General research interest

Calculus of Variations and Optimal control - Convex and nonsmooth analysis - Optimization theory

Ongoing research

Convex Optimal Control

A fully convex optimal control problem is a continuous optimization problem where all the data has an underlying convex structure, like the Linear-Quadratic regulator. My main concern lies on problems with state constraints and impulses.

Systems with uncertainty

I'm studying dynamical systems where the initial position is not perfectly known and only its probability distribution may be known. In this setting, control systems do not evolve anymore in a normed vector space, but in a space of probability measures.

Controlled sweeping processes

These are classical control systems coupled with a differential inclusion induced by a normal cone to a moving set. I'm mainly concerned with understanding optimality conditions and the value function of the correspoding optimal control problem.

Applied problems

Optimal control has become an interdisciplinary field embracing any area where a dynamical system interferes. I'm in particular interested in applications in biomedical treatments, biological processes and mining.

Organized events

Upcoming

Latin American Congress on Industrial and Applied Mathematics, 19 -23 January 2026, Valparaíso, Chile: LACIAM 2026

Past

Workshop on Optimal Control Theory and Related Fields, 4 -7 December 2023, Valparaíso, Chile: WOpCOT

V-Encuentro de Optimización, 21 - 21 October 2022, Valparaíso, Chile: V-Encuentro - 2022

Workshop on Optimal Control Theory at INSA Rouen Normandie, 22 - 24 June 2022, Rouen, France: WOCT - 2022

Control of State-Constrained Dynamical Systems: School and Workshop, 24 - 27 September 2019, Valparaíso, Chile: CoSCDS - 2019

Mini-symposium Optimal Control and Dynamical Systems in 6th International Conference on Continuous Optimization, 5 - 8 August 2019, Berlin, Germany: ICCOPT 2019

Publications

Published/ In press papers

Subgradient evolution of value functions of discrete-time convex Bolza problems (with J. Deride and M. Solla) in Journal of Convex Analysis : (Journal version) ; (PDF)
Hamilton-Jacobi-Bellman approach for optimal control problems of sweeping processes (with M. Palladino and E. Vilches) in Applied Mathematics & Optimization : (Journal version) ; (PDF)
Sensitivity Analysis of the Set of Sustainable Thresholds (with P. Gajardo and T. Guilmeau) in Set-Valued and Variational Analysis: (Journal version) ; (PDF)
Relationship Between the Maximum Principle and Dynamic Programming for Minimax Problems (with H. Zidani) in Applied Mathematics & Optimization : (Journal version) ; (PDF)
Optimality Conditions for Linear-Convex Optimal Control Problems with Mixed Constraints (with J. Becerril) in Journal of Optimization Theory and Applications : (Journal version) ; (PDF)
Optimal control of the sweeping process with a nonsmooth moving set (with M. Palladino) in SIAM Journal on Control and Optimization : (Journal version) ; (PDF)
On the set of robust sustainable thresholds (with P. Gajardo and A. Picarelli) in Natural Resource Modeling : (Journal version - open access)
Optimality conditions for the continuous model of the final open pit problem (with J. Amaya and E. Molina) in Optimization Letters : (Journal version) ; (PDF)
A Characteristic Method for Fully Convex Bolza Problems over Arcs of Bounded Variation (with P. Wolenski) in SIAM Journal on Control and Optimization : (Journal version) ; (PDF)
Pareto fronts of the set of sustainable thresholds for constrained control systems (with P. Gajardo) in Applied Mathematics & Optimization : (Journal version) ; (PDF)
The viability kernel of a dynamical systems with mixed constraints: A level sets approach (with P. Gajardo) in Systems & Control Letters : (Journal version) ; (PDF)
An algorithm for maximizing the biogas production in a chemostat (with A. Haddon) in Journal of Optimization Theory and Applications : (Journal version) ; (PDF)
On the construction of nearly time-optimal continuous feedback laws around switching manifolds (with F. Ancona) in ESAIM: Control, Optimisation and Calculus of Variations : (Journal version) ; (PDF)
Hamilton-Jacobi-Bellman equations for optimal control processes with convex state constraints (with R. Vinter and H. Zidani) in Systems & Control Letters : (Journal version) ; (PDF)
Discontinuous solutions of Hamilton-Jacobi equations on networks (with P.J. Graber and H. Zidani) in Journal of Differential Equations : (Journal version) ; (PDF)
HJB approach for state constrained optimal control problems (with A. Picarelli) in Optimal Control: Novel Directions and Applications, (Editors: D. Tonon, M.A. Aronna and D. Kalise), Lectures Notes in Mathematics, Volume 2180: (Link)
The Mayer and minimum time problems with stratified state constraints (with P. Wolenski and H. Zidani) in Set-Valued and Variational Analysis: (Journal version) ; (PDF)
Constrained and impulsive Linear Quadratic control problems (with P. Wolenski) in Proceedings of the 20th World Congress of the International Federation of Automatic Control 2017: (Journal version) ; (PDF)
Self-dual approximations to fully convex impulsive systems (with P. Wolenski) in Proceedings of the 55th IEEE Conference on Decision and Control 2016: (Journal version) ; (PDF)
Legendre transform and applications to finite and infinite optimization in Set-Valued and Variational Analysis: (Journal version) ; (PDF)
Stratified discontinuous differential equations and sufficient conditions for robustness in Discrete and Continuous Dynamical Systems - Series A: (Journal version) ; (PDF)
Infinite horizon problems on stratifiable state-constraints sets (with H. Zidani) in Journal of Differential Equations: (Journal version) ; (PDF)

