Consensus problems for discrete-time multi-agent systems were focused on. In order to design effective consensus protocols, which were aimed at ensuring that the concerned states of agents converged to a common value,...Consensus problems for discrete-time multi-agent systems were focused on. In order to design effective consensus protocols, which were aimed at ensuring that the concerned states of agents converged to a common value, a new consensus protocol for general discrete-time multi-agent system was proposed based on Lyapunov stability theory. For discrete-time multi-agent systems with desired trajectory, trajectory tracking and formation control problems were studied. The main idea of trajectory tracking problems was to design trajectory controller such that each agent tracked desired trajectory. For a type of formation problem with fixed formation structure, the formation structure set was introduced. According to the formation structure set, each agent can track its individual desired trajectory. Finally, simulations were provided to demonstrate the effectiveness of the theoretical results. The mlmerical results show that the states of agents converge to zero with consensus protocol, which is said to achieve a consensus asymptotically. In addition, through designing appropriate trajectory controllers, the simulation results show that agents converge to the desired trajectory asymptotically and can form different formations.展开更多
This paper explores the application of noncooperative game theory together with the concept of Nash equilibrium to the investigation of some basic problems on multi-scale structure, especially the meso-scale structure...This paper explores the application of noncooperative game theory together with the concept of Nash equilibrium to the investigation of some basic problems on multi-scale structure, especially the meso-scale structure in the multi-phase complex systems in chemical engineering. The basis of this work is the energy-minimization-multi-scale （EMMS） model proposed by Li and Kwauk （1994） and Li, et al. （2013） which identifies the multi-scale structure as a result of ＇compromise-in-competition between dominant mechanisms＇ and tries to solve a multi-objective optimization problem. However, the existing methods often integrate it into a problem of single objective optimization, which does not clearly reflect the ＇compromise-in-competition＇ mechanism and causes heavy computation burden as well as uncertainty in choosing suitable weighting factors. This paper will formulate the compromise in competition mechanism in EMMS model as a noncooperative game with constraints, and will describe the desired stable system state as a generalized Nash equilibrium. Then the authors will investigate the game theoretical approach for two typical systems in chemical engineering, the gas-solid fluidiza- tion （GSF） system and turbulent flow in pipe. Two different cases for generalized Nash equilibrinm in such systems will be well defined and distinguished. The generalize Nash equilibrium will be solved accurately for the GSF system and a feasible method will be given for turbulent flow in pipe. These results coincide with the existing computational results and show the feasibility of this approach, which overcomes the disadvantages of the existing methods and provides deep insight into the mechanisms of multi-scale structure in the multi-phase complex systems in chemical engineering.展开更多
基金Projects(60474029,60774045,60604005) supported by the National Natural Science Foundation of ChinaProject supported by the Graduate Degree Thesis Innovation Foundation of Central South University,China
文摘Consensus problems for discrete-time multi-agent systems were focused on. In order to design effective consensus protocols, which were aimed at ensuring that the concerned states of agents converged to a common value, a new consensus protocol for general discrete-time multi-agent system was proposed based on Lyapunov stability theory. For discrete-time multi-agent systems with desired trajectory, trajectory tracking and formation control problems were studied. The main idea of trajectory tracking problems was to design trajectory controller such that each agent tracked desired trajectory. For a type of formation problem with fixed formation structure, the formation structure set was introduced. According to the formation structure set, each agent can track its individual desired trajectory. Finally, simulations were provided to demonstrate the effectiveness of the theoretical results. The mlmerical results show that the states of agents converge to zero with consensus protocol, which is said to achieve a consensus asymptotically. In addition, through designing appropriate trajectory controllers, the simulation results show that agents converge to the desired trajectory asymptotically and can form different formations.
基金supported by the National Natural Science Foundation of China under Grant Nos.11688101,91634203,61304159by the National Center for Mathematics and Interdisciplinary Sciences
文摘This paper explores the application of noncooperative game theory together with the concept of Nash equilibrium to the investigation of some basic problems on multi-scale structure, especially the meso-scale structure in the multi-phase complex systems in chemical engineering. The basis of this work is the energy-minimization-multi-scale （EMMS） model proposed by Li and Kwauk （1994） and Li, et al. （2013） which identifies the multi-scale structure as a result of ＇compromise-in-competition between dominant mechanisms＇ and tries to solve a multi-objective optimization problem. However, the existing methods often integrate it into a problem of single objective optimization, which does not clearly reflect the ＇compromise-in-competition＇ mechanism and causes heavy computation burden as well as uncertainty in choosing suitable weighting factors. This paper will formulate the compromise in competition mechanism in EMMS model as a noncooperative game with constraints, and will describe the desired stable system state as a generalized Nash equilibrium. Then the authors will investigate the game theoretical approach for two typical systems in chemical engineering, the gas-solid fluidiza- tion （GSF） system and turbulent flow in pipe. Two different cases for generalized Nash equilibrinm in such systems will be well defined and distinguished. The generalize Nash equilibrium will be solved accurately for the GSF system and a feasible method will be given for turbulent flow in pipe. These results coincide with the existing computational results and show the feasibility of this approach, which overcomes the disadvantages of the existing methods and provides deep insight into the mechanisms of multi-scale structure in the multi-phase complex systems in chemical engineering.
