My Master's thesis under Prof. Abhishek Halder focuses on designing an Optimal Covariance Steering Algorithm in Continuous Time with Hilbert-Schmidt Terminal Cost for Linear Stochastic Systems over a finite time horizon. While there has been a growing literature on fixed-horizon LQ covariance steering problems with terminal cost for the discrete-time case, its continuous-time version remains relatively unexplored.

A key reason for the imbalance between discrete- and continuous-time formulations lies in computational tractability. The discrete-time problem naturally leads to a semidefinite program that can be solved with off-the-shelf interior-point solvers. In contrast, the continuous-time formulation with terminal cost gives rise to a coupled nonlinear system of matricial ODEs, for which a principled and computationally efficient algorithm had remained unclear.

My research introduces a soft constraint via the Hilbert–Schmidt Terminal Cost, along with a quadratic cost on the control input and the state. The necessary conditions of optimality lead to a coupled matrix ODE two-point boundary value problem with nonlinear split boundary conditions. To solve this, I designed a Matricial Recursive Algorithm with a fast convergence rate, grounded in linear fractional transformations parameterized by the state transition matrix of the associated Hamiltonian system.

The proposed algorithm was tested and validated on a close-proximity rendezvous scenario by modeling the relative motion of a service spacecraft to a target satellite in LEO using Clohessy–Wiltshire dynamics with stochastic disturbances. Our broader motivation is to derive a custom algorithm to solve the boundary-value problem with a Wasserstein terminal cost. This work takes a significant step in that direction, laying the algorithmic groundwork toward handling the full Wasserstein gradient in future extensions.