This paper focuses on the development of optimality conditions for a bilevel optimal control problem with pure state constrains in the upper level and a finite-dimensional parametric optimization problem in the lower level. After transforming the problem into an equivalent single-level problem we concentrate on the derivation of a necessary optimality condition of Pontryagin-type. We point out ...

<p style='text-indent:20px;'>In this paper, we consider an optimal control problem in which a dynamical system is controlled by nonlinear Caputo fractional state equation. The investigated the case when Pontryagin maximum principle degenerates, that is, it satisfied trivially. Then second order optimality conditions are derived for considered problem.</p>

One discrete problem of optimal population dynamics control with a controllable initial condition is considered. The process described by nonlinear system Fredholm-type difference equations. An analogue the L.S. Pontryagin’ maximum principle proved imposing series smoothness conditions on right side equation. linearized and Euler equation are for case convexity openness domain, which first-orde...

In the present paper, two optimal control problems are studied using Lie geometric methods and applying Pontryagin Maximum Principle at level of a new working space, called algebroid. It is proved that framework algebroid more suitable than cotangent bundle in order to find solutions some driftless affine systems with holonomic distributions. Finally, an economic application given.

Li et al. (2018) have proposed a regularization of the forward–backward sweep iteration for solving Pontryagin maximum principle in optimal control problems. The authors prove global convergence continuous time case. In this article we show that their proof can be extended to case numerical discretization by symplectic Runge–Kutta pairs. We demonstrate with simple experiment.

In this paper some geometric structures on Finsler Lie algeboids are studied and h-basic distinguished connections introduced. Specially, Ichijy? connection that is a special investigated. The generalized Berwald algebroids presented, as particular case of Wagner-Ichijy? connection, studied. Moreover, the Wagner algebroid introduced equivalent conditions for space given. Finally, an optimal con...

This paper begins with a geometric statement of constraint optimization problems, which include both equality and inequality-type restrictions. The cost to optimize is curvilinear functional defined by given differential one-form, while the optimal state be determined curve connecting two points, among all curves satisfying some primal feasibility conditions. resulting outcome an invariant Frit...

This paper presents an underwater robot control system using combination principle among sliding mode control (SMC), Pontryagin maximum principle and linear PI control. The SMC switches according to the Pontryagin’s time optimal control principle, in which the solution is obtained by using neural network approach to yield a time optimal response at its reaching phase. PI control is used in plac...

We propose a decomposition method for the solution of a dynamic portfolio optimization problem which fits the formulation of a multistage stochastic programming problem. The method allows to obtain time and nodal decomposition of the problem in its arborescent formulation applying a discrete version of Pontryagin Maximum Principle. The solution of the decomposed problems is coordinated through ...

Faculty of Civil and Environmental Engineering P-O Gutman 2004-02-20 Abstract When using the Pontryagin Maximum Principle in optimal control problems, the most difficult part of the numerical solution is associated with the non-linear operation of the maximization of the Hamiltonian over the control variables. For a class of problems, the optimal control vector is a vector function with continu...