73 citations · 129 across the 8 of their papers we have counts for
8 papers
A Note on Nesterov's Accelerated Method in Nonconvex Optimization: a Weak Estimate Sequence Approach
Jingjing Bu, Mehran Mesbahi
We present a variant of accelerated gradient descent algorithms, adapted from Nesterov's optimal first-order methods, for weakly-quasi-convex and weakly-quasi-strongly-convex funct…
Policy Gradient-based Algorithms for Continuous-time Linear Quadratic Control
Jingjing Bu, Afshin Mesbahi, Mehran Mesbahi
We consider the continuous-time Linear-Quadratic-Regulator (LQR) problem in terms of optimizing a real-valued matrix function over the set of feedback gains. The results developed…
Global Convergence of Policy Gradient Algorithms for Indefinite Least Squares Stationary Optimal Control
Jingjing Bu, Mehran Mesbahi
We consider policy gradient algorithms for the indefinite least squares stationary optimal control, e.g., linear-quadratic-regulator (LQR) with indefinite state and input penalizat…
Global Convergence of Policy Gradient for Sequential Zero-Sum Linear Quadratic Dynamic Games
Jingjing Bu, Lillian J. Ratliff, Mehran Mesbahi
We propose projection-free sequential algorithms for linear-quadratic dynamics games. These policy gradient based algorithms are akin to Stackelberg leadership model and can be ext…
LQR through the Lens of First Order Methods: Discrete-time Case
Jingjing Bu, Afshin Mesbahi, Maryam Fazel +1
We consider the Linear-Quadratic-Regulator (LQR) problem in terms of optimizing a real-valued matrix function over the set of feedback gains. Such a setup facilitates examining the…
On Topological Properties of the Set of Stabilizing Feedback Gains
Jingjing Bu, Afshin Mesbahi, Mehran Mesbahi
This work presents a fairly complete account on various topological and metrical aspects of feedback stabilization for single-input-single-output (SISO) continuous and discrete tim…
On Topological and Metrical Properties of Stabilizing Feedback Gains: the MIMO Case
Jingjing Bu, Afshin Mesbahi, Mehran Mesbahi
In this paper, we discuss various topological and metrical aspects of the set of stabilizing static feedback gains for multiple-input-multiple-output (MIMO) linear-time-invariant (…
Nonlinear Observability via Koopman Analysis: Characterizing the Role of Symmetry
Afshin Mesbahi, Jingjing Bu, Mehran Mesbahi
This paper considers the observability of nonlinear systems from a Koopman operator theoretic perspective--and in particular--the effect of symmetry on observability. We first exam…