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Optimal Control

Reachability analysis and efficient computation for nonlinear/hybrid systems

Approximate algorithms that can solve the Hamilton-Jacobi-Isaacs (HJI) PDE for game theory or Hamilton-Jacobi-Bellman (HJB) PDE for optimal control (or optimization problems in general) in real-time. For approximation, we use a polytopic approximation method. read more

Hybrid Optimal Control of Autopilot Modes for Aircraft Trajectory Design in Air Traffic Control

With the increasing demands for air transportation, air traffic control strategies have been focused on the efficient, safe, and clean operation which can cope with a large amount of traffic. Here, optimal aircraft trajectories generation is one of the important parts in these efforts. An aircraft’s trajectory is dependent on the aircraft’s dynamics and can be controlled by a number of flight modes. The switching of flight modes occurs in normal operation during any flight phase or in any abnormal situation such as obstacle avoidance or go-around, which needs a deviation from a nominal trajectory. In any case, the efficient and safe mode switching should be provided. read more

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