Work

Approximations and bounds for optimal controls via finite Fourier series

Year: 2025

Type: article

Abstract: This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable finite Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control problem into an unconstrained optimization one is proposed. A quadratic control problem in the context of Newtonian mechanics is solved to demonstrate the proposed algorithm and various computational results are presented. Use of automatic differentiation is explored to circumvent the elaborated gradient computation in the first-order optimization procedure. Furthermore, mean square error bounds are derived for the case of one and two-dimensional Fourier series approximations, suggesting a general bound for problems with state space of n dimensions.

Source: Physica Scripta

DOI: 10.1088/1402-4896/adb7a2

Authors: Gabriel Nicolosi, Terry Friesz, Christopher Griffin

Institutions: Missouri University of Science and Technology, Pennsylvania State University, Applied Research Laboratory at Penn State

Language: English

Topic: Advanced Control Systems Optimization

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,400

Funders: National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation