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We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that…
In this paper, we study a class of finite-time control problems for discrete-time positive linear systems with time-varying state parameters. Although several interesting control problems appearing in population biology, economics, and…
Operators of Electric Autonomous Mobility-on-Demand (E-AMoD) fleets need to make several real-time decisions such as matching available vehicles to ride requests, rebalancing idle vehicles to areas of high demand, and charging vehicles to…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…
We investigate how to control optimally a traffic flow through a junction on the line by acting only on speed reduction or traffic light at the junction. We show the existence of an optimal control and, under structure assumptions, provide…
Reliable long-time storage of arbitrary quantum states is a key element for quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment, we introduce an optimized sequence of $N$…
In this paper, we study an optimal control problem for a macroscopic mechanical tumour model based on the phase field approach. The model couples a Cahn--Hilliard type equation to a system of linear elasticity and a reaction-diffusion…
The choice of objective is critical for the performance of an optimal controller. When control requirements vary during operation, e.g. due to changes in the environment with which the system is interacting, these variations should be…
We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close,…
This study describes the development of a novel numerical optimization framework to maximize the endurance of unmanned aerial vehicles (UAVs). We address the problem of numerically determining the optimal thrust and cruise angle of attack…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
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…
Dipolar Bose-Einstein condensates have recently attracted much attention in the world of quantum many body experiments. While the theoretical principles behind these experiments are typically supported by numerical simulations, the…
In this work we focus on a recently introduced method [1] to construct the external potential $v$ that, for a given initial state, produces a prescribed time-dependent density in an interacting quantum many-body system. We show how this…
Urban intersections, merging roadways, roundabouts, and speed reduction zones along with the driver responses to various disturbances are the primary sources of bottlenecks in corridors that contribute to traffic congestion. The…
This paper studies the decay of an objective functional using a new control technique within Pontryagin's framework. Convergence analysis is carried out on the infinite-dimensional space of Tokamak plasma dynamical state as described by…
We analytically solve the finite-time control problem of driving an overdamped particle via an optical trap under costly measurement. By formulating this mesoscopic information engine within the Partially Observable Markov Decision Process…
Most modern control systems are switched, meaning they have continuous as well as discrete decision variables. Switched systems often have constraints called dwell-time constraints (e.g., cycling constraints in a heat pump) on the switching…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…