A Constructive Semi-global Differential Game Design Method for Multi-agent Systems under Input Constraint and Collision Avoidance

The constructive semi-global differential game concept is introduced into the multi-agent's cooperative controller designing of typical autonomous unmanned systems subject to controller input constraint as well as the collision avoidance requirements simultaneously. The problem of driving each agent which is assume to subject to input constraint nonlinearity from the initial position to a desired one and at the same time avoiding collisions (referring to both static obstacles and other agents) is modeled and transformed into multi-agent's collision avoidance problem. In view of the requirement that different agents working together might possibly have individual but conflicting purpose (such as in the multi-missile cooperative detection requiring slowly and continuing actions vs fast formation control scenario, and multi-agents' fast arriving vs avoiding different kinds of obstacles). The differential game theory provided a mechanism or framework for investigating different kinds of problems in which several players seek to achieve individual purposes or goals, which might be competing rather than cooperation. In view of the input constraints, the problem is reduced as a semi-global differential game. Conditions are established to guarantee input constraints are satisfied, and mainly by using the Hamilton-Jacobi-Isaacs (HJI for short) PDIs and as well as ε-Nash equilibria. The semi-global property of the states are also guaranteed. It provides a description in terms of the invariant set for the overall differential game system under constraint controller input. Illustrative examples are carried out to verify the effectiveness of the method, and also the feasibility of the suggested control protocols.