Core Concepts
The authors introduce a novel approach using the Koopman operator to reformulate stochastic optimal control problems, leading to a standard LQR solution. By leveraging this method, they address the computational challenges associated with dual control in SOC.
Abstract
The paper discusses the application of the Koopman operator theory to stochastic optimal control problems, presenting a new formulation that simplifies the solution process. It highlights the limitations of traditional methods and demonstrates the effectiveness of the proposed approach through a numerical example. The integration of Extended Kalman Filter for state uncertainty propagation enhances computational efficiency in solving dual control problems.
Stats
"It has been more than seven decades since the introduction of the theory of dual control [1]."
"In recent years, however, the use of Koopman operator theory for control applications has been emerging."
"We target solving a dual control problem of a general differentiable nonlinear system using a quadratic cost."
"The eKF is simple and widespread in navigation, robotics, computer vision, power systems, and many other fields."
"Dynamic Programming is 'very unscalable' with state dimension and therefore restrictive."
Quotes
"The paper presents a new reformulation of the stochastic optimal control problem that yields a standard LQR problem with dual control as its solution."
"Our approach leverages the Koopman operator, switching the challenge from solution finding to problem formulation."
"The eKF approximation offers an appealing finite-dimensional representation of state uncertainty from a computational perspective."