Combined Plant and Control Co-design via Solutions of Hamilton-Jacobi-Bellman Equation Based on Physics-informed Learning

TL;DR

This paper introduces a physics-informed neural network approach to solve uncertain control co-design problems by directly addressing the Hamilton-Jacobi-Bellman PDE, enabling more accurate and efficient simultaneous plant and controller optimization.

Contribution

It proposes a novel PDE-based solution algorithm for uncertain control co-design using physics-informed neural networks, improving upon traditional Monte Carlo methods.

Findings

Effective simultaneous plant and controller design demonstrated.

PINN-based method outperforms traditional uncertainty propagation methods.

Numerical examples validate the approach's accuracy and efficiency.

Abstract

This paper addresses integrated design of engineering systems, where physical structure of the plant and controller design are optimized simultaneously. To cope with uncertainties due to noises acting on the dynamics and modeling errors, an Uncertain Control Co-design (UCCD) problem formulation is proposed. Existing UCCD methods usually rely on uncertainty propagation analyses using Monte Calro methods for open-loop solutions of optimal control, which suffer from stringent trade-offs among accuracy, time horizon, and computational time. The proposed method utilizes closed-loop solutions characterized by the Hamilton-Jacobi-Bellman equation, a Partial Differential Equation (PDE) defined on the state space. A solution algorithm for the proposed UCCD formulation is developed based on PDE solutions of Physics-informed Neural Networks (PINNs). Numerical examples of regulator design problems are provided, and it is shown that simultaneous update of PINN weights and the design parameters effectively works for solving UCCD problems.