Two methods, combining controllability and Lyapunov stability, are presented for estimating reachability boundaries for nonlinear control systems. The controllability method is exact, but lacks appropriate boundary conditions in certain cases and is effectively restricted to two-dimensional problems. The approximate Lyapunov method combines Lyapunov stability theory with a controllability maximum principle. The Lyapunov estimate of the reachable set generally differs from the actual reachable set, but the estimate is conservative (i.e., guaranteed to contain the actual reachable set), does not require integration of the equations of motion, and is applicable to n-dimensional systems. Both methods are applied to an example of a prey-predator fishery with bounded harvesting efforts.
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