# Sequential Hierarchical Least-Squares Programming for Prioritized Non-Linear Optimal Control

## TL;DR

This paper introduces a sequential hierarchical least-squares programming method with trust-region and step-filter techniques, designed for prioritized non-linear optimal control, demonstrating improved computational efficiency and global convergence.

## Contribution

It presents a novel hierarchical step-filter approach with a nullspace trust-region method for solving prioritized non-linear optimal control problems.

## Key findings

- Efficiently solves prioritized non-linear optimal control problems.
- Maintains global convergence through hierarchical step-filter.
- Demonstrates superior performance on benchmark functions and inverse kinematics.

## Abstract

We present a sequential hierarchical least-squares programming solver with trust-region and hierarchical step-filter with application to prioritized discrete non-linear optimal control. It is based on a hierarchical step-filter which resolves each priority level of a non-linear hierarchical least-squares programming via a globally convergent sequential quadratic programming step-filter. Leveraging a condition on the trust-region or the filter initialization, our hierarchical step-filter maintains this global convergence property. The hierarchical least-squares programming sub-problems are solved via a sparse reduced Hessian based interior point method. It leverages an efficient implementation of the turnback algorithm for the computation of nullspace bases for banded matrices. We propose a nullspace trust region adaptation method embedded within the sub-problem solver towards a comprehensive hierarchical step-filter. We demonstrate the computational efficiency of the hierarchical solver on typical test functions like the Rosenbrock and Himmelblau's functions, inverse kinematics problems and prioritized discrete non-linear optimal control.

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Source: https://tomesphere.com/paper/2302.11891