Autonomous systems operating in real-world conditions often have to contend with environmental disturbance behavior that is unknown a priori. We present a method for efficiently computing reachable sets for continuous-time systems with partially unknown dynamics. Our main assumption is that, given any hyperrectangle of states, lower and upper bounds for the unknown components are available. With this assumption, the theory of mixed monotone systems allows us to formulate an efficient method for computing a hyperrectangular set that overapproximates the reachable set of the system. We apply this formulation to a dynamical system navigating towards a goal region while avoiding unsafe regions of the state space. We derive a model predictive control scheme that avoids the unsafe region and ensures the system is always within reach of a conservative, a priori guaranteed safe region, thus always ensuring feasibility until the goal is reachable. We also consider the problem of tracking a reference trajectory for systems with partially unknown dynamics. We develop a modified embedding system, a single controlled trajectory of which corresponds to a controlled forward invariant interval tube around the reference trajectory. We conclude the presentation by proposing the additional work to be undertaken to complete this dissertation.