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

TL;DR

This paper addresses integrated design of engineering systems, where physical structure of the plant and controller design are optimized simultaneously and an Uncertain Control Co-design (UCCD) problem formulation is proposed based on PDE solutions of Physics-informed Neural Networks (PINNs).

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.

Figures (4)

• Figure 1: Schematic diagram of the proposed UCCD method
• Figure 2: Results for CCD of planer system
• Figure 3: Results of UCCD for stochastic LQR problem
• Figure : UCCD by solutions of HJB using PINN

Theorems & Definitions (1)

• Remark 1