We develop input-to-state stability (ISS) and inverse-optimal formulations for directional pursuit and evasion between nonholonomic vehicles whose steering acts on angular velocity rather than on heading. In contrast with classical geometric pursuit–evasion and proportional-navigation guidance, which yield intercepts at unspecified angles determined by initial conditions, we achieve prescribed-angle outcomes: directional interception (“from behind the evader”) and directional escape (“behind the pursuer”). Each scenario grants a kinematic advantage to one player and admits a clear outcome—capture or escape (in a particularly precise format of escape, which we call “spinaway”). The resulting feedback laws exhibit ISS properties: finite-time with zero asymptotic gain for interception, polynomially asymptotic with infinite asymptotic gain for escape. Without solving Hamilton–Jacobi–Isaacs equations, the designs are shown to be inverse optimal with respect to quadratic costs penalizing steering effort in proportion to range. The work introduces the first unified, provably ISS, and analytically explicit optimal framework for nonholonomic pursuit–evasion.
Miroslav Krstic (Thu,) studied this question.