Optimal Spacecraft Guidance with Asynchronous Measurements and Noisy Impulsive Controls

We develop an optimal guidance law to steer a stochastic linear system to a final state while minimizing mean squared deviation from a target state. We assume the controller receives noiseless, full-state measurements at discrete times and the control is composed of impulsive inputs with one or many sources of control-linear noise. Measurement and control events are scheduled a priori, yet they are not necessarily synchronous. In addition, this letter presents the following innovations to our previous work: extension to time-varying systems, inclusion of additive noise in the system dynamics, accommodation of arbitrarily many control-linear noise sources, and application as a neighboring guidance algorithm about a nonlinear trajectory. We provide a complete solution to this new optimization problem, presented as a main theorem, and prove that the optimal control remains linear in the initial state, the target state, and the sampled measurements. We formalize an optimal guidance algorithm to compute the state feedback gains before flight. The algorithm is demonstrated for guidance about a spacecraft trajectory, and its performance is analyzed numerically for different measurement and control schedules.