Two methods are presented for investigating reachable sets for nonlinear control systems. One method, based on a reachability maximum principle, lacks appropriate boundary conditions if the reachable set is not closed. The main result of the paper is an approximate method employing a Lyapunov-type function and an associated optimization problem, both involving a parameter vector. For each value of the parameter vector the resulting estimate for the reachable set (and the intersection of all such estimates) is guaranteed to contain the actual reachable set. The method is applicable to systems of any dimension and does not require integration of the equations of motion.

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