# T-PFC: A Trajectory-Optimized Perturbation Feedback Control Approach

## TL;DR

This paper introduces T-PFC, a perturbation feedback control method for nonlinear stochastic systems that achieves near-optimal performance with significantly reduced computational complexity compared to traditional methods.

## Contribution

The paper develops a decoupling principle enabling a perturbation-based control approach that is computationally efficient and near-optimal for nonlinear stochastic control problems.

## Key findings

- Validates the approach through extensive numerical simulations.
- Achieves performance comparable to Nonlinear Model Predictive Control.
- Requires less computational effort than NMPC.

## Abstract

Traditional stochastic optimal control methods that attempt to obtain an optimal feedback policy for nonlinear systems are computationally intractable. In this paper, we derive a decoupling principle between the open loop plan, and the closed loop feedback gains, that leads to a perturbation feedback control based solution to optimal control problems under action uncertainty, that is near-optimal to the third order. Extensive numerical simulations validate the theory, revealing a wide range of applicability, coping with medium levels of noise. The performance is compared with Nonlinear Model Predictive Control in several difficult robotic planning and control examples that show near identical performance to NMPC while requiring much lesser computational effort. It also leads us to raise the bigger question as to why NMPC should be used in robotic control as opposed to perturbation feedback approaches.