In this article, we propose a discrete mathematical model which describes the propagation of drug phenomenon in human population. The population is unscrewed five compartments: "S" People likely to become addicts, "M" Moderate "H" Heavy "T" receiving addiction treatment, "R" recovered people who have completely abstained from addiction. Our goal find better strategy reduce number heavy addicts ...

A new sequential quadratic Hamiltonian method for computing optimal relaxed controls a class of control problems governed by ordinary differential equations is presented. This iterative approach based on the characterisation means Pontryagin maximum principle in framework Young measures, and it belongs to family successive approximations schemes. The ability proposed optimisation solve with reg...

With the rapid development of science and technology, application wireless sensor networks (WSNs) is more widely. It has been widely concerned by scholars. Viruses are one main threats to WSNs. In this paper, based on principle epidemic dynamics, we build a SEIR propagation model with mutated virus in WSNs, where E nodes infectious cannot be repaired S or R nodes. Subsequently, basic reproducti...

We consider a variable-structure optimal control problem described in different domains by hyperbolic integro-differential equation and Volterra integral equation, respectively. The quality functional is terminal. A formula for the increment of criterion constructed an analogue L.S. Pontryagin's maximum principle proved investigating on special McShane-type variations.

We study two nilpotent affine control systems derived from the dynamic and of a vertical rolling disc that is simplification differential drive wheeled mobile robot. For both systems, their controllable Lie algebras are calculated optimal problems formulated, Hamiltonian ODEs using Pontryagin maximum principle. These completely determine energetically trajectories between states. Then, novel nu...

We present a discrete analog of the recently introduced Hamilton– Pontryagin variational principle in Lagrangian mechanics. This unifies two, previously disparate approaches to discrete Lagrangian mechanics: either using the discrete Lagrangian to define a finite version of Hamilton’s action principle, or treating it as a symplectic generating function. This is demonstrated for a discrete Lagra...

This paper develops a reduction theory for Dirac structures that includes in a unified way, reduction of both Lagrangian and Hamiltonian systems. It includes the reduction of variational principles and in particular, the Hamilton–Pontryagin variational principle. It also includes reduction theory for implicit Lagrangian systems that could be degenerate and have constraints. In this paper we foc...

In various real-world applications, there is a necessity given to steer processes in time. More and more it becomes acknowledged in science and engineering, that these processes exhibit discontinuities. Our paper on theory of control (especially, optimal control) and on theory of dynamical systems gives a contribution to this natural or technical fact. One of the central results of our paper is...

The title of this session pitting Dynamic Programming against Control Theory is misleading since dynamic programming (DP) is an integral part of the discipline of control theory. However, it is timely to discuss the relative merits of DP and other empirical solution approaches to control problems in agricultural economics, and equally importantly, how control theory can be used to pose more use...