Bounded and inverse optimal formation stabilization of second-order agents

Abstract This paper formulates and solves a new problem of both bounded and inverse optimal formation stabilization control for a group of second-order dynamic mobile agents with collision avoidance and limited sensing range. The control design is based on new Lyapunov functions, new non-zero convergence and dominating lemmas, new pairwise collision avoidance functions, and forwarding and inverse optimal control design methods. The proposed formation stabilization control design guarantees no collision between any agents, “almost global” asymptotic stability of desired equilibrium points and instability of undesired equilibrium points, an infinite gain margin, bounded controls by a pre-specified constant, and minimization of a cost function that penalizes both stabilization errors and the control inputs without having to solve a Hamilton–Jacobi–Bellman or Hamilton–Jacobi–Isaacs equation.