Computation of time-optimal control problem with variation evolution principle

Abstract

An effective form of the Variation Evolving Method (VEM), which originates from the continuous-time dynamics stability theory, is developed for the classic time-optimal control problem with control constraint. Within the mathematic derivation, the Pontryagin's Minimum Principle (PMP) optimality conditions are used. Techniques including limited integrator and corner points are introduced to capture the right solution. The variation dynamic evolving equation may be reformulated as the Partial Differential Equation (PDE), and then discretized as finite-dimensional Initial-value Problem (IVP) to be solved with common Ordinary Differential Equation (ODE) integration methods. An illustrative example is solved to show the effectiveness of the method. In particular, the VEM is further developed to be more flexible in treating the boundary conditions of the Optimal Control Problem (OCP), by initializing the transformed IVP with arbitrary initial values of variables.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1709.02242, arXiv:1703.10263

References in corpus (1)

• A Variation Evolving Method for Optimal Control

Cited by in corpus (4)

• Computation of Optimal Control Problems with Terminal Constraint via Variation Evolution
• Optimal Control Computation via Evolution Partial Differential Equation with Arbitrary Definite Conditions
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• Compact Formulation of the First Evolution Equation for Optimal Control Computation