Gradient method for finding optimal scheduling in infinite dimensional models of chemotherapy.
Hamiltonian trajectories and saddle points in mathematical economics
High-performance simulation-based algorithms for an alpine ski racer's trajectory optimization in heterogeneous computer systems
Effective, simulation-based trajectory optimization algorithms adapted to heterogeneous computers are studied with reference to the problem taken from alpine ski racing (the presented solution is probably the most general one published so far). The key idea behind these algorithms is to use a grid-based discretization scheme to transform the continuous optimization problem into a search problem over a specially constructed finite graph, and then to apply dynamic programming to find an approximation...
Joint queue-perturbed and weakly coupled power control for wireless backbone networks
Wireless Backbone Networks (WBNs) equipped with Multi-Radio Multi-Channel (MRMC) configurations do experience power control problems such as the inter-channel and co-channel interference, high energy consumption at multiple queues and unscalable network connectivity. Such network problems can be conveniently modelled using the theory of queue perturbation in the multiple queue systems and also as a weak coupling in a multiple channel wireless network. Consequently, this paper proposes a queue perturbation...
Minimizing energy use for a road expansion in a transportation system using optimal control theory.
Minimizing the fuel consumption of a vehicle from the Shell Eco-marathon: a numerical study
We apply four different methods to study an intrinsically bang-bang optimal control problem. We study first a relaxed problem that we solve with a naive nonlinear programming approach. Since these preliminary results reveal singular arcs, we then use Pontryagin’s Minimum Principle and apply multiple indirect shooting methods combined with homotopy approach to obtain an accurate solution of the relaxed problem. Finally, in order to recover a purely bang-bang solution for the original problem, we...
Modelling and control in pseudoplate problem with discontinuous thickness
This paper concerns an obstacle control problem for an elastic (homogeneous) and isotropic) pseudoplate. The state problem is modelled by a coercive variational inequality, where control variable enters the coefficients of the linear operator. Here, the role of control variable is played by the thickness of the pseudoplate which need not belong to the set of continuous functions. Since in general problems of control in coefficients have no optimal solution, a class of the extended optimal control...
Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments
This review aims at presenting a synoptic, if not exhaustive, point of view on some of the problems encountered by biologists and physicians who deal with natural cell proliferation and disruptions of its physiological control in cancer disease. It also aims at suggesting how mathematicians are naturally challenged by these questions and how they might help, not only biologists to deal theoretically with biological complexity, but also physicians to optimise therapeutics, on which last point the...
More on nonconvexities in an optimal growth model.
Multi-agent avoidance control using an -matrix property.
Multiobjective optimal control of HIV dynamics.
Multiscale modeling and mathematical problems related to tumor evolution and medical therapy.
Nash equilibrium for a multiobjective control problem related to wastewater management
This paper is concerned with mathematical modelling in the management of a wastewater treatment system. The problem is formulated as looking for a Nash equilibrium of a multiobjective pointwise control problem of a parabolic equation. Existence of solution is proved and a first order optimality system is obtained. Moreover, a numerical method to solve this system is detailed and numerical results are shown in a realistic situation posed in the estuary of Vigo (Spain).
Objective function design for robust optimality of linear control under state-constraints and uncertainty
We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.
Objective function design for robust optimality of linear control under state-constraints and uncertainty
We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.
On the alpine ski with dry friction and air resistance. Some optimization problems for it
In the present work, divided in three parts, one considers a real skis-skier system, , descending along a straight-line with constant dry friction; and one schematizes it by a holonomic system , having any number of degrees of freedom and subjected to (non-ideal) constraints, partly one-sided. Thus, e.g., jumps and also «steps made with sliding skis» can be schematized by . Among the Lagrangian coordinates for two are the Cartesian coordinates and of its center of mass, , relative...
On the control of a truncated general immigration process through the introduction of a predator.
On the real-time emission control - case study application
Optimal campaign in the smoking dynamics.
Optimal control for a class of compartmental models in cancer chemotherapy
We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are...