Generalist Space Systems Transformers:

• Developing an AI-driven space systems platform for comprehensive spacecraft within the aerospace industry

System Identification of Non-linear Aerodynamic Parameters of Aircraft:

• Developed system identification methodologies to estimate non-linear aerodynamic parameters of aircraft

• Conducted extensive data analysis and modeling to characterize complex aerodynamic behaviors

• Utilized techniques such as sparse regression algorithms for parameter estimation

• Validated model accuracy through comparison with flight data and refined models for improved performance

  Sparse-Collocation based Optimal Control of Vehicles using Hamilton-Jacobi Equation:

  • Developed a Semi-Analytical (SA) methodology to obtain a canonical transformation that rectifies the flow of a dynamical system
  • Solved the Two Point Boundary Value Problem (TPBVP) using Hamilton-Jacobi Equation (HJE)
  • Utilized Sparse Approximation method to fit a surface around collocation points
  • Verified the SA solution with the open-loop solution using bvp4c in MATLAB

  Leveraging Hamiltonian Structure for Accurate Uncertainty Propagation:

  • Propagated the probability density function (pdf) of a non-linear system using Fokker-Plank-Kolmogorov Equation (FPKE)
  • A minimum number of collocation points are utilized which are computed through the non-product quadrature method known as the Conjugate Unscented Transformation (CUT) method
  • Exploited the Hamiltonian structure in conjunction with sparse approximation algorithm to curtail the curse of dimensionality

  Reachability Analysis using Sparse-Collocation Method:

  • Reachability analysis of a general non-linear system is computed due to the presence of uncertainties in the initial condition, control input and external disturbances
  • Collocation based method is used to approximate the transition probability density function (pdf) at any given time
  • Utilized Sparse Approximation method to fit a surface around collocation points, which are computed through the non-product quadrature method known as the Conjugate Unscented Transformation (CUT) method
  • Utilized minimum set of polynomial expansion as a convex optimization problem to find the sparse approximation solution

  Stochastic Reachability Analysis for general Non-Linear Systems:

  • Computed the reachability analysis of a general non-linear system by approximating the state pdf at any given instant of time
  • CUT points provides the minimum number of collocation points to propagate the dynamical system
  • Utilized a minimum set of polynomial expansion as a convex optimization problem to find the sparse solution

  Reachability Analysis for the Hypersonic Re-entry Problem:

  • Used CUT method to drive the uncertainty in control input to compute the reachability for the hypersonic reentry model
  • Multi-dimensional expectation integrals are computed using CUT quadrature method to obtain desired order statistical moments
  • Numerical results for the first and second order moments are computed for two different maneuvers examples

  A Computationally Efficient Approach for Stochastic Reachability Set Analysis:

  • Formulated the problem of computing reachability set of a system in a probabilistic manner
  • Utilized the Convolution and Principle of Maximum Entropy (PME) techniques to find the pdf of a system at any given time
  • Verified numerical results using MC simulations

  An Optimal Trajectory Planning Based on Load Distribution for a Multi-lift System:

  • Developed an optimal trajectory planning method for a multi-lift system using direct and indirect collocation method
  • Applied direct collocation-based method to find a solution
  • Implemented indirect collocation-based method to verify the solution obtained from the direct collocation method
  • Used non-linear solvers such as fmincon and fsolve to solve the optimization problem