Trajectory optimization

Relaxation (psychology)

Mathematics

Agronomy

Biology

Algorithm

Statistics

Mathematical optimization

Regular polygon

Convex optimization

Optimization problem

Stochastic control

Artificial intelligence

Psychology

Controller (irrigation)

Covariance

Control (management)

Estimation of covariance matrices

Covariance matrix

CMA-ES

Geometry

Computer science

Control theory (sociology)

Social psychology

Optimal control

Journal of Guidance Control and Dynamics

This paper outlines a novel approach to the design of optimal space trajectories under significant uncertainty. Finite-horizon covariance control, i.e., the steering of a system from an initial probability distribution to a desired one at a prescribed time, is employed to plan an optimal nominal path along with a robust feedback controller that compensates for exogenous in-flight disturbances. A mindful convexification strategy is devised to recast the nonlinear covariance control problem as a deterministic convex optimization problem. The convexification is based on a convenient change of variables that allows for relaxing the covariance matrix discrete-time propagation into a set of semidefinite cone constraints. While featuring a larger feasible space, the relaxed problem shares the same optimal solution as the original one. The lossless property of the relaxation is analytically proven by leveraging optimal control theory and discussed on the basis of numerical experiments. Monte Carlo campaigns are carried out to validate the in-flight performance of the attained control policies.

Convex Approach to Covariance Control with Application to Stochastic Low-Thrust Trajectory Optimization