Multitime dynamic programming for multiple integral actions

Abstract

Multitime Hamilton-Jacobi-Bellman PDE, Divergence, Multitime dynamic programming, Multitime maximum principle,

Multivariate Optimal Control with Payoffs Defined by Submanifold Integrals

“…Reaching the above ideas, as well as the ideas developed throughout this paper, was possible after a consistent analysis of multivariate optimal control problems, from different points of views and more extensively than the preliminary approach initiated by Cesari [14] for Dieudonne-Rashevsky problems. For instance, the multivariate optimal control achieved new dimensions by considering other types of cost functionals (stochastic integrals [22], curvilinear-type integrals [23], or mixt payoffs containing both multiple or curvilinear integrals [24]), as well as various types of evolution dynamics (second order partial differential equations, nonholonomic constraints [25]), or different working techniques (multivariate dynamic programming [26], multivariate needle-shaped variations [24,27]). The applicative features of the multivariate Pontryagin's maximum principle were emphasized in [5], where the minimal submanifolds, the harmonic maps, or the Plateau problem were approached under this new light.…”

KT‐pseudoinvex multidimensional control problem

“…In this paper, following the control and variational problems considered in the works of Mititelu, Udrişte and Ţevy, Treanţă,() Jayswal et al, and Antczak and Pitea, as a natural continuation of these, we introduce a new class of control problems governed by multiple integrals and m ‐flow type partial differential equation (PDE) constraints. More precisely, we consider a multidimensional control problem of minimizing a multiple‐integral cost functional subject to nonlinear equality and inequality constraints involving first‐order partial derivatives.…”

“…Udrişte 21 and Rapcsák 22 proposed a generalization of convexity on manifolds, and Pini 23 introduced the notion of invex function on Riemannian manifolds. Other approaches have been well documented in the works of Barani and Pouryayevali 24 and Agarwal et al 25 In this paper, following the control and variational problems considered in the works of Mititelu, 26 Udrişte andŢevy, 27 Treanţȃ, 28-30 Jayswal et al, and 31 Antczak and Pitea, 32 as a natural continuation of these, we introduce a new class of control problems governed by multiple integrals and m-flow type partial differential equation (PDE) constraints. More precisely, we consider a multidimensional control problem of minimizing a multiple-integral cost functional subject to nonlinear equality and inequality constraints involving first-order partial derivatives.…”

Viscosity Solution in Multi Time Hybrid Games

“…A similar statement is true for the case of multiple integral payoff. All variables and functions must satisfy suitable conditions [1][2][3]. One of important evolution problem is a multi time hybrid differential game, with two teams of players, whose Bolza payoff is the sum between a path independent curvilinear integral (mechanical work) and a function of the final event (the terminal cost, penalty term) and whose evolution PDE is an m-flow.…”