Discretisation for Optimal Control of Nonlinear System with Noises
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Abstract
This paper presents an optimal control framework for nonlinear systems with noise using Hamiltonian-based discretisation to enhance the approximation of stochastic differential equations. It employes the symplectic Euler method and Newton’s iteration, guided by Pontryagin’s maximum principle to solve implicit equations, incorporating Gaussian white noise into the Hamiltonian formulation of state and costate dynamics. Numerical simulations on the van der Pol oscillator and Lorenz system demonstrate the proposed method’s efficacy, achieving an average local truncation error reduction of 41% for the van der Pol oscillator and 1.1% for the Lorenz system, whilst reducing computational time by 27% on average for the Lorenz system, though often slower for the van der Pol oscillator. The method efficiently regulates noise, preserving dynamics, and minimising errors, contributing a robust numerical approach to nonlinear system control with advanced noise-handling capabilities.
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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