Cooperative differential game model with continuous updating

The paper considers and describes the class of cooperative differential games with continuous updating. Such a class of differential games is new, at the moment only the classnoncooperative game models with continuous updating have been studied. This paper describes the process of constructing cooperative strategies, cooperative trajectory, characteristicfunction and cooperative solution with continuous updating. Cooperative case of limited resource extraction game model with continuous updating is considered. Optimal strategies,characteristic function and cooperative solution are constructed. The Shapley vector is used as a cooperative solution. The numerical simulation results are demonstrated in the Matlabenvironment.

Experimental and Analytical Nonzero-Sum Differential Game-Based Control of a 7-DOF Robotic Manipulator

We formulate a Nash-based feedback control law for an Euler-Lagrange system to yield a solution to non-cooperative differential game. The robot manipulators are broadly utilized in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler-Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution in order to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability.

A Simplest Differential Game on a Plane with Four Participants

Introduction. The article presents a simplest differential game with four participants. The players move on a plane and can do simple movements. The game under considering comes down to a cooperative differential game. The dynamic stability of such optimality principles as the S-kernel and Shapley vector is shown. Materials and Methods. The standard procedures of the cooperative game theory are applied to the analysis and decision of a cooperative differential game. The conditional and optimum trajectories, along which the players move, are found using the Pontryagin’s maximum principle. When constructing the characteristic function, the minimax approach is used. Results. The optimum strategy of the players, conditional and optimum trajectories of their movements at various ways of formation of coalitions are written out explicitly. The characteristic function is constructed according to the accepted max-min principle; the S-kernel and Shapley vector are considered as a decision. The components of the Shapley vector are written out explicitly; the fact that the Shapley vector is an element of the S-kernel and nonemptiness of the S-kernel, when the players are moving along an optimum trajectory, are shown. Using the results of the static cooperative game theory for researching differential games, we face the problems, which are connected with specifics of the differential equations of the movement. As a priority, the problem of the dynamic stability of the optimality principles under consideration is identified. In the work, the dynamic stability of the Shapley vector and S-kernel is shown. Discussion and Conclusion. The results of the research show that the analysis of the dynamic stability of the optimality principles considered is relevant.

Distributed cooperative deployment of heterogeneous autonomous agents: a Pareto suboptimal approach

SUMMARYThe paper presents a distributed cooperative control law for autonomous deployment of a team of heterogeneous agents. Deployment problems deal with the coordination of groups of agents in order to cover one or more assigned areas of the operational space. In particular, we consider a team composed by agents with different dynamics, sensing capabilities, and resources available for the deployment. Sensing heterogeneity is addressed by means of the descriptor function framework, an abstraction that provides a set of mathematical tools for describing both agent sensing capabilities and the desired deployment. A distributed cooperative control law is then formally derived finding a suboptimal solution of a cooperative differential game, where the agents are interested in achieving the requested deployment, while optimizing the resources usage according to their dynamics. The control law effectiveness is proven by theoretical arguments, and supported by numerical simulations.