Related papers: Linear Quadratic Control with Risk Constraints
Irregular linear quadratic control (LQ, was called Singular LQ) has been a long-standing problem since 1970s. This paper will show that an irregular LQ control (deterministic) is solvable (for arbitrary initial value) if and only if the LQ…
Understanding the optimization landscape of linear quadratic regulation (LQR) problems is fundamental to the design of efficient reinforcement learning solutions. Recent work has made significant progress in characterizing the landscape of…
We study quadratic optimal stochastic control problems with control dependent noise state equation perturbed by an affine term and with stochastic coefficients. Both infinite horizon case and ergodic case are treated. To this purpose we…
Recent progress in reinforcement learning has led to remarkable performance in a range of applications, but its deployment in high-stakes settings remains quite rare. One reason is a limited understanding of the behavior of reinforcement…
Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) control are foundational and extensively researched problems in optimal control. We investigate LQR and LQG problems with semi-adversarial perturbations and time-varying…
This paper presents a state and state-input constrained variant of the discrete-time iterative Linear Quadratic Regulator (iLQR) algorithm, with linear time-complexity in the number of time steps. The approach is based on a projection of…
We introduce a new problem setting for continuous control called the LQR with Rich Observations, or RichLQR. In our setting, the environment is summarized by a low-dimensional continuous latent state with linear dynamics and quadratic…
This paper presents a constrained iterative Linear Quadratic Regulator (iLQR) framework for nonlinear optimal control problems with box constraints on both states and control inputs. We incorporate logarithmic barrier functions into the…
Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal,…
We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…
Control of linear dynamics with multiplicative noise naturally introduces robustness against dynamical uncertainty. Moreover, many physical systems are subject to multiplicative disturbances. In this work we show how these dynamics can be…
A powerful result from behavioral systems theory known as the fundamental lemma allows for predictive control akin to Model Predictive Control (MPC) for linear time invariant (LTI) systems with unknown dynamics purely from data. While most…
The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all…
We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose…
This article presents a unified approach to quadratic optimal control for both linear and nonlinear discrete-time systems, with a focus on trajectory tracking. The control strategy is based on minimizing a quadratic cost function that…
The problem of controller reduction has a rich history in control theory. Yet, many questions remain open. In particular, there exist very few results on the order reduction of general non-observer based controllers and the subsequent…
This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality…
End-to-end engineering design pipelines, in which designs are evaluated using concurrently defined optimal controllers, are becoming increasingly common in practice. To discover designs that perform well even under the misspecification of…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
A new paradigm is proposed for the robustification of the LQG controller against distributional uncertainties on the noise process. Our controller optimizes the closed-loop performances in the worst possible scenario under the constraint…