On the finite horizon Nash equilibrium solution in the differential game approach to formation control

The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution. These equations (if solvable) can be solved numerically by using the terminal value and the backward iteration. To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game. The main contributions of this paper are as follows. First, the existence of Nash equilibrium controls for the discrete-time formation control problem is shown. Second, a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed. An illustrative example is given to justify the models and solution.