30 citations · 61 across the 30 of their papers we have counts for
29 papers · 1 filter
Linear Exponential Quadratic Gaussian Covariance Steering
Chiran B. Cherian, Yasemin Isik, Abhishek Halder
We formulate and analyze the linear exponential quadratic Gaussian (LEQG) covariance steering problem in continuous time over a given deadline (finite time horizon). The solution f…
Neural Schrödinger Bridge with Sinkhorn Losses: Application to Data-driven Minimum Effort Control of Colloidal Self-assembly
Iman Nodozi, Charlie Yan, Mira Khare +2
We show that the minimum effort control of colloidal self-assembly can be naturally formulated in the order-parameter space as a generalized Schrödinger bridge problem -- a class o…
Optimal Mass Transport over the Euler Equation
Charlie Yan, Iman Nodozi, Abhishek Halder
We consider the finite horizon optimal steering of the joint state probability distribution subject to the angular velocity dynamics governed by the Euler equation. The problem and…
A Physics-informed Deep Learning Approach for Minimum Effort Stochastic Control of Colloidal Self-Assembly
Iman Nodozi, Jared O'Leary, Ali Mesbah +1
We propose formulating the finite-horizon stochastic optimal control problem for colloidal self-assembly in the space of probability density functions (PDFs) of the underlying stat…
A Note on the Hausdorff Distance between Norm Balls and their Linear Maps
Shadi Haddad, Abhishek Halder
We consider the problem of computing the (two-sided) Hausdorff distance between the unit and norm balls in finite dimensional Euclidean space for $1 \…
Certifying the Intersection of Reach Sets of Integrator Agents with Set-valued Input Uncertainties
Shadi Haddad, Abhishek Halder
We consider the problem of verifying safety for a pair of identical integrator agents in continuous time with compact set-valued input uncertainties. We encode this verification pr…
A Distributed Algorithm for Measure-valued Optimization with Additive Objective
Iman Nodozi, Abhishek Halder
We propose a distributed nonparametric algorithm for solving measure-valued optimization problems with additive objectives. Such problems arise in several contexts in stochastic le…
Schrödinger Meets Kuramoto via Feynman-Kac: Minimum Effort Distribution Steering for Noisy Nonuniform Kuramoto Oscillators
Iman Nodozi, Abhishek Halder
We formulate and solve the problem of finite horizon minimum control effort steering of the state probability distribution between prescribed endpoint joints for a finite populatio…
Boundary and Taxonomy of Integrator Reach Sets
Shadi Haddad, Abhishek Halder
Over-approximating the forward reach sets of controlled dynamical systems subject to set-valued uncertainties is a common practice in systems-control engineering for the purpose of…
Stochastic Uncertainty Propagation in Power System Dynamics using Measure-valued Proximal Recursions
Abhishek Halder, Kenneth F. Caluya, Pegah Ojaghi +1
We present a proximal algorithm that performs a variational recursion on the space of joint probability measures to propagate the stochastic uncertainties in power system dynamics…
On the Convexity of Discrete Time Covariance Steering in Stochastic Linear Systems with Wasserstein Terminal Cost
Isin M. Balci, Abhishek Halder, Efstathios Bakolas
In this work, we analyze the properties of the solution to the covariance steering problem for discrete time Gaussian linear systems with a squared Wasserstein distance terminal co…
Global Convergence of Second-order Dynamics in Two-layer Neural Networks
Walid Krichene, Kenneth F. Caluya, Abhishek Halder
Recent results have shown that for two-layer fully connected neural networks, gradient flow converges to a global optimum in the infinite width limit, by making a connection betwee…
Density-based Stochastic Reachability Computation for Occupancy Prediction in Automated Driving
Shadi Haddad, Abhishek Halder, Baljeet Singh
We propose a stochastic reachability computation framework for occupancy prediction in automated driving by directly solving the underlying transport partial differential equation…
Reflected Schrödinger Bridge: Density Control with Path Constraints
Kenneth F. Caluya, Abhishek Halder
How to steer a given joint state probability density function to another over finite horizon subject to a controlled stochastic dynamics with hard state (sample path) constraints?…
Wasserstein Proximal Algorithms for the Schrödinger Bridge Problem: Density Control with Nonlinear Drift
Kenneth F. Caluya, Abhishek Halder
We study the Schrödinger bridge problem (SBP) with nonlinear prior dynamics. In control-theoretic language, this is a problem of minimum effort steering of a given joint state prob…
Finite Horizon Density Steering for Multi-input State Feedback Linearizable Systems
Kenneth F. Caluya, Abhishek Halder
In this paper, we study the feedback synthesis problem for steering the joint state density or ensemble subject to multi-input state feedback linearizable dynamics. This problem is…
Proximal Recursion for the Wonham Filter
Abhishek Halder, Tryphon T. Georgiou
This paper contributes to the emerging viewpoint that governing equations for dynamic state estimation, conditioned on the history of noisy measurements, can be viewed as gradient…
The Convex Geometry of Integrator Reach Sets
Shadi Haddad, Abhishek Halder
We study the convex geometry of the forward reach sets for integrator dynamics in finite dimensions with bounded control. We derive closed-form expressions for the volume and the d…
Gradient Flow Algorithms for Density Propagation in Stochastic Systems
Kenneth F. Caluya, Abhishek Halder
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time…
Hopfield Neural Network Flow: A Geometric Viewpoint
Abhishek Halder, Kenneth F. Caluya, Bertrand Travacca +1
We provide gradient flow interpretations for the continuous-time continuous-state Hopfield neural network (HNN). The ordinary and stochastic differential equations associated with…
Finite Horizon Density Control for Static State Feedback Linearizable Systems
Kenneth F. Caluya, Abhishek Halder
We consider the problem of steering the joint state probability density function of a static feedback linearizable control system over finite time horizon. Potential applications i…
Optimal Control of Thermostatic Loads for Planning Aggregate Consumption: Characterization of Solution and Explicit Strategies
Fernando A. C. C. Fontes, Abhishek Halder, Jorge Becerril +1
We consider the problem of planning the aggregate energy consumption for a set of thermostatically controlled loads for demand response, accounting price forecast trajectory and th…
DeGroot-Friedkin Map in Opinion Dynamics is Mirror Descent
Abhishek Halder
We provide a variational interpretation of the DeGroot-Friedkin map in opinion dynamics. Specifically, we show that the nonlinear dynamics for the DeGroot-Friedkin map can be viewe…
Proximal Recursion for Solving the Fokker-Planck Equation
Kenneth F. Caluya, Abhishek Halder
We develop a new method to solve the Fokker-Planck or Kolmogorov's forward equation that governs the time evolution of the joint probability density function of a continuous-time s…