribed performance and asymptotically converge to the NE of the game. Then, we develop a first-order gradient-based algorithm. To remove some restrictions on this first-order algorithm, we propose two discontinuous dynamical system-based algorithms using tools from non-smooth analysis and adaptive control. We study the special case in optimization problems. Then, we investigate the robustness of the algorithms. It can be proven that the proposed algorithms can guarantee asymptotic convergence to the Nash equilibrium with prescribed performance in the presence of bounded disturbances. Furthermore, we consider a second-order dynamical system solution. The simulation results verify the effectiveness and efficiency of the algorithms, in terms of their convergence rate and disturbance rejection ability.
关键词:  Nash equilibrium seeking · Non-cooperative games · Prescribed performance · Disturbance rejection
DOI:https://doi.org/10.1007/s11768-023-00169-4
基金项目:This work was supported by the RIE2020 Industry Alignment Fund—Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s).
Nash equilibrium seeking with prescribed performance
Chao Sun1,Guoqiang Hu1,2
(1 Continental-NTU Corporate Lab, Nanyang Technological University, 639798 Nanyang, Singapore;2 School of Electrical and Electronic Engineering, Nanyang Technological University, 639798 Nanyang, Singapore)
Abstract:
In thiswork,we study aNash equilibrium (NE) seeking problem for stronglymonotone non-cooperative games with prescribed performance. Unlike general NE seeking algorithms, the proposed prescribed-performance NE seeking laws ensure that the convergence error evolves within a predefined region. Thus, the settling time, convergence rate, and maximum overshoot of the algorithm can be guaranteed. First, we develop a second-order Newton-like algorithm that can guarantee prescribed performance and asymptotically converge to the NE of the game. Then, we develop a first-order gradient-based algorithm. To remove some restrictions on this first-order algorithm, we propose two discontinuous dynamical system-based algorithms using tools from non-smooth analysis and adaptive control. We study the special case in optimization problems. Then, we investigate the robustness of the algorithms. It can be proven that the proposed algorithms can guarantee asymptotic convergence to the Nash equilibrium with prescribed performance in the presence of bounded disturbances. Furthermore, we consider a second-order dynamical system solution. The simulation results verify the effectiveness and efficiency of the algorithms, in terms of their convergence rate and disturbance rejection ability.
Key words:  Nash equilibrium seeking · Non-cooperative games · Prescribed performance · Disturbance rejection