Computation of Optimal Control Problems with Terminal Constraint via Variation Evolution

Abstract

Enlightened from the inverse consideration of the stable continuous-time dynamics evolution, the Variation Evolving Method (VEM) analogizes the optimal solution to the equilibrium point of an infinite-dimensional dynamic system and solves it in an asymptotically evolving way. In this paper, the compact version of the VEM is further developed for the computation of Optimal Control Problems (OCPs) with terminal constraint. The corresponding Evolution Partial Differential Equation (EPDE), which describes the variation motion towards the optimal solution, is derived, and the costate-free optimality conditions are established. The explicit analytic expressions of the costates and the Lagrange multipliers adjoining the terminal constraint, related to the states and the control variables, are presented. With the semi-discrete method in the field of PDE numerical calculation, the EPDE is discretized as finite-dimensional Initial-value Problems (IVPs) to be solved, with common Ordinary Differential Equation (ODE) numerical integration methods.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1709.02242, arXiv:1712.09702, arXiv:1711.02998, arXiv:1703.10263

References in corpus (2)

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

Cited by in corpus (6)

• On the Computation of Optimal Control Problems with Terminal Inequality Constraint via Variation Evolution
• Computation of Optimal Control Problems with Terminal Constraint via Modified Evolution Partial Differential Equation
• Solve the General Constrained Optimal Control Problem with Common Integration Method
• The Third Evolution Equation for Optimal Control Computation
• The Direct Shooting Method is a Complete Method
• Compact Formulation of the First Evolution Equation for Optimal Control Computation