The term"dual control"refers to the dual objective of simultaneously balancing exploration and exploitation. Problems of this kind have been studied for nearly a century. This paper is devoted to theory and methodology relevant for optimal control of linear time-invariant systems whose parameters are initially unknown and must be learned by active probing. We review the main ideas underlying four major research directions: Multi-armed bandits, self-tuning regulators, regret rate minimizing controllers, and minimax optimal dual controllers. The first three have a long history and rich literature, whereas the fourth provides a promising framework for robust dual control.
While recent advances in minimax dual control have led to exact solutions for uncertain general linear time-invariant systems as well as (sub)optimal dual controllers, corresponding results for linear positive systems are still lacking. This paper aims to fill this gap and thereby pave the way toward scalable dual cont...
Fethi Bencherki, Tomas J. Meijer, Anders Rantzer· 0 citations
We present DAOCP, a dual active set solver for linear quadratic optimal control problems with stage-wise equality and inequality constraints. Active set methods are leading Model Predictive Control benchmarks for full-body robotics, but existing solvers operate on dense QPs, while typical problem dimensions favor metho...
Alberto Zaupa, Samuel Erickson, Mikael Johansson· 0 citations
In this work, we study policy optimization under domain randomization for linear quadratic control, focusing on learning a single state-feedback controller that minimizes the average cost across systems with uncertain dynamics. We propose a policy iteration algorithm with a step-size rule that preserves stability acros...
We consider control-affine optimal control problems on the torus, where the dynamics and cost functions are only accessed through samples. Starting from a weak formulation of such problems, we derive a dual, a primal, and a primal-dual formulation, compatible with stochastic optimization. We show convergence of stochas...
Eloıse Berthier, Z. Kobeissi, F. Bach· 0 citations
A novel spectrum assignment method is proposed to obtain an initial stabilizer for PI in continuous-time indefinite stochastic linear quadratic control with the help of the Lyapunov-type operator's spectrum, which is gradually approximated from the stable auxiliary system by adjusting a cumulative factor, thereby obtai...
Passivity-based control (PBC) is a nonlinear control design framework that has proven adequate for controlling a wide range of systems, especially physical ones. Their main ingredients are physical quantities such as energy and dissipation, making the control design more intuitive and endowing the controllers with a ph...
P. Borja, Romeo Ortega· 0 citations
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