Related papers: On the Solution of General Impulse Control Problem…
A self-learning approach for optimal feedback gains for finite-horizon nonlinear continuous time control systems is proposed and analysed. It relies on parameter dependent approximations to the optimal value function obtained from a family…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
This paper presents a numerical method to calculate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying…
It is strange but fruitful to think about the functions as random processes. Any function can be viewed as a martingale (in many different ways) with discrete time. But it can be useful to have continuous time too. Processes can emulate…
This paper investigates large-population stochastic control problems in which agents share their state information and cooperate to minimize a convex cost functional. The latter is decomposed into individual and coupling costs, with the…
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…
This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…
Feedback optimization refers to a class of methods that steer a control system to a steady state that solves an optimization problem. Despite tremendous progress on the topic, an important problem remains open: enforcing state constraints…
We investigate propagation of convexity and convex ordering on a typical discrete-time stochastic optimal control problem, namely the pricing of swing option. The dynamics of the underlying asset is modelled by the Euler scheme of a…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
This paper shows how to find lower bounds on, and sometimes solve globally, a large class of nonlinear optimal control problems with impulsive controls using semi-definite programming (SDP). This is done by relaxing an optimal control…
In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…
We present an explicit solution to the discrete-time Bellman equation for minimax optimal control of positive systems under unconstrained disturbances. The primary contribution of our result relies on deducing a bound for the disturbance…
We study the convergence of an $N$-particle Markovian controlled system to the solution of a family of stochastic McKean-Vlasov control problems, either with a finite horizon or Schr\"odinger type cost functional. Specifically, under…
In this paper, we deal with a minimum time problem in presence of a time delay $\tau.$ The value function of the considered optimal control problem is no longer defined in a subset of $\mathbb{R}^{n}$, as it happens in the undelayed case,…
In this paper, we propose a new policy iteration algorithm to compute the value function and the optimal controls of continuous time stochastic control problems. The algorithm relies on successive approximations using linear-quadratic…
We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…
We consider an optimal control problem governed by a rate-inde\-pendent system with non-convex energy. The state equation is approximated by means of viscous regularization w.r.t.\ to hierarchy of two different Hilbert spaces. The…
We consider a control problem where the system is driven by a decoupled as well as a coupled forward-backward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are…