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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:…
We present a novel approach to control design for nonlinear systems which leverages model-free policy optimization techniques to learn a linearizing controller for a physical plant with unknown dynamics. Feedback linearization is a…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
It is well known that highly volatile control laws, while theoretically optimal for certain systems, are undesirable from an engineering perspective, being generally deleterious to the controlled system. In this article we are concerned…
In this paper, we investigate the optimal output tracking problem for linear discrete-time systems with unknown dynamics using reinforcement learning and robust output regulation theory. This output tracking problem only allows to utilize…
Domain randomization is a simple, effective, and flexible scheme for obtaining robust feedback policies aimed at reducing the sim-to-real gap due to model mismatch. While domain randomization methods have yielded impressive demonstrations…
Linear dynamical systems that obey stochastic differential equations are canonical models. While optimal control of known systems has a rich literature, the problem is technically hard under model uncertainty and there are hardly any…
Inverse reinforcement learning (IRL) for linear systems seeks a cost function whose optimal controller reproduces an expert policy from data. Existing data-driven methods for discrete-time linear systems are largely built on iterative…
Direct data-driven optimal control provides an elegant end-to-end paradigm, yet its real-time applicability is often hindered by the growing dimensionality of online decision variables. Recent breakthroughs, notably Data-EnablEd Policy…
This paper studies the relationship between state feedback policies and disturbance response policies for the standard Linear Quadratic Regulator (LQR). For open-loop stable plants, we establish a simple relationship between the optimal…
We propose a new risk-constrained reformulation of the standard Linear Quadratic Regulator (LQR) problem. Our framework is motivated by the fact that the classical (risk-neutral) LQR controller, although optimal in expectation, might be…
This paper first presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Then, by introducing several sequences of bounded linear operators, the…
The data-driven linear quadratic regulator (ddLQR) is a widely studied control method for unknown dynamical systems with disturbance. Existing approaches, both indirect, i.e., those that identify a model followed by model-based design, and…
The linear quadratic regulator (LQR) problem is a cornerstone of automatic control, and it has been widely studied in the data-driven setting. The various data-driven approaches can be classified as indirect (i.e., based on an identified…
Recent analyses of certain gradient descent optimization methods have shown that performance can degrade in some settings - such as with stochasticity or implicit momentum. In deep reinforcement learning (Deep RL), such optimization methods…
In this paper, we propose a structured linear parameterization of a feedback policy to solve the model-free stochastic optimal control problem. This parametrization is corroborated by a decoupling principle that is shown to be near-optimal…
In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of the solution of a gradient flow. We show through a simple…
This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances, and in presence of some amplitude constraints on the control…
We consider reinforcement learning (RL) methods for finding optimal policies in linear quadratic (LQ) mean field control (MFC) problems over an infinite horizon in continuous time, with common noise and entropy regularization. We study…
Linear Quadratic Regulator (LQR) is often combined with feedback linearization (FBL) for nonlinear systems that have the nonlinearity additive to the input. Conventional approaches estimate and cancel the nonlinearity based on the first…