Research 

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

• Robustness and risk in mean-field games 

• 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

We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics. Since the direct Schrödinger bridge between Gaussian mixtures is generally not available in closed form, we introduce a lifted path-space construction in which each trajectory is augmented with a source--target component label. Consequently, the problem decomposes into Gaussian component-to-component Schrödinger bridges with explicit marginal, drift, and cost formulas, while the mixture-level assignment reduces to a finite-dimensional entropic coupling problem with a Sinkhorn scaling form. We then analyze the projection obtained by discarding or forgetting the label. By construction, the projected law satisfies the original Gaussian-mixture endpoint constraints, but its relative entropy generally differs from the lifted relative entropy by a nonnegative conditional label-information gap. This gap reveals a path-space obstruction: the lifted optimizer cannot, in general, be identified with the direct unlabeled Schrödinger bridge after projection. We also derive the posterior-averaged Markov drift associated with the projected marginal flow, prove a kinetic-energy upper bound, and identify a common path-potential condition under which the projection gap vanishes. Several numerical illustrations showing density and shape control are recorded for a self-contained exposition. 

Publication: 

• S. Ganguly, G. Rapakoulias, P. Tsiotras

(arXiv version) Lifted Schrödinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions.
Under review, Mathematics of Control, Signals, and Systems, Springer.

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.

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.

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: 

• S. Das, S. Ganguly

(arXiv version) OT-DETECT: An optimal transport-driven technique for attack detection in cyber-physical systems. 

Under review, IEEE Signal Processing Letters.

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 Optimal Transport (UOT) fixes this by allowing controlled mass creation/annihilation via a penalty that trades off transport effort against deviation from prescribed marginals. 

In the following articles, for the first time: 

• For Gaussian reference measures, we provide a closed-form solution for the UOT problem

• We introduce the density control paradigm: unbalanced density control (UDC) for distribution steering of constrained discrete-time linear systems based on UOT.  

• We established that both UOT and UDC problems admit globally optimal convex reformulations for Gaussian reference measures. 

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: 

• S. Ganguly, K. Kashima

(extended arXiv version) Robust maximum hands-off control: existence, robust Pontryagin maximum principle, and equivalence. 

Automatica (to appear), 2026.

• S. Ganguly, A. Aravind, S. Das, M. Nagahara, D. Chatterjee

Sparse robust optimal control: theory and numerics.

IEEE Transactions on Automatic Control (to appear), 2026.

Publication: 

• V. Upadhyay, S. Ganguly, K. Kashima, D. Chatterjee

Minmax density transportation for parabolic PDEs: a direct optimal control perspective.

Under revision, IEEE Transactions on Automatic Control.

Publications: 

Journals:

• S. Ganguly, D. Chatterjee

(doi, extended arXiv version) Explicit feedback synthesis driven by quasi-interpolation for nonlinear robust model predictive control.

IEEE Transactions on Automatic Control, 2025.

• S. Ganguly, D. Chatterjee

(doi) Exact solutions to minmax optimal control problems for constrained noisy linear systems.

IEEE Control Systems Letters (LCSS), 2024. 

• S. Ganguly, S. Gupta, D. Chatterjee

(arXiv version) Data-driven learning of constrained feedback for explicit robust predictive control: an approximation theoretic view.

Under review, Optimization and Engineering, Springer, 2026. 

Publications: 

Journals:

• S. Ganguly, R.A. D'Silva, D. Chatterjee

(arXiv version, doi) QuITO v.2: Numerical solutions with Uniform Error Guarantees to Optimal Control Problems under Path Constraints

IEEE Transactions on Automatic Control, 2025.

• V. Upadhyay, S. Ganguly, D. Chatterjee

Exact algorithmic solutions to a class of constrained optimal control problems via lossless convexification for digital control.

Automatica (to appear), 2026.

• S. Ganguly, N. Randad, R.A. D'Silva, Mukesh. Raj. S, D. Chatterjee

(doi) QuITO: Numerical software for constrained nonlinear optimal control problems. 

SoftwareX, Elsevier, 2024.

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.

• S. Ganguly, N. Randad, D. Chatterjee, R. Banavar 

(doi) Constrained trajectory synthesis via quasi-interpolation.

IEEE conference on decision and control, Dec 6-9, 2022, Cancun, Mexico. 

Patent granted:

• N. Randad, S. Ganguly, D. Chatterjee, R. Banavar 

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.

• R.A. D'Silva, S. Ganguly, D. Chatterjee, R. Banavar 

System and method of automatically generating optimal control trajectory for driving a multi-agent AUV system.

Patent no. 572126, Application no. 2024210060700, 2025, The Patent Office Journal No. 22/2025.

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).

Publications: 

Journal:

• S. Ganguly, S. Das, D. Chatterjee, R. Banavar 

(doi, extended arXiv version) Discrete-time Pontryagin maximum principle under rate constraints: Necessary conditions for optimality.

Asian Journal of Control, Wiley, 2024, 

Conference:

• S. Ganguly, S. Das, D. Chatterjee, R. Banavar 

(doi) Rate-constrained discrete-time maximum principle.

7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Berlin, Germany, Oct 2021.