We consider in this paper, mixed relaxed-singular stochastic control problems, where the control variable has two components, the first being measure-valued and the second singular. The control domain is not necessarily convex and the system is governed by a nonlinear stochastic differential equation, in which the measure-valued part of the control enters both the drift and the diffusion coeffi...

In a standard free end nonsmooth control problem in finite dimensional state space, a nonsmooth maximum principle is proved, in which the adjoint inclusion is sharper than the usual one. For end constrained problems, the same result holds, provided conditions ensuring local controllability are satisfied. The adjoint inclusion is expressed by means of a type of generalized gradient of the pseudo...

Abstract The paper presents differential equations of the movement horizontal spindle drum compiled using 2nd kind Lagrange equations. task was set on how to control a drum. speed Pontriyagin maximum principle set, and requirement for optimal guidance based quality criteria studied. Through formation Hamilton-Pontryagin function, conjugate functions were composed. These made it possible obtain ...

Efficient train driving plays a vital role in reducing the overall energy consumption railway sector. An minimising control strategy can be computed using framework given by optimal theory; particular, Pontryagin maximum principle used. Our optimisation approach is based on an algorithm presented Khmelnitsky that considers electric trains equipped with regenerative braking. A derivation of Khme...

Abstract: In this paper we study second order sufficient conditions for the strong-local optimality of singular Pontryagin extremals. In particular, we focus on the minimum-time problem for a control-affine system with vector inputs. We use Hamiltonian methods to prove that the coercivity of a suitably-defined second variation plus an involutivity assumption on the distribution of the controlle...

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...

with n, m > 2, Ω ⊂ R, m < p <∞ and a compact set A ⊂ R with nonempty interior. In the case of a convex integrand f(s, ξ, · ) and a convex restriction set A = K, the global minimizers of (1.1) − (1.3) satisfy optimality conditions in the form of Pontryagin’s principle 01) even though the usual regularity condition for the equality operator (1.2) fails. 02) The question arises whether the Pontrya...

with n, m > 2, Ω ⊂ R, m < p < ∞ and a compact set K ⊂ R with nonempty interior. In the case of a convex integrand f(s, ξ, · ) and a convex restriction set K, the global minimizers of (1.1) − (1.3) satisfy optimality conditions in the form of Pontryagin’s principle 01) even though the usual regularity condition for the equality operator (1.2) fails. 02) The question arises whether the Pontryagin...