Related papers: A class of singular control problems with tipping …
We discuss tipping phenomena (critical transitions) in nonautonomous systems using an example of a bistable ecosystem model with environmental changes represented by time-varying parameters [Scheffer et al., Ecosystems, 11 (2008), pp.…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
Rate-induced tipping is an instability that occurs in a system when its time-dependent rate parameter becomes larger than a threshold value. We investigate a Pearson diffusion process, a diffusion process having solutions staying in a…
This paper concerns rollout and certainty-equivalent rollout policies for stochastic shortest path problems with absorbing terminal states. The main result provides a direct non-asymptotic performance certificate for a fixed rollout policy:…
We introduce a novel 'one-shot' solution technique resolving an open problem (Karatzas et al., Finite-fuel singular control with discretionary stopping, Stochastics 71:1-2 (2000)). Unexpectedly given the convexity of the latter problem, its…
The purpose of this article is to study a new problem of stochastic control, related to Walsh's spider diffusion, named: stochastic optimal scattering control. The optimal scattering control of the spider diffusion at the junction point is…
We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities $\mathcal{P}$. The maturity is specified as the hitting time to level $0$ of…
The purpose of this paper is two-fold: We extend the well-known relation between optimal stopping and randomized stopping of a given stochastic process to a situation where the available information flow is a filtration with no a priori…
The Switch Point Algorithm is a new approach for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…
We study a class of singular stochastic control problems for a one-dimensional diffusion $X$ in which the performance criterion to be optimised depends explicitly on the running infimum $I$ (or supremum $S$) of the controlled process. We…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
In this paper, we consider a self-triggered formulation of model predictive control. In this variant, the controller decides at the current sampling instant itself when the next sample should be taken and the optimization problem be solved…
The behavior of a stationary inverted point mass pendulum pivoted at its lower end in a gravitational potential is studied under the influence of statistical fluctuations. It is shown using purely classical equations that the pendulum…
We consider a two-sided singular stochastic control problem with a risk-sensitive ergodic criterion. In particular, we consider a stochastic system whose uncontrolled dynamics are modelled by a linear diffusion. The control that can be…
In this paper, we study the regularity of the value function associated with a stochastic control problem where two controls act simultaneously on a modulated multidimensional diffusion process. The first is a switching control modelling a…
For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach…
We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…
Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the…