Related papers: A Crime/S.I.R. optimal control problem
We present and compare two different optimal control approaches applied to SEIR models in epidemiology, which allow us to obtain some policies for controlling the spread of an epidemic. The first approach uses Dynamic Programming to…
In this paper, we investigate an optimal control problem with terminal stochastic linear complementarity constraints (SLCC), and its discrete approximation using the relaxation, the sample average approximation (SAA) and the implicit Euler…
This research introduces a new approach utilizing optimal control theory (OCT) to assess the Social Optimum (SO) of a vaccination game, navigating the intricate considerations of cost, availability, and distribution policies. By integrating…
In this paper we study and solve an optimal control problem motivated by applications in quantum and classical physics. Although apparently simple, this optimal control problem is not easy to solve and we resort to various elaborated…
In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new…
In optimal control problem, policy iteration (PI) is a powerful reinforcement learning (RL) tool used for designing optimal controller for the linear systems. However, the need for an initial stabilizing control policy significantly limits…
Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
We propose a primal--dual technique that applies to infinite dimensional equality constrained problems, in particular those arising from optimal control. As an application of our general framework, we solve a control-constrained double…
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.…
We analyze an optimal control version of a simple SIRS epidemiology model. The policy maker can adopt policies to diminish the contact rate between infected and susceptible individuals, at a specific economic cost. The arrival of a vaccine…
Probabilistic control design is founded on the principle that a rational agent attempts to match modelled with an arbitrary desired closed-loop system trajectory density. The framework was originally proposed as a tractable alternative to…
First, let $u_{g}$ be the unique solution of an elliptic variational inequality with source term $g$. We establish, in the general case, the error estimate between $u_{3}(\mu)=\mu u_{g_{1}}+ (1-\mu)u_{g_{2}}$ %(the convex combination of two…
We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity…
The minimum-time control problem consists in finding a control policy that will drive a given dynamic system from a given initial state to a given target state (or a set of states) as quickly as possible. This is a well-known challenging…
How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem.…
In this paper we study the problem of synthesizing optimal control policies for uncertain continuous-time nonlinear systems from syntactically co-safe linear temporal logic (scLTL) formulas. We formulate this problem as a sequence of…
A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction…
This paper investigates the social optimality of linear quadratic mean field control systems with unmodeled dynamics. The objective of agents is to optimize the social cost, which is the sum of costs of all agents. By variational analysis…
We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…