Related papers: Pontryagin Maximum Principle for finite dimensiona…
We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…
Optimal control deals with optimization problems in which variables steer a dynamical system, and its outcome contributes to the objective function. Two classical approaches to solving these problems are Dynamic Programming and the…
We consider the stochastic control of a semi-linear stochastic partial differential equations (SPDE) of McKean-Vlasov type. Based on a recent novel approach to the Lions derivative for Banach space valued functions, we prove the Gateaux…
This paper investigates the optimal control problem for a class of nonlinear fully coupled forward-backward stochastic difference equations (FBS$\Delta$Es). Under the convexity assumption of the control domain, we establish a variational…
We obtain a generalization of Noether's invariance principle for optimal control problems with equality and inequality state-input constraints. The result relates the invariance properties of the problems with the existence of conserved…
Motivated by infinite-dimensional optimal control problems with endpoint state constraints, in this Note, we introduce the notion of finite codimensional exact controllability for evolution equations. It is shown that this new…
In this paper, an open problem is solved, for the stochastic optimal control problem with delay where the control domain is nonconvex and the diffusion term contains both control and its delayed term. Inspired by previous results by \O…
The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields,…
In this paper we study reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions. Our approach emphasizes the role of…
For a class of path-dependent stochastic evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. In this infinite-dimensional control…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
Incorporating force bounds is crucial for realistic control implementations in physical systems. Here, we investigate the fastest possible synchronisation of a Li\'enard system to its limit cycle using a bounded external force. To tackle…
We study some optimal control problems associated to the evolution of two isothermal, incompressible, immisible fluids in a two-dimensional bounded domain. The Cahn- Hilliard-Navier-Stokes model consists of a Navier-Stokes equation…
This work introduces a sequential convex programming framework for non-linear, finite-dimensional stochastic optimal control, where uncertainties are modeled by a multidimensional Wiener process. We prove that any accumulation point of the…
This paper is concerned with devising the nonlinear optimal guidance for intercepting a stationary target with a fixed impact time. According to Pontryagin's Maximum Principle (PMP), some optimality conditions for the solutions of the…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…
We derive first-order Pontryagin optimality conditions for stochastic optimal control with deterministic controls for systems modeled by rough differential equations (RDE) driven by Gaussian rough paths. This Pontryagin Maximum Principle…
Using the Pontryagin maximum principle, the generic structure of optimal policies is deduced for typical quantum control tasks involving coherent lasers, magnetic fields and reservoir engineering. In addition, the periodic optimization is…
We consider an infinite-horizon optimal control problem with an asymptotic terminal constraint. For the the weakly overtaking criterion and the overtaking criterion, necessary boundary conditions on co-state arcs are deduced, these…
In this paper, we consider stochastic control problems on the Sierpinski gasket. An order comparison lemma is derived using heat kernel estimate for Brownian motion on the gasket. Using the order comparison lemma and techniques of BSDEs, we…