New sweep algorithm for solving a continuous linear-quadratic optimization problem with unseptable boundary conditions

TL;DR

This paper introduces a new sweep algorithm for solving continuous linear-quadratic optimization problems with unseparated boundary conditions, leveraging Hamiltonian matrix symmetry to improve solution methods.

Contribution

The paper presents a novel sweep algorithm that exploits Hamiltonian matrix symmetry to efficiently solve LQP problems with complex boundary conditions.

Findings

The algorithm effectively solves LQP with unseparated boundary conditions.

Symmetry properties of the Hamiltonian matrix simplify the solution process.

Illustrative example demonstrates the algorithm's practical application.

Abstract

A new algorithm for solving the solution of the linear-quadratic optimization problem (LQP) with unseparated boundary conditions in the continuous case is given. Using the properties of symmetry of the corresponding Hamiltonian matrix, the Euler-Lagrange equations, it is shown that linear algebraic equations for determining the missing initial data of the system being solved have a symmetric principal matrix. The results are illustrated by the example of LQP optimization (stationary case) with minimal control actions.