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Chen, Junmin,Wang, Xian,He, Zhen The Youngnam Mathematical Society 2013 East Asian mathematical journal Vol.29 No.3
In this paper, a new monotonicity, $M({\cdot},{\cdot})$-monotonicity, is introduced in Banach spaces, and the resolvent operator of an $M({\cdot},{\cdot})$-monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with $M({\cdot},{\cdot})$-monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the convergence of the sequences generated by the proximal point algorithms in Banach spaces. The results in this paper extend and improve some known results in the literature.
Junmin Chen,Xian Wang,Zhen He 영남수학회 2013 East Asian mathematical journal Vol.29 No.3
In this paper, a new monotonicity, M(·,·)-monotonicity, is introduced in Banach spaces, and the resolvent operator of an M(·,·)-monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with M(·,·)-monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the convergence of the sequences generated by the proximal point algorithms in Banach spaces. The results in this paper extend and improve some known results in the literature.
Optimal Incremental-containment Control of Two-order Swarm System Based on Reinforcement Learning
Haipeng Chen,Wenxing Fu,Kang Chen,Junmin Liu,Dengxiu Yu 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.10
In this paper, the optimal incremental-containment control of two-order swarm system based on reinforcement learning (RL) is proposed to avoid the dilemma that the number of agents in a swarm system is immutable, which is essential for a swarm system that cannot meet the containment demands and need more agents to expand the containment range. Notably, the number of agents in a swarm system with a traditional containment controller is immutable, which limits the containment range that the swarm system can achieve. Besides, in traditional optimal control theory, it is obtained by solving the Hamilton-Jacobi-Bellman (HJB) equation, which is difficult to solve due to the unknown nonlinearity. To overcome these problems, several contributions are made in this paper. Firstly, in order to overcome the dilemma that the number of agents in the swarm system is immutable, the incremental-containment control is proposed. Secondly, considering the error and control input as the optimization goal, the optimal cost function is introduced and the optimal incremental-containment control is proposed to reduce resource waste and increase hardware service life. Furthermore, based on the proposed optimal incrementalcontainment control, the controller is designed by a new RL based on the backstepping method. The Lyapunov function is used to prove the stability of controller. The simulation show the efficiency of the proposed controller.
Jiaxi Chen,Junmin Li 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.3
This paper studies the consensus of mixed-order unknown periodic time-vary parameterized nonlinear multi-agent systems over heterogeneous network topology. The follower is represented by a first-order or secondorder periodic parameterized dynamic system, and the leader is presented through a second-order dynamic system. For unknown leader dynamics and bounded input disturbances, a differential adaptive parameter learning law is designed. For unknown periodic time-varying parameters, a repetitive learning law is designed based on the design method of repeated learning. Based on Lyapunov-like stability theory and repetitive learning control method, a new repetitive learning controller is designed and a sufficient condition of consensus for the MAS is also given in this paper. Unlike some existing results, this study is a fully distributed result. Finally, a simulation example is given to verify the effectiveness of this study.
Guopei Chen,Ying Yang,Junmin Li 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.2
In this paper, extended differential Petri nets (EDPNs), a new extension of differential Petri nets (DPNs), is proposed. Compared with the existing extension of DPNs, EDPNs has two improvements: (1) the restriction on the enabling condition that depends on the weight of arc is relaxed, i.e., allow the enabling condition has more general form; (2) the definition is extended for the weight of arc. By these two improvements, EDPNs presents larger flexibility and modeling power than the existing extension of DPNs. Using this model, the stability of hybrid dynamical systems (HDS) is studied. A new Lyapunov’s stability theorem of HDS is given. Furthermore, by using the information of index matrix and a new composite energy function, the stability theorem of linear HDS is obtained.
A HYBRID ITERATIVE METHOD OF SOLUTION FOR MIXED EQUILIBRIUM AND OPTIMIZATION PROBLEMS
Lijuan Zhang,Junmin Chen 영남수학회 2010 East Asian mathematical journal Vol.26 No.1
In this paper, we introduce a hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of finitely many nonexpansive mappings and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We show that the iterative sequences converge strongly to a common element of the three sets. The results extended and improved the corresponding results of L.-C.Ceng and J.-C.Yao.