Optimal Control Computation via Evolution Partial Differential Equation with Arbitrary Definite Conditions

Abstract

The compact Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. It is further developed to be more flexible in solving the Optimal Control Problems (OCPs), by relaxing the definite conditions from a feasible solution to an arbitrary one for the derived Evolution Partial Differential Equation (EPDE). To guarantee the validity, an unconstrained Lyapunov functional that has the same minimum as the original OCP is constructed, and it ensures the evolution towards the optimal solution from infeasible solutions. With the semi-discrete method, the EPDE is transformed to the finite-dimensional Initial-value Problem (IVP), and then solved with common Ordinary Differential Equation (ODE) numerical integration methods. Illustrative examples are presented to show the effectiveness of the proposed method.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1709.02242, arXiv:1711.02998

References in corpus (2)

• Variation Evolving for Optimal Control Computation, a Compact Way
• Computation of time-optimal control problem with variation evolution principle

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• Computation of Optimal Control Problems with Terminal Constraint via Modified Evolution Partial Differential Equation
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• The Direct Shooting Method is a Complete Method
• Compact Formulation of the First Evolution Equation for Optimal Control Computation