Optimal control of UAVs using the sparse grid characteristic method

Real-time optimal maneuvering of unmanned vehicles using feedback control requires efficient computational algorithms. Stability and tracking controls of UAVs have been widely used. However, the optimal control of UAVs that requires minimizing a cost functional is challenging. The approach in this paper is based on a sparse grid characteristic method. Sparse grids are used to mitigate the curse of dimensionality in solving the HJB equation. At each grid point, the optimal control is computed using the characteristic method based on the Pontryagin Maximum (or Minimum) Principle. The algorithm consists of two parts, the off-line computational algorithm to solve the HJB equation for the design of a feedback control-law and the on-line algorithm for real-time receding horizon control using interpolation. The method is applied to a UAV model to test the closed-loop control.