On time-optimal feedback control

Time-optimal feedback control can be computed by solving the Hamilton-Jacobi-Bellman (HJB) equation. To date, this problem has not been solved for nonlinear systems, such as articulated robotic manipulators, partly due to the difficulty in efficiently finding a solution to the HJB equation. In this paper, a new sufficient optimality condition for time-optimal feedback control is presented. It generalizes the previous sufficient conditions, the HJB equation and a Lyapunov-based condition derived by Nahi (1964). The new condition is satisfied by a class of piecewise C² continuous functions, termed generalized value functions, as demonstrated in an example for a simple nonlinear system.