Rare Event Chance-Constrained Optimal Control Using Polynomial Chaos and Subset Simulation

Abstract

This study develops a ccoc framework capable of handling rare event probabilities. Therefore, the framework uses the gpc method to calculate the probability of fulfilling rare event constraints under uncertainties. Here, the resulting cc evaluation is based on the efficient sampling provided by the gpc expansion. The subsim method is used to estimate the actual probability of the rare event. Additionally, the discontinuous cc is approximated by a differentiable function that is iteratively sharpened using a homotopy strategy. Furthermore, the subsim problem is also iteratively adapted using another homotopy strategy to improve the convergence of the Newton-type optimization algorithm. The applicability of the framework is shown in case studies regarding battery charging and discharging. The results show that the proposed method is indeed capable of incorporating very general cc within an ocp at a low computational cost to calculate optimal results with rare failure probability cc.

Stochastic optimal control for autonomous driving applications via polynomial chaos expansions

“…In general, stochastic nonlinear optimal control is computationally demanding and poses significant challenges to nonlinear optimization solvers. Distributed numerical frameworks for nonlinear optimal control 37 could be explored in the future to improve robustness and facilitate real‐time applications of the proposed methodology.…”

Recent Advances on Optimization for Control, Observation, and Safety

“…Piprek et al [9] provide a sampling approach to approximate the chance constraints in the formulation of optimal control problems for stochastic dynamical systems to capture rare events. The applicability of the proposed approach is demonstrated in a battery charging-discharging problem.…”

Trajectory/Path-Following Controller Based on Nonlinear Jerk-Level Error Dynamics

“…The general idea of the control approach of the paper is depicted in Figure 1: The desired trajectory is generated by a suitable method, e.g., geometric approaches [15,16], (robust) optimal control [17][18][19][20], or shortest path methods [21]. As the aircraft is generally never able to follow the path exactly, either due to imperfect planning or disturbances (e.g, wind or model errors), a deviation between the aircraft reference point R and the trajectory foot point F arises.…”