Related papers: Regret-Optimal LQR Control
This paper studies online solutions for regret-optimal control in partially observable systems over an infinite-horizon. Regret-optimal control aims to minimize the difference in LQR cost between causal and non-causal controllers while…
We consider control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing an online controller which minimizes regret against the best…
We consider measurement-feedback control in linear dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing an online controller which competes with the optimal…
We present an optimisation-based method for synthesising a dynamic regret optimal controller for linear systems with potentially adversarial disturbances and known or adversarial initial conditions. The dynamic regret is defined as the…
Inspired by online learning, data-dependent regret has recently been proposed as a criterion for controller design. In the regret-optimal control paradigm, causal controllers are designed to minimize regret against a hypothetical optimal…
Recent literature has made much progress in understanding \emph{online LQR}: a modern learning-theoretic take on the classical control problem in which a learner attempts to optimally control an unknown linear dynamical system with fully…
This paper presents a synthesis method for robust, regret optimal control. The plant is modeled in discrete-time by an uncertain linear time-invariant (LTI) system. An optimal non-causal controller is constructed using the nominal plant…
In this paper, we propose and analyze a new method for online linear quadratic regulator (LQR) control with a priori unknown time-varying cost matrices. The cost matrices are revealed sequentially with the potential for future values to be…
This paper presents a synthesis method for the generalised dynamic regret problem, comparing the performance of a strictly causal controller to the optimal non-causal controller under a weighted disturbance. This framework encompasses both…
The Linear Quadratic Regulator (LQR) framework considers the problem of regulating a linear dynamical system perturbed by environmental noise. We compute the policy regret between three distinct control policies: i) the optimal online…
The filtering problem of causally estimating a desired signal from a related observation signal is investigated through the lens of regret optimization. Classical filter designs, such as $\mathcal H_2$ (Kalman) and $\mathcal H_\infty$,…
We consider the problem of controlling a Linear Quadratic Regulator (LQR) system over a finite horizon $T$ with fixed and known cost matrices $Q,R$, but unknown and non-stationary dynamics $\{A_t, B_t\}$. The sequence of dynamics matrices…
We consider estimation and control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing causal estimators and controllers which…
Inspired by competitive policy designs approaches in online learning, new control paradigms such as competitive-ratio and regret-optimal control have been recently proposed as alternatives to the classical $\mathcal{H}_2$ and…
We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller…
We consider the problem of online adaptive control of the linear quadratic regulator, where the true system parameters are unknown. We prove new upper and lower bounds demonstrating that the optimal regret scales as…
As we move towards safety-critical cyber-physical systems that operate in non-stationary and uncertain environments, it becomes crucial to close the gap between classical optimal control algorithms and adaptive learning-based methods. In…
In this paper, we study the dynamic regret of online linear quadratic regulator (LQR) control with time-varying cost functions and disturbances. We consider the case where a finite look-ahead window of cost functions and disturbances is…
The Linear-Quadratic Regulation (LQR) problem with unknown system parameters has been widely studied, but it has remained unclear whether $\tilde{ \mathcal{O}}(\sqrt{T})$ regret, which is the best known dependence on time, can be achieved…
We study the problem of adaptive control of the stochastic linear quadratic regulator (LQR) with constraints that must be satisfied at every time step. Prior work on the multidimensional problem has shown $\tilde{O}(T^{2/3})$ regret and…