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This study presents a model predictive control approach for seizure reduction in a computational model of epilepsy. The differential dynamic programming (DDP) algorithm is implemented in a model predictive fashion to optimize a controller for suppressing seizures in a chaotic oscillator model. The chaotic oscillator model uses proportional-integral (PI) controller to represent the internal control mechanism that maintains stable neural activity in a healthy brain. In the pathological case, the gains of this PI controller are reduced, preventing sufficient feedback to suppress correlation increase between normal and pathological brain dynamics. This increase in correlation leads to synchronization of oscillator dynamics leading to the destabilization of neural activity and epileptic behavior. The pathological case of the chaotic oscillator model is formulated as an optimal control problem, which we solve using the dynamic programming principle. We propose using model predictive control with differential dynamic programming optimization as a possible method for controlling epileptic seizures in known models of epilepsy.

In this work we present a sampling-based algorithm designed to solve game-theoretic control problems and risk-sensitive stochastic optimal control problems. The cornerstone of the proposed approach is the formulation of the problem in terms of forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear version of the Feynman-Kac lemma, we obtain a probabilistic representation of the solution to the nonlinear Hamilton-Jacobi-Isaacs equation, expressed in the form of a decoupled system of FBSDEs. This system of FBSDEs can then be simulated by employing linear regression techniques. Utilizing the connection between stochastic differential games and risk-sensitive optimal control, we demonstrate that the proposed algorithm is also applicable to the latter class of problems. Simulation results validate the algorithm.

In this paper we consider a differential game of pursuit and evasion involving two players with constant, but different, speeds, and different maneuverability constraints. Specifically, the evader has limited maneuverability, while the pursuer is completely agile. This problem is an asymmetric version of the well-known Game of Two Cars. The aim of this paper is to derive the optimal strategies of the two players and characterize areas of initial conditions that lead to capture if the pursuer acts optimally, and areas that guarantee evasion regardless of the pursuer's strategy. It is shown that the problem reduces to a special version of Zermelo's Navigation Problem (ZNP) for the pursuer. Therefore, the well-known ZNP solution can be used to validate the results obtained through the differential game framework as well as to characterize the time-optimal trajectories. The results are directly applicable to collision avoidance problems.