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We consider the effects of parameter uncertainty on the optimal radiation schedule in the context of the linear-quadratic model. Our interest arises from the observation that if inter-patient variations in OAR and tumor sensitivities to…
In this paper we consider optimal control problems where the control variable is a potential and the state equation is an elliptic partial differential equation of a Schr\"odinger type, governed by the Laplace operator. The cost functional…
A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space.…
Radiotherapy treatment planning is a challenging large-scale optimization problem plagued by uncertainty. Following the robust optimization methodology, we propose a novel, spatially based uncertainty set for robust modeling of radiotherapy…
We solve the optimal control problem of a one-dimensional reflected stochastic differential equation, whose coefficients can be path dependent. The value function of this problem is characterized by a backward stochastic partial…
Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of…
We address the risk bounded trajectory optimization problem of stochastic nonlinear robotic systems. More precisely, we consider the motion planning problem in which the robot has stochastic nonlinear dynamics and uncertain initial…
The linear Boltzmann equation can be solved with separation of variables in one dimension, i.e., in three-dimensional space with planar symmetry. In this method, solutions are given by superpositions of eigenmodes which are sometimes called…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…
Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. In this paper, we assume that $a$ is bounded, i.e., that $|a| \le…
The relativistic Boltzmann equation in bounded domains has been widely used in physics and engineering, for example, Tokamak devices in fusion reactors.In spite of its importance, there has, to the best of our knowledge, been no…
This work addresses the problem of kinematic trajectory planning for mobile manipulators with non-holonomic constraints, and holonomic operational-space tracking constraints. We obtain whole-body trajectories and time-varying kinematic…
We study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling such system with a control being a Lipschitz vector field on a fixed control set $\omega$. We prove…
A distributed optimal control problem for a diffuse interface model, which physical context is that of tumour growth dynamics, is addressed. The system we deal with comprises a Cahn--Hilliard equation for the tumour fraction coupled with a…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
The phenomenological textbook equations for the charge and heat transport are extensively used in a number of fields ranging from semiconductor devices to thermoelectricity. We provide a rigorous derivation of transport equations by solving…
We study Mean Field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
This paper discusses a method enabling optimal control of nonlinear systems that are subject to parametric uncertainty. A stochastic optimal tracking problem is formulated that can be expressed in function of the first two stochastic…