I am interested in the use of analytic and computational tools for automated decision-making and control of interconnected dynamic systems. These are ubiquitous in modern applications, such as robotic agents, distributed power generation or biology, to name a few.

My research revolves around the decentralized stochastic optimal control and statistical estimation of spatially-distributed dynamic systems: both, spatially discrete (large-scale networks composed of interacting agents) and continuous (dynamics of the system described by PDEs).

Particularly, I aim to find the conditions under which centralized optimal controllers and estimators exhibit an inherent degree of decentralization, which system and problem parameters enhance local information exchange between subsystems for control and estimation, and to develop and apply novel mathematical tools and formulations for the design of sparsely-structured and sparsity-promoting controllers and for distributed optimization. Furthermore, I am interested in understanding how the statistical properties of the noise present in the system dynamics and measurements affect the decentralization of the optimal controllers and estimators.

Keywords: decentralized and distributed control, large-scale dynamic systems, stochastic optimal control, automated decision-making, distributed optimization, statistical estimation.

PUBLICATIONS:

Journals

[2018] J. Arbelaiz, A. U. Oza and J. W. M. Bush. Promenading Pairs: Dynamics and Stability. Phys. Rev. Fluids 3, 013604

Conferences

[2022] J. Arbelaiz, E. Jensen, B. Bamieh, A. Hosoi, A. Jadbabaie, L. Lessard. Information Structures of the Kalman Filter for the Elastic Wave Equation, IFAC Conference on Networked Systems 2022 (NecSys 2022), ETH Zurich, Switzerland. (submitted, under review)

[2021] J. Arbelaiz, B. Bamieh, A. Hosoi and A. Jadbabaie, Optimal structured controllers for spatially invariant systems: a convex formulation, 60th Conference on Decision and Control 2021 (CDC 2021), Austin, Texas, USA. (invited session: Distributed optimization and learning for Networked Systems)

[2020] J. Arbelaiz, B. Bamieh, A. Hosoi and A. Jadbabaie, Distributed Kalman filtering for spatially-invariant diffusion processes: the effect of noise on communication requirements, 59th Conference on Decision and Control 2020 (CDC 2020), Jeju Island, Republic of Korea.

[2020] J. Arbelaiz, A. Hosoi, A. Jadbabaie and B. Bamieh, On the spatial-localization of optimal control and estimation for diffusion, Mathematical Theory of Networks and Systems (MTNS), University of Cambridge, Cambridge, UK (invited session: Control across Scales)

[2020] J. Arbelaiz, A. Hosoi, A. Jadbabaie and B. Bamieh, The effect of stochastic disturbances on the communication requirements for control: the case of spatially-invariant dynamic systems, poster and talk in Women in Data Science (WiDS20) Conference, Microsoft Research Center, Cambridge, MA.

[2020] J. Arbelaiz, A. Hosoi, A. Jadbabaie and B. Bamieh, Effect of compliance and stochastic disturbances on optimal controllers: implications for the control of the continuum, contributed lecture in SIAM MS20 Conference, Bilbao, Spain.

[2018] J. Arbelaiz and A. Hosoi. Crawling Strategies and Uncertainty Handling. APS March Meeting 2018, Los Angeles, CA.

Preprints

[2019] J. Arbelaiz and J. Tordesillas. Personalized Cancer Chemotherapy Schedule: a numerical comparison of performance and robustness in model-based and model-free scheduling methodologies.