Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems

Abstract

The framework of linear parameter-varying (LPV) systems has shown to be a powerful tool for the design of controllers for complex nonlinear systems using linear tools. In this work, we derive novel methods that allow to synthesize LPV state-feedback controllers directly from only a single sequence of data and guarantee stability and performance of the closed-loop system. We show that if the measured open-loop data from the system satisfies a persistency of excitation condition, then the full open-loop and closed-loop input-scheduling-state behavior can be represented using only the data. With this representation we formulate data-driven analysis and synthesis problems, where the latter yields controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalized ${\mathcal{H}}_2$-norm and ${\ell }_2$-gain of the closed-loop system. The controllers are synthesized by solving a semi-definite program. Additionally, we provide a synthesis method to handle noisy measurement data. Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis in multiple simulation studies, including a nonlinear unbalanced disc system.

31 pages

References in corpus (9)

• Data-Driven Model Predictive Control with Stability and Robustness Guarantees
• Combining Prior Knowledge and Data for Robust Controller Design
• Data-Driven Gain Scheduling Control of Linear Parameter-Varying Systems using Quadratic Matrix Inequalities
• Affine Parameter-Dependent Lyapunov Functions for LPV Systems with Affine Dependence
• Data-driven Dissipativity Analysis of Linear Parameter-Varying Systems
• A Learning- and Scenario-based MPC Design for Nonlinear Systems in LPV Framework with Safety and Stability Guarantees
• Decoupling parameter variation from noise: Biquadratic Lyapunov forms in data-driven LPV control
• LPV Modeling of the Atmospheric Flight Dynamics of a Generic Parafoil Return Vehicle
• Data-based system representations from irregularly measured data

Cited by in corpus (1)

• A Linear Parameter-Varying Approach to Data Predictive Control