A mixed-type SDRE model with a Kalman filter for prescribed impact angle guidance

In this article, we address the finite-horizon nonlinear control problem in the presence of process disturbances and sensor noise by employing the continuous-time state-dependent Riccati equation (SDRE) framework and a continuous Kalman filter, called the C-SDRE-KF. The major computational bottlenecks of the C-SDRE-KF framework are the need to solve two continuous-time algebraic Riccati equations (CAREs) and one Lyapunov equation and to evaluate the matrix exponential at each iteration. To alleviate this computational burden, we propose a mixed continuous/discrete-time SDRE method with a discrete Kalman filter, termed the Mi-SDRE-DKF. In this approach, CARE is solved by the structure-preserving doubling algorithm (SDA) and a structure-preserving binary powering algorithm is designed to leverage the Lyapunov equation and matrix exponential computations while eliminating the need to solve the additional CARE required in the continuous Kalman filter. These components are integrated into a unified framework for jointly computing control inputs and state estimates. The proposed Mi-SDRE-DKF framework is tested on the prescribed impact angle guidance (IAG) problem. Our numerical results demonstrate that the Mi-SDRE-DKF framework provides state estimates that closely match those produced by the C-SDRE-KF framework while offering substantially improved computational efficiency and overall performance.