Complete Solution of a Differential Game with Linear Dynamics and Bounded Controls

Abstract

A zero-sum finite-horizon differential game with linear dynamics and bounded controls is considered. The target set is a given hyperplane in the state space. The cost function is the distance between the terminal state and this hyperplane. The complete game solution is obtained in two classes of controls: open-loop and feedback-based controls.

Increasing Pursuer Capturability by Using Hybrid Dynamics

“…We propose here an approach to the solution different from the one by . Due to Glizer and Turetsky (2008), the solution is determined by the sign of H(ϑ p ), wherê…”

Robust pursuit of a hybrid evader — The generalized solution

“…The regular region (ϑ, z) ∈ D 1 is filled with trajectories generated by the pair of candidate optimal strategies u 0 (ϑ, z) = v 0 (ϑ, z) = sign z(ϑ) and the value of the game depends on the initial conditions. In singular region the optimal strategies are arbitrary subject to (13) for (ϑ, z) ∈ D 0 , and the value of the game is constant.…”

“…The RHDG optimal pursuer feedback strategy is obtained by the game space decomposition [10], [13] into two regions. One of these regions (regular) is completely covered by candidate optimal trajectories.…”

“…Proof: Theorem 5 in [13] provides the general solution of a scalar differential game with bounded controls. This solution is based on the behavior of a so-called "determining function".…”

“…In the fixed dynamics version of the game, the dynamics of each player is completely described by the respective vector ω i = (a max i , τ i ), i = p, e. Such a game has been studied extensively, see [10], [11], [12], [13]. It was shown that this game has a closed-loop saddle-point solution, completely determined by the pair (ω p , ω e ).…”