Related papers: Necessary conditions involving Lie brackets for im…
We obtain higher order necessary conditions for a minimum of a Mayer optimal control problem connected with a nonlinear, control-affine system, where the controls range on an m-dimensional Euclidean space. Since the allowed velocities are…
We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…
We consider affine control systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions of local controllability around this equilibrium, involving the iterated Lie…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
We consider control systems governed by nonlinear O.D.E.'s that are affine in the time-derivative du/dt of the control u. The latter is allowed to be an integrable, possibly of unbounded variation function, which gives the system an…
We consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. To this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
We consider an optimal control problem for a system governed by a Volterra integral equation with impulsive terms. The impulses act on both the state and the control; the control consists of switchings at discrete times. The cost functional…
The paper extends an impulsive control-theoretical framework towards dynamic systems in the space of measures. We consider a transport equation describing the time-evolution of a conservative "mass" (probability measure), which represents…
We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…
This paper provides a framework for deriving a new set of necessary conditions for adverse control problems among two players. The distinguish feature of such problems is that the first player has a priori knowledge on the second player…
For a symmetric system, we want to study the problem of crossing an hypersurface in the neighborhood of a given point, when we suppose that all of the available vector fields are tangent to the hypersurface at the point. Classically one…
We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…
This paper is the first part of our series work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, both drift and diffusion terms may contain the control variable but the control region…
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…
We investigate an everywhere defined notion of solution for control systems whose dynamics depend nonlinearly on the control $u$ and state $x,$ and are affine in the time derivative $\dot u.$ For this reason, the input $u,$ which is allowed…
We introduce discontinuous solutions to nonlinear impulsive control systems with state time delays in the dynamics and derive necessary optimality conditions in the form of a Maximum Principle for associated optimal control problems. In the…
The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…