Probabilistic ODE Solvers for Integration Error-Aware Model Predictive Control
arxiv(2024)
摘要
Appropriate time discretization is crucial for nonlinear model predictive
control. However, in situations where the discretization error strongly depends
on the applied control input, meeting accuracy and sampling time requirements
simultaneously can be challenging using classical discretization methods. In
particular, neither fixed-grid nor adaptive-grid discretizations may be
suitable, when they suffer from large integration error or exceed the
prescribed sampling time, respectively. In this work, we take a first step at
closing this gap by utilizing probabilistic numerical integrators to
approximate the solution of the initial value problem, as well as the
computational uncertainty associated with it, inside the optimal control
problem (OCP). By taking the viewpoint of probabilistic numerics and
propagating the numerical uncertainty in the cost, the OCP is reformulated such
that the optimal input reduces the computational uncertainty insofar as it is
beneficial for the control objective. The proposed approach is illustrated
using a numerical example, and potential benefits and limitations are
discussed.
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