Dissertations

Doctorate degree: Optimal control problems on well-structured domains and stratified feedback controls: (PDF)
Mathematical Engineering degree: Pseudo-metrics induced by Legendre type functions and dynamic optimization methods.: (PDF)

Submitted

A minimality property of the value function in optimal control over the Wasserstein space (with A. Prost)
Optimality conditions for a class of hybrid optimal control problems with mixed and pure state constraints (with P. Toledo)

Work in progress

Fully-Convex impulsive optimal control problems subject to differential inclusions (with J. Becerril)
Linear-quadratic optimal control problem under probability knowledge of the initial condition (with O. Jerhaoui)
General convergence for self-dual approximations to fully convex impulsive systems (with E. Treumún and P. Wolenski)

Invited Talks

HJB Approach for Optimal Control Problems of Sweeping Processes in 3rd International Conference on Variational Analysis and Optimization, January 2024, Santiago, Chile.
Hamilton-Jacobi-Bellman Approach for Optimal Control Problems of Sweeping Processes in SIAM Conference on Control and its Applications, July 2023, Philadelphia, USA.
Optimal control of the Sweeping Process with a non-smooth moving set in LAWOC 2022, January 2023, Rancagua, Chile.
Optimal Control Problems on Well-structured Domains in Workshop on Algebraic Real Geometry and Optimization, Septiembre 2022, Santiago, Chile.
Optimality Conditions for Linear-Convex Optimal Control Problems with Mixed Constraints in 9th French-Chilean Meeting on Optimization, June 2022, Perpignan, France.
A Characteristic Method for Fully Convex Bolza Problems over Arcs of Bounded Variation in Workshop on Optimal Control & Mean Field Games, October 2019, Rio de Janeiro, Brazil.
Hamilton-Jacobi-Bellman approach for optimal control problems of sweeping processes in 6th International Conference on Continuous Optimization, August 2019, Berlin, Germany.
Generalized Characteristic Method for Fully Convex Impulsive Systems in 14th Viennese Conference on Optimal Control and Dynamic Games, July 2018, Vienna, Austria.
Self-Dual Approximations to Fully Convex Impulsive Systems in XXXI Jornada de Matemática de la Zona Sur, April 2018, Valdivia, Chile.
Generalized Characteristic Method for Fully Convex Impulsive Systems in International Workshop on Optimization and Variational Analysis, January 2018, Rancagua, Chile.
Legendre Transform And Applications To Finite And Infinite Optimization in Workshop on Dynamics and Algorithms in Convex Optimization, December 2017, Santiago, Chile.
Constrained and impulsive Linear Quadratic control problems in Mathematical Congress of the Americas, July 2017, Montreal, Canada.
Constrained and impulsive Linear Quadratic control problems in 20th IFAC World Congress, July 2017, Toulouse, France.
Self-dual approximations to fully convex impulsive systems in 55th IEEE CDC 2016 & Workshop, December 2016, Las Vegas, USA.
Discontinuous solutions of Hamilton-Jacobi-Bellman equations on networks in HJ2016: Hamilton-Jacobi Equations : New trends and applications, May - June 2016, Rennes, France.
Self-dual approximations to fully convex impulsive systems in ECOPT 2015 & Workshop, December 2015, Santiago, Chile.
