Abstract
The paper considers shrinking horizon model predictive control (MPC) as an approximation to the optimal finite horizon control. Recent theoretical results bounding the error of such an approximation in terms of the discretization time-step and accuracy of the preview are discussed, and illustrated/confirmed through a computational case study of spacecraft rendezvous and docking. In addition, we consider the effects of inexactness in solving the optimization problem in the shrinking horizon MPC and examine properties and benefits of the implementation based on a gradient descent method with warm-starting and a varying number of iterations per time step.
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