A train travels from one station to the next along a level track. The journey must be completed within a given time and it is desirable to minimise the energy required to drive the train. It has been shown with an appropriate formulation of the problem that an optimal strategy exists and that this strategy must satisfy a Pontryagin type criterion. In this paper the Pontryagin principle will be ...

We provide a new, simpler, and more direct proof of the well known fact that for autonomous optimal control problems the Pontryagin extremals evolve on a level surface of the respective Pontryagin Hamiltonian. Given sets Ω ⊆ R and F ⊆ R, constants a < b, and two continuous functions L(x, u) : R × Ω → R and φ(x, u) : R ×Ω → R with continuous derivatives with respect to x, we define the autonomou...

Abstract In this paper, we propose an optimal control problem for HIV infection model with cellular and humoral immune responses, logistic growth of uninfected cells, cell-to-cell spread, saturated infection, cure rate. The describes the interaction between infected free viruses, responses. We use two functions in our to show effectiveness drug therapy on inhibiting virus production preventing ...

We present an extension of some results higher order calculus variations and optimal control to generalized functions. The framework is the category smooth functions, which includes Schwartz distributions, while sharing many nonlinear properties with ordinary prove Euler–Lagrange equations, D’Alembert principle in differential form, du Bois–Reymond optimality condition Noether’s theorem. start ...

This thesis is devoted to the spread of virus in human society. First, we modified original basic epidemiological model, and divide system into M different types. The optimal control problem formulated for changes compartments states. total cost then minimized, Pontryagin maximum principle used solve this nonlinear problem. Next, prove that policy has simple structure. Finally, fit propagation ...

This work introduces a sequential convex programming framework for non-linear, finitedimensional stochastic optimal control, where uncertainties are modeled by multidimensional Wiener process. We prove that any accumulation point of the sequence iterates generated is candidate locally-optimal solution original problem in sense Pontryagin Maximum Principle. Moreover, we provide sufficient condit...

In this report, we state and prove rstand second-order necessary conditions in Pontryagin form for optimal control problems with pure state and mixed control-state constraints. We say that a Lagrange multiplier of an optimal control problem is a Pontryagin multiplier if it is such that Pontryagin's minimum principle holds, and we call optimality conditions in Pontryagin form those which only in...

We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls two-level quantum systems by means piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in cases with one and two controls. Exact speed limits established as a function sampling period. observe numerically exponential convergence towards minimum time continuous limit...