A Variation Evolving Method for Optimal Control
This work addresses the challenge of solving optimal control problems for researchers in control theory, offering a globally stable approach that leverages ODE solvers.
The paper proposes a new method for solving optimal control problems by transforming them into initial-value problems using a virtual time dimension, ensuring global stability and convergence to the optimal solution from any initial guess.
A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a virtual dimension, the variation time, a dynamic system that describes the variation motion is deduced from the Optimal Control Problem (OCP), and the optimal solution is its equilibrium point. Through this method, the intractable OCP is transformed to the Initial-value Problem (IVP) and it may be solved with mature Ordinary Differential Equation (ODE) numerical integration methods. Especially, the deduced dynamic system is globally stable, so any initial value will evolve to the extremal solution ultimately.