10 citations · 16 across the 6 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…
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…