Related papers: Maximum principle for recursive optimal control pr…
We analyze the problem of stochastic optimal control of SDEs where the driver includes a self-exciting stochastic process. Due to the non-Markovian nature of the problem, we apply the stochastic maximum principle approach. We derive a…
Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum…
An effective form of the Variation Evolving Method (VEM), which originates from the continuous-time dynamics stability theory, is developed for the classic time-optimal control problem with control constraint. Within the mathematic…
We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and…
We consider a problem of optimal control of an infinite horizon system governed by forward-backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial information in…
This article is concerned with the second order necessary conditions for the stochastic optimal control problem of stochastic evolution equation with model uncertainty when the traditional Pontryagin-type maximum principle holds trivially…
From economics point of view, we investigate a new optimal control problem driven by a stochastic differential equation with a multi-time states cost functional. By constructing a series of first-order adjoint equations, we establish the…
The turnpike phenomenon stipulates that the solution of an optimal control problem in large time, remains essentially close to a steady-state of the dynamics, itself being the optimal solution of an associated static optimal control…
In this research paper, we examine an optimal control problem involving a dynamical system governed by a nonlinear Caputo fractional time-delay state equation. The primary objective of this study is to obtain the necessary conditions for…
This paper is dedicated to the elementary proof of Pontryagin's maximum principle for problems with free right end point. The proof for the standard problem is taken from the monography of Ioffe and Tichomirov. We assume piecewise…
This paper considers the problem of partially observed optimal control for forward stochastic systems which are driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field…
This article considers a discrete-time robust optimal control problem on matrix Lie groups. The underlying system is assumed to be perturbed by exogenous unmeasured bounded disturbances, and the control problem is posed as a min-max optimal…
We consider a particular instance of the lift of controlled systems recently proposed in the theory of irreversible thermodynamics and show that it leads to a variational principle for an optimal control in the sense of Pontryagin. Then we…
Exploiting our previous results on higher order controlled Lagrangians in [Nonlinear Anal. {\bf 207} (2021), 112263], we derive here an analogue of the classical first order Pontryagin Maximum Principle (PMP) for cost minimising problems…
This paper examines the stochastic maximum principle (SMP) for a forward-backward stochastic control system where the backward state equation is characterized by the backward stochastic differential equation (BSDE) with quadratic growth and…
This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. A biological prey-predator model is also analyzed with a modification function growth in prey…
Spike variation technique plays a crucial role in deriving Pontryagin's type maximum principle of optimal controls for differential equations of several types, including ordinary differential equations (ODEs), partial differential equations…
A Pontryagin maximum principle for an optimal control problem in three dimensional linearized compressible viscous flows is established using the Ekeland variational principle. The controls are distributed over a bounded domain, while the…
In this paper, we obtain the maximum principle for optimal controls of stochastic systems with jumps by introducing a new method of variation. The control is allowed to enter both diffusion and jump term and the control domain need not to…
In this paper we develop a variational method for the Loewner equation in higher dimensions. As a result we obtain a version of Pontryagin's maximum principle from optimal control theory for the Loewner equation in several complex…