Embedded Files
I was always an optimizer, I wanted the best for the least effort.
- Alessio Figalli.
I'm broadly interested in the mathematical theory of AI, ML, and control, more specifically:
Generative AI through the lens of optimal control and mass transportation
Optimal transport: theory and algorithms, and application to control problems
PDE constrained optimal control
Attack and anomaly detection in cyber-physical systems
Stochastic optimal control theory, viable algorithms, and applications
Approximation theory (approximation capabilities of neural networks)
Sparsity and its manifestations under uncertainty (via the lens of robust optimizaiton)
Covariance control problems
Schrödinger bridge via lifting: feasibility, regularity, and path-space obstructions
Coming soon.
Publication:
S. Ganguly, G. Rapakoulias, P. Tsiotras
Lifted Schrödinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions.
Nonlinear optimal control and optimal stopping for SDEs: stochastic HJB equations and variation analysis
This work develops a theoretical framework for nonlinear stochastic optimal control and optimal stopping by establishing a density-based deterministic representation of the underlying SDE. Our primary engine is a Fokker--Planck transformation that rewrites the controlled Fokker-Planck equation as a continuity equation. Leveraging Stein-type identities, we show that the associated distributional dynamic programming equation admits the same second-order differential operator as the distributional stochastic Hamilton-Jacobi-Bellman formulation. Building on this representation, we formulate an optimal control problem with state-dependent terminal-time assignment and terminal distributional constraints and derive the first-order necessary conditions using variational analysis.
Publication:
A. Selim, S. Ganguly, A. Pakniyat, P. Tsiotras
(arXiv version) Nonlinear stochastic optimal control and optimal stopping using the Fokker--Planck transformation.
Under review, Applied Mathematics and optimization, Springer.
Covariance control of Markov jump linear systems
Markov jump linear systems arise in several applications, for example:
aerospace and robotics
power systems and communication networks
fault-tolerant control architectures
macroeconomic and financial systems.
where an abrupt structural change cannot be neglected, and a control (perhaps under constraints) synthesis is necessary. In many applications, however, random switching is only one source of uncertainty. A second important source of uncertainty is stochastic noise, whose effect scales with the current state or the applied control, which is more appropriately represented by multiplicative noise rather than purely additive noise.
For this class of systems, we study a finite-horizon covariance steering problem with both state- and control-dependent multiplicative noise. We show that the feasible controls may be represented by mode-dependent linear feedback together with feedforward and independent random components, and we highlight that, in contrast to the case without multiplicative noise, a purely affine state-feedback law does not in general suffice. For computation, using techniques from convex analysis, we establish a lossless SDP relaxation technique for efficient computation.
Publication:
W. Fangji, S. Ganguly, P. Tsiotras
(arXiv version) Covariance steering for Markov jump dynamics with multiplicative noise.
Under review, IEEE Transactions on Automatic Control.
Anomaly detection for cyber-physical systems: an optimal transport prespective
Much of the attack/anomaly detection literature for cyber–physical control systems is built on convenient but indefensible assumptions: (a) Gaussian noise/residual models, (b) an attacker whose statistics are known (or can be meaningfully parameterized), (c) i.i.d. or stationary data streams, and (d) a “well-behaved” adversary that politely attacks either sensors or actuators, rather than coordinating both or adapting online. These assumptions are not minor technicalities—they often drive the theory while being violated by construction in realistic CPS settings.
To move beyond this, we use optimal transport and data-driven distributionally robust optimization to design detection rules that do not rely on fragile parametric/independence assumptions. Our approach yields algorithmic recipes with explicit robustness, and a min–max optimal detector equipped with finite-sample guarantees, including concentration bounds for the false-positive rate under distributional ambiguity and adversarial perturbations.
Publication:
(arXiv version) OT-DETECT: An optimal transport-driven technique for attack detection in cyber-physical systems.
Submitted.
Unbalanced controlled optimal transport: theory and viable algorithms
Balanced optimal transport compares distributions by redistributing mass only: it moves measures from where it is to where it should be, under strict mass conservation. This is powerful, but brittle in settings where mass can appear, disappear, split, or aggregate (e.g., births/deaths, dropouts, occlusions, unmodeled inflow/outflow), because forcing conservation can misattribute “creation/destruction” to long-distance transport. Unbalanced OT (UOT) fixes this by allowing controlled mass creation/annihilation via a penalty that trades off transport effort against deviation from prescribed marginals.
We develop unbalanced density control (UDC) for the density control of constrained discrete-time linear systems based on UOT. Our primary result is that both UOT and UDC problems admit globally optimal convex reformulations for Gaussian reference measures.
Publication:
H. Nakashima, S. Ganguly, K. Kashima
(arXiv version) Unbalanced optimal transport and control of discrete-time linear systems.
To Appear in the Proceedings of Mathematical Theory of Networked Systems 2026, Waterloo, Canada.
H. Nakashima, S. Ganguly, K. Kashima
(arXiv version) Globally Solving Unbalanced Optimal Transport and Density Control For Gaussian Distributions.
Under review, IEEE Transactions on Automatic Control.
