Feedback necessary optimality conditions for a class of terminally constrained state-linear variational problems inspired by impulsive control

Abstract

We consider a class of rightpoint-constrained state-linear (but non convex) optimal control problems, which takes its origin in the impulsive control framework. The main issue is a strengthening of the Pontryagin Maximum Principle for the addressed problem. Towards this goal, we adapt the approach, based on feedback control variations due to V.A. Dykhta [4, 5, 6, 7]. Our necessary optimality condition, named the feedback maximum principle, is expressed completely in terms of the classical Maximum Principle, but is shown to discard non-optimal extrema. As a connected result, we derive a certain form of duality for the considered problem, and propose the dual version of the proved necessary optimality condition.

A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations

“…Introduction. Modelling and optimal control of many practical systems in engineering, science and economics traditionally involve Ordinary Differential Equation (ODE) systems of integer orders [2,24,25,27,28,29,30]. While integer order ODE systems are adequate for capturing the evolution of most standard phenomena, it has been shown over the last two decades that many complex systems in solid mechanics, viscoelastics, gas diffusion and heat conduction in porous media, signal and image processing, bio-engineering, biology, economics and financial engineering are better modelled by systems with fractional or non-integer-order differential equations (cf., for example, [3,4,5,6,7,8,22,23,26]).…”