57 citations · 143 across the 21 of their papers we have counts for
23 papers
Approximation of Optimal Control Problems for the Navier-Stokes equation via multilinear HJB-POD
Maurizio Falcone, Gerhard Kirsten, Luca Saluzzi
We consider the approximation of some optimal control problems for the Navier-Stokes equation via a Dynamic Programming approach. These control problems arise in many industrial ap…
A New Algorithm for the LQR Problem with Partially Unknown Dynamics
Agnese Pacifico, Andrea Pesare, Maurizio Falcone
We consider an LQR optimal control problem with partially unknown dynamics. We propose a new model-based online algorithm to obtain an approximation of the dynamics the contr…
Convergence of the Value Function in Optimal Control Problems with Unknown Dynamics
Andrea Pesare, Michele Palladino, Maurizio Falcone
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assum…
Convergence results for an averaged LQR problem with applications to reinforcement learning
Andrea Pesare, Michele Palladino, Maurizio Falcone
In this paper, we will deal with a Linear Quadratic Optimal Control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on…
A tree structure algorithm for optimal control problems with state constraints
Alessandro Alla, Maurizio Falcone, Luca Saluzzi
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function bas…
Multidimensional smoothness indicators for first-order Hamilton-Jacobi equations
Maurizio Falcone, Giulio Paolucci, Silvia Tozza
The lack of smoothness is a common feature of weak solutions of nonlinear hyperbolic equations and is a crucial issue in their approximation. This has motivated several efforts to…
On the segmentation of astronomical images via level-set methods
Silvia Tozza, Maurizio Falcone
Astronomical images are of crucial importance for astronomers since they contain a lot of information about celestial bodies that can not be directly accessible. Most of the inform…
Error estimates for a tree structure algorithm solving finite horizon control problems
Luca Saluzzi, Alessandro Alla, Maurizio Falcone
In the Dynamic Programming approach to optimal control problems a crucial role is played by the value function that is characterized as the unique viscosity solution of a Hamilton-…
A High-Order Scheme for Image Segmentation via a modified Level-Set method
Maurizio Falcone, Giulio Paolucci, Silvia Tozza
In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of…
Convergence of Adaptive Filtered Schemes for First Order Evolutionary Hamilton-Jacobi Equations
Maurizio Falcone, Giulio Paolucci, Silvia Tozza
We consider a class of "filtered" schemes for first order time dependent Hamilton-Jacobi equations and prove a general convergence result for this class of schemes. A typical filte…
An efficient DP algorithm on a tree-structure for finite horizon optimal control problems
Alessandro Alla, Maurizio Falcone, Luca Saluzzi
The classical Dynamic Programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Ja…
Error analysis for POD Approximations of infinite horizon problems via the Dynamic Programming approach
Alessandro Alla, Maurizio Falcone, Stefan Volkwein
In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function…
A dynamic domain decomposition for a class of second order semi-linear equations
Simone Cacace, Maurizio Falcone
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic d…
Analysis and approximation of some Shape-from-Shading models for non-Lambertian surfaces
Silvia Tozza, Maurizio Falcone
The reconstruction of a 3D object or a scene is a classical inverse problem in Computer Vision. In the case of a single image this is called the Shape-from-Shading (SfS) problem an…
An efficient filtered scheme for some first order Hamilton-Jacobi-Bellman equations
Olivier Bokanowski, Maurizio Falcone, Smita Sahu
We introduce a new class of "filtered" schemes for some first order non-linear Hamilton-Jacobi-Bellman equations. The work follows recent ideas of Froese and Oberman (SIAM J. Numer…
Two semi-Lagrangian fast methods for Hamilton-Jacobi-Bellman equations
Simone Cacace, Emiliano Cristiani, Maurizio Falcone
In this paper we apply the Fast Iterative Method (FIM) for solving general Hamilton-Jacobi-Bellman (HJB) equations and we compare the results with an accelerated version of the Fas…
An Efficient Policy Iteration Algorithm for Dynamic Programming Equations
Alessandro Alla, Maurizio Falcone, Dante Kalise
We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iterat…
An adaptive POD approximation method for the control of advection-diffusion equations
Alessandro Alla, Maurizio Falcone
We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive…
A semi-Lagrangian scheme for the game -Laplacian via -averaging
M. Falcone, S. Finzi Vita, T. Giorgi +1
We present and analyze an approximation scheme for the two-dimensional game -Laplacian in the framework of viscosity solutions. The approximation is based on a semi-Lagrangian s…
An approximation scheme for an Eikonal Equation with discontinuous coefficient
Adriano Festa, Maurizio Falcone
We consider the stationary Hamilton-Jacobi equation where the dynamics can vanish at some points, the cost function is strictly positive and is allowed to be discontinuous. More pr…
Can local single-pass methods solve any stationary Hamilton-Jacobi-Bellman equation?
Simone Cacace, Emiliano Cristiani, Maurizio Falcone
The use of local single-pass methods (like, e.g., the Fast Marching method) has become popular in the solution of some Hamilton-Jacobi equations. The prototype of these equations i…
Numerical approximation of Nash equilibria for a class of non-cooperative differential games
Simone Cacace, Emiliano Cristiani, Maurizio Falcone
In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite…
A patchy Dynamic Programming scheme for a class of Hamilton-Jacobi-Bellman equations
Simone Cacace, Emiliano Cristiani, Maurizio Falcone +1
In this paper we present a new algorithm for the solution of Hamilton-Jacobi-Bellman equations related to optimal control problems. The key idea is to divide the domain of computat…