On the linear quadratic data-driven control

The classical approach for solving control problems is model based: first a model representation is derived from given data of the plant and then a control law is synthesized using the model and the control specifications. We present an alternative approach that circumvents the explicit identification of a model representation. The considered control problem is finite horizon linear quadratic tracking. The results are derived assuming exact data and the optimal trajectory is constructed off-line

Statistical Learning Theory for Control: A Finite Sample Perspective

This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been substantial progress across all areas of control, the theory is most well-developed when it comes to linear system identification and learning for the linear quadratic regulator, which are the focus of this manuscript. From a theoretical perspective, much of the labor underlying these advances has been in adapting tools from modern high-dimensional statistics and learning theory. While highly relevant to control theorists interested in integrating tools from machine learning, the foundational material has not always been easily accessible. To remedy this, we provide a self-contained presentation of the relevant material, outlining all the key ideas and the technical machinery that underpin recent results. We also present a number of open problems and future directions.Comment: Survey Paper, Submitted to Control Systems Magazine. Second version contains additional motivation for finite sample statistics and more detailed comparison with classical literatur

Data-Driven Predictive Control for Multi-Agent Decision Making With Chance Constraints

In the recent literature, significant and substantial efforts have been dedicated to the important area of multi-agent decision-making problems. Particularly here, the model predictive control (MPC) methodology has demonstrated its effectiveness in various applications, such as mobile robots, unmanned vehicles, and drones. Nevertheless, in many specific scenarios involving the MPC methodology, accurate and effective system identification is a commonly encountered challenge. As a consequence, the overall system performance could be significantly weakened in outcome when the traditional MPC algorithm is adopted under such circumstances. To cater to this rather major shortcoming, this paper investigates an alternate data-driven approach to solve the multi-agent decision-making problem. Utilizing an innovative modified methodology with suitable closed-loop input/output measurements that comply with the appropriate persistency of excitation condition, a non-parametric predictive model is suitably constructed. This non-parametric predictive model approach in the work here attains the key advantage of alleviating the rather heavy computational burden encountered in the optimization procedures typical in alternative methodologies requiring open-loop input/output measurement data collection and parametric system identification. Then with a conservative approximation of probabilistic chance constraints for the MPC problem, a resulting deterministic optimization problem is formulated and solved efficiently and effectively. In the work here, this intuitive data-driven approach is also shown to preserve good robustness properties. Finally, a multi-drone system is used to demonstrate the practical appeal and highly effective outcome of this promising development in achieving very good system performance.Comment: 10 pages, 6 figure

Data-driven Identification and Prediction of Power System Dynamics Using Linear Operators

In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust approach for data-driven approximation of Koopman operator for the identification of nonlinear power system dynamics. The identified model is used for the prediction of state trajectories in the power system. The application of the framework is illustrated using an IEEE nine bus test system.Comment: Accepted for publication in IEEE Power and Energy System General Meeting 201