Related papers: The Parallelization of Riccati Recursion
This paper proposes a parallelizable algorithm for linear-quadratic model predictive control (MPC) problems with state and input constraints. The algorithm itself is based on a parallel MPC scheme that has originally been designed for…
We study a linear quadratic optimal control problem with stochastic coefficients and a terminal state constraint, which may be in force merely on a set with positive, but not necessarily full probability. Under such a partial terminal…
First-order methods for quadratic optimization such as OSQP are widely used for large-scale machine learning and embedded optimal control, where many related problems must be rapidly solved. These methods face two persistent challenges:…
This paper studies a discrete-time stochastic control problem with linear quadratic criteria over an infinite-time horizon. We focus on a class of control systems whose system matrices are associated with random parameters involving unknown…
This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC)…
In this paper, we solve the long-standing fundamental problem of irregular linear--quadratic (LQ) optimal control, which has received significant attention since the 1960s. We derive the optimal controllers via the key technique of finding…
In the context of autonomous driving, the iterative linear quadratic regulator (iLQR) is known to be an efficient approach to deal with the nonlinear vehicle model in motion planning problems. Particularly, the constrained iLQR algorithm…
Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop…
It is a longstanding unsolved problem to characterize the optimal feedback controls for general linear quadratic optimal control problem of stochastic evolution equation with random coefficients. A solution to this problem is given in [21]…
In this article we study the optimal control problem with quadratic functionals for a linear Volterra integro-differential equation in Hilbert spaces. With the finite history seen as an (additional) initial datum for the evolution,…
Optimal control problems with a very large time horizon can be tackled with the Receding Horizon Control (RHC) method, which consists in solving a sequence of optimal control problems with small prediction horizon. The main result of this…
This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with constant coefficients. It is proved that the non-emptiness of the admissible control set for all initial state is…
This paper introduces a novel Model Predictive Control (MPC) implementation for legged robot locomotion that leverages GPU parallelization. Our approach enables both temporal and state-space parallelization by incorporating a parallel…
Iterative linear quadratic regulator (iLQR) has gained wide popularity in addressing trajectory optimization problems with nonlinear system models. However, as a model-based shooting method, it relies heavily on an accurate system model to…
An online policy learning problem of linear control systems is studied. In this problem, the control system is known and linear, and a sequence of quadratic cost functions is revealed to the controller in hindsight, and the controller…
This paper is concerned with a discrete-time mean-field stochastic linear-quadratic optimal control problem arose from financial application. Through matrix dynamical optimization method, a group of linear feedback controls is investigated.…
This paper addresses an open problem in the area of linear quadratic optimal control. We consider the regular, infinite-horizon, stability-modulo-a-subspace, indefinite linear quadratic problem under the assumption that the dynamics are…
Optimal control is often used in robotics for planning a trajectory to achieve some desired behavior, as expressed by the cost function. Most works in optimal control focus on finding a single optimal trajectory, which is then typically…
In this paper, we consider the problem of distributed optimal control of linear dynamical systems with a quadratic cost criterion. We study the case of output feedback control for two interconnected dynamical systems, and show that the…
We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator…