Related papers: The Parallelization of Riccati Recursion
We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen as a promising class of solution strategies, by forming…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
Linear-quadratic regulator (LQR) is a landmark problem in the field of optimal control, which is the concern of this paper. Generally, LQR is classified into state-feedback LQR (SLQR) and output-feedback LQR (OLQR) based on whether the full…
A gradient-based method is proposed for solving the linear quadratic regulator (LQR) problem for linear systems with nonlinear dependence on time-invariant probabilistic parametric uncertainties. The approach explicitly accounts for model…
This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional. It involves BSDEs in $L^1$ whose well-posedness is a subtle issue. A suitable framework has been adopted so that…
Factor graph represents the factorization of a probability distribution function and serves as an effective abstraction in various autonomous machine computing tasks. Control is one of the core applications in autonomous machine computing…
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…
We present a parallel algorithm for the undirected $s,t$-mincut problem with floating-point valued weights. Our overarching algorithm uses an iteratively reweighted least squares framework. This generates a sequence of Laplacian linear…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
In Model Predictive Control (MPC) the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem at each sample in the control loop. The main computational effort is often spent on computing the search…
Optimal control theory and machine learning techniques are combined to formulate and solve in closed form an optimal control formulation of online learning from supervised examples with regularization of the updates. The connections with…
This paper presents an efficient parallel Cholesky factorization and triangular solve algorithm for the Karush-Kuhn-Tucker (KKT) systems arising in multistage optimization problems, with a focus on model predictive control and trajectory…
This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward…
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…
A Linear-quadratic optimal control problem is considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which turns out to be a linear mean-field…
We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping…
The use of Model Predictive Control in industry is steadily increasing as more complicated problems can be addressed. Due to that online optimization is usually performed, the main bottleneck with Model Predictive Control is the relatively…
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional…
In this paper, we present a novel method for computing the optimal feedback gain of the infinite-horizon Linear Quadratic Regulator (LQR) problem via an ordinary differential equation. We introduce a novel continuous-time Bellman error,…
This note introduces a new analytic approach to the solution of a very general class of finite-horizon optimal control problems formulated for discrete-time systems. This approach provides a parametric expression for the optimal control…