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This paper considers the problem of designing a Receding Horizon Control (RHC) law for craft defending a harbor from one intruder or a group of intruders. The heart of a RHC law is the optimization problem that must be solved at the start of each sample time to determine the control to be used over this sample time. The challenge is to formulate an optimization problem that captures the control objectives and to develop computational techniques that are fast enough to solve this problem in a small fraction of the sampling time. Since the strategy of the intruders is not known to the defenders, we propose three alternative worst case minmax optimization problems that capture likely intruder scenarios and demonstrate that these can be solved fast enough to be used in real time implementation. In addition, we present several numerical simulations as well as human-computer experiments that illustrate what happens in this “defend-intrude” game. We have decided against attempting to extend classical pursuit-evasion results (see (Isaacs 1954)) to our RHC problem because our complex boundary conditions and the size of the state space make solving the Hamilton-Jacobi-Bellman-Isaacs equations in real time impractical.