Robust maximum hands-off optimal control: necessary conditions, equivalence, and numerical algorithms
We developed a robust version of the well-known maximum hands-off control principle for sparse optimal control. For a class of uncertain systems, we leverage results from a robust Pontryagin-type maximum principle to theoretically demonstrate that the robust L^0 and robust L^1 problems are equivalent. Moreover, by leveraging tools from robust optimization, we provide a numerical algorithm for their efficient and tractable solutions.
Publications:
(extended arXiv version) Robust maximum hands-off control: existence, robust Pontryagin maximum principle, and equivalence.
Automatica (provisionally accepted), 2026.
S. Ganguly, A. Aravind, S. Das, M. Nagahara, D. Chatterjee
Sparse robust optimal control: theory and numerics.
To appear in IEEE Transactions on Automatic Control, 2026.
Minmax density transportation of PDE-constrained optimal control problems
Publication:
Minmax density transportation for parabolic PDEs: a direct optimal control perspective.
Under revision, IEEE Transactions on Automatic Control.
Data-driven Gromov-Wasserstein density transportation
We devised a data-driven density transportation algorithm tailored for unknown linear systems, aiming to morph an initial density into a prescribed terminal form while preserving its intrinsic structure. To achieve this, we harness the power of the Gromov-Wasserstein optimal transport distance in concert with state-of-the-art data-driven methodologies, ensuring precision and adaptability.
Publication:
H. Nakashima, S. Ganguly, K. Kashima
(extended arXiv version) Data-driven Gromov-Wasserstein Density Steering.
IEEE CDC, Rio de Janeiro, 2025.
Formation shape control via controlled optimal transport
Given a set of agents (for example a swarm of robots) sometimes a relevant objective is to achieve a specific shape irrelevant of the distance, rotation, or angle between the agents. Only the shape is important. Employing the Gromov-Wasserstein optimal transport metric, in this work, we developed a controlled optimal transport-driven algorithm to control the shape of a group of agents in a formation.
Publication:
H. Nakashima, S. Ganguly, K. Morimoto, K. Kashima
(arXiv version) Formation shape control using the Gromov-Wasserstein metric.
Learning for dynamics and control conference (L4DC), Proceedings of the Machine Learning Research (PMLR), Michigan, USA, 2025.
Data-driven distributionally robust MPC via semi-definite semi-infinite programming
Publication:
S. Das, S. Ganguly, A. Aravind, D. Chatterjee
(doi, extended arXiv version) Data-driven distributionally robust MPC via semi-infinite semidefinite programming: an application to finance
Mathematical Theory of Networked Systems (MTNS), 2024, Aug, 19-23, Cambridge
Fast and explicit solutions to robust model predictive control problems
Publications:
Journals:
(doi, extended arXiv version) Explicit feedback synthesis driven by quasi-interpolation for nonlinear robust model predictive control.
IEEE Transactions on Automatic Control,.
(doi) Exact solutions to minmax optimal control problems for constrained noisy linear systems
IEEE Control Systems Letters (LCSS).
S. Ganguly, S. Gupta, D. Chatterjee
Data-driven learning of constrained feedbacks for explicit robust predictive control: an approximation theoretic view.
Under review.
QuITO: Constrained trajectory optimization for ODE-constrained nonlinear optimal control problems.
Publications:
Journals:
(arXiv version) QuITO v.2: Numerical solutions with Uniform Error Guarantees to Optimal Control Problems under Path Constraints
To appear in IEEE Transactions on Automatic Control, 2025.
S. Ganguly, N. Randad, R.A. D'Silva, Mukesh. Raj. S, D. Chatterjee
(doi) QuITO: Numerical software for constrained nonlinear optimal control problems.
SoftwareX, Vol 24, 2023,
Conferences:
S. Das, S. Ganguly, A. Muthyala, D. Chatterjee
(doi) Towards continuous-time constrained MPC: a novel trajectory optimization algorithm
IEEE Conference on Decision & Control (CDC-2023), Dec 13-15, Singapore, extended arXiv version.
(doi) Constrained trajectory synthesis via quasi-interpolation.
IEEE conference on decision and control (CDC-2022), Dec 6-9, Cancun, Mexico.
Patent granted:
Method and trajectory management controller for constrained trajectory optimization
Patent no 430622, application no. 202221040362, The Patent Office Journal No. 18/2023, Dated 05/05/2023.
Software packages
QuITO v.1: a MATLAB-based numerical package with a GUI for solving direct trajectory optimization and constrained nonlinear optimal control problems.
GitHub Repository (written jointly with Nakul Randad, Rihan Aaron D'Silva, and Mukesh S.).
QuITO v.2: new transcription algorithm with automatic change point detection and mesh refinement modules.
GitHub Repository (written jointly with Rihan Aaron D'Silva).
Rate constrained Pontryagins maximum principle on Euclidean spaces
Publications:
Journal:
(doi, extended arXiv version) Discrete-time Pontryagin maximum principle under rate constraints: Necessary conditions for optimality.
Asian Journal of Control, 2024,
Conference:
(doi) Rate constrained discrete-time maximum principle
7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Berlin, Germany, Oct 2021.
Google Sites
Report abuse