Path Planning Using a Novel Finite Horizon Suboptimal Controller

A study was conducted to demonstrate path planning using a novel finite horizon suboptimal controller. The state-dependent Riccati equation (SDRE) method for infinite horizon optimal control of nonlinear systems was used to conduct the investigations. A state-dependent differential Riccati equation was introduced to provide an approximate closed-form solution to the finite horizon optimal control problem. The relation between Hamilton-Jacobi-Bellman (HJB) partial differential equation and the state-dependent differential Riccati equation was investigated. An approximate method was suggested for solving the differential Riccati equation and the performance of the developed technique was investigated with path-planning problems for the approach and landing (A&L) phase of a reusable launch vehicle (RLV), such that the vehicle landed in a fixed and prespecified downrange with the least possible vertical velocity and flight-path angle.