On the construction of continuous suboptimal feedback laws in SIAM Conference on Control and its Applications, July 2015, Paris, France.
Principes d'optimalité et l'approche HJB pour le problème de Mayer sous contraintes d'état in Journées annuelles GdR MOA, December 2014, Limoge, France.
Infinite horizon problems on stratifiable state constraints sets in AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 2014, Madrid, Spain.
Infinite horizon problems on stratifiable state constraints sets in NetCo: New Trends in Optimal Control, June 2014, Tours, France.
Infinite horizon problems on stratifiable state constraints sets in Conference MODE, March 2014, Rennes, France.
Stratified ODEs and necessary conditions for robustness in OMPC 2013 - SADCO Workshop, September 2013, Bayreuth, Germany.
Stratified ODEs and necessary conditions for robustness in International Conference IFIP TC 7, September 2013, Klagenfurt, Austria.
Infinite horizon problems on stratifiable state constraints sets in International conference ICCOPT 2013, July 2013, Lisbon, Portugal.
Hessian Riemannian metrics on convex sets and related optimization methods in International conference EURO 2012, July 2012, Vilnius, Lithuania.

Grants

Ongoing

2023 - 2026 FONDECYT grant number 1231049: Convexity and Duality in Optimal Control (Principal investigator)
2024- 2025 MATH AmSud grant number 23-MATH-17: VIPS: Variational Analysis in Probability Spaces with Applications to Optimal Control Theory (Researcher)
2024- 2025 USM grant number PI_M_24_08: Nonlinear Optimization Techniques for Enhancing the Performance of MMCC and Their Implementation in Digital Control Platforms (Co-investigator)

Finished

2021 - 2023 ANID-ECOS grant number ECOS200064 : Sensitivity Analysis of State Constrained Optimal Control Problems (Chilean Principal investigator)
2020 - 2023 FONDECYT grant number 1200355: Sustainable thresholds, viability, and optimization (Co-investigator)
2019 - 2021 FONDECYT grant number 11190456: State constrained optimal control of nonsmooth dynamical systems (Principal investigator)
2018 - 2019 REDES grant number REDI170200: Estudio de problemas de Control Óptimo gobernados por Procesos de Arrastre: Teoría y Aplicaciones (Principal investigator)
2018 - 2019 MATH AmSud grant number 18-MATH-05: MOVECO : Modeling, Optimization and Viability for Epidemics Control (Researcher).
2017 - 2020 FONDECYT grant number 3170485: Study of stratified optimal control problems via level-sets approach: theory and applications (Principal investigator)
2011 - 2014 Marie Curie Fellowship, grant number 264735-SADCO: Sensitivity Analysis for Deterministic Control Design Initial Training Network (ITN-SADCO) (PhD student)

Education

High School
Instituto Nacional (2001-2004)

Top 10% of class 2004.

Mathematical Engineering Degree
Universidad de Chile (2005-2011)

Advisor: Felipe Álvarez
Mention: Distinción Máxima (Cum Laude)

PhD in Applied Mathematics
ENSTA Paris (lnstitut Polytechnique de Paris) (2011-2015)

Advisors: Hasnaa Zidani and Frédéric Jean
Mention: Très honorable (Cum Laude)

Postdoctoral researcher
Louisiana State University (2015-2017)

Supervisor: Peter Wolenski

Teaching