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We present the FlipDyn, a dynamic game in which two opponents (a defender andan adversary) choose strategies to optimally takeover a resource that involvesa dynamical system. At any time instant, each player can take over the resourceand thereby control the dynamical system after incurring a state-dependent anda control-dependent costs. The resulting model becomes a hybrid dynamicalsystem where the discrete state (FlipDyn state) determines which player is incontrol of the resource. Our objective is to compute the Nash equilibria ofthis dynamic zero-sum game. Our contributions are four-fold. First, for anynon-negative costs, we present analytical expressions for the saddle-pointvalue of the FlipDyn game, along with the corresponding Nash equilibrium (NE)takeover strategies. Second, for continuous state, linear dynamical systemswith quadratic costs, we establish sufficient conditions under which the gameadmits a NE in the space of linear state-feedback policies. Third, for scalardynamical systems with quadratic costs, we derive the NE takeover strategiesand saddle-point values independent of the continuous state of the dynamicalsystem. Fourth and finally, for higher dimensional linear dynamical systemswith quadratic costs, we derive approximate NE takeover strategies and controlpolicies which enable the computation of bounds on the value functions of thegame in each takeover state. We illustrate our findings through a numericalstudy involving the control of a linear dynamical system in the presence of anadversary.

FlipDyn with Control: Resource Takeover Games with Dynamics