# Recursive Feasibility Guided Optimal Parameter Adaptation of Differential Convex Optimization Policies for Safety-Critical Systems

arXiv: https://arxiv.org/abs/2109.10949 · HTML: https://mlsanity.com/paper/2109.10949/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2021.

## Built on by (most cited first, 7 of 7)

- [Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Driving](https://mlsanity.com/paper/2203.02401/) (2022)
- [Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments](https://mlsanity.com/paper/2201.01347/) (2022)
- [Differentiable Safe Controller Design through Control Barrier Functions](https://mlsanity.com/paper/2209.10034/) (2022)
- [Learning Adaptive Safety for Multi-Agent Systems](https://mlsanity.com/paper/2309.10657/) (2023)
- [FORESEE: Prediction with Expansion-Compression Unscented Transform for Online Policy Optimization](https://mlsanity.com/paper/2209.12644/) (2022)
- [Autotuning Bipedal Locomotion MPC with GRFM-Net for Efficient Sim-to-Real Transfer](https://mlsanity.com/paper/2409.15710/) (2024)
- [Optimal Parameter Adaptation for Safety-Critical Control via Safe Barrier Bayesian Optimization](https://mlsanity.com/paper/2503.19349/) (2025)

## Abstract (arXiv)

Quadratic Program(QP) based state-feedback controllers, whose inequality constraints bound the rate of change of control barrier(CBFs) and lyapunov function with a class-K function of their values, are sensitive to the parameters of these class-K functions. The construction of valid CBFs, however, is not straightforward, and for arbitrarily chosen parameters of the QP, the system trajectories may enter states at which the QP either eventually becomes infeasible, or may not achieve desired performance. In this work, we pose the control synthesis problem as a differential policy whose parameters are optimized for performance over a time horizon at high level, thus resulting in a bi-level optimization routine. In the absence of knowledge of the set of feasible parameters, we develop a Recursive Feasibility Guided Gradient Descent approach for updating the parameters of QP so that the new solution performs at least as well as previous solution. By considering the dynamical system as a directed graph over time, this work presents a novel way of optimizing performance of a QP controller over a time horizon for multiple CBFs by (1) using the gradient of its solution with respect to its parameters by employing sensitivity analysis, and (2) backpropagating these as well as system dynamics gradients to update parameters while maintaining feasibility of QPs.