One-Shot Verification of Dissipativity Properties From Input–Output Data

Due to their relevance in controller design and robustness analysis, we present a novel framework to find and verify dissipativity properties for discrete-time linear time-invariant systems from only one input–output trajectory. Introducing a new data-driven formulation for dissipativity, we obtain necessary and sufficient conditions for dissipativity based only on a definiteness condition on a single data-dependent matrix. Furthermore, we provide a promising relaxation in the case of measurement noise, which, as illustrated in numerous numerical examples, works remarkably well.

[1]  Raymond A. de Callafon,et al.  IDENTIFICATION FOR CONTROL , 2009 .

[2]  Bo Wahlberg,et al.  Non-parametric methods for L2-gain estimation using iterative experiments , 2010, Autom..

[3]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[4]  P. Rapisarda,et al.  On Lyapunov functions and data-driven dissipativity , 2017 .

[5]  Frank Allgöwer,et al.  Determining dissipation inequalities from input-output samples , 2017 .

[6]  Frank Allgöwer,et al.  A trajectory-based framework for data-driven system analysis and control , 2019, 2020 European Control Conference (ECC).

[7]  Frank Allgöwer,et al.  Some problems arising in controller design from big data via input-output methods , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[8]  G. Zames.  On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivity , 1966 .

[9]  P. Moylan,et al.  Dissipative Dynamical Systems: Basic Input-Output and State Properties , 1980 .

[10]  Nikolai Matni,et al.  On the Sample Complexity of the Linear Quadratic Regulator , 2017, Foundations of Computational Mathematics.

[11]  D.L. Elliott,et al.  Feedback systems: Input-output properties , 1976, Proceedings of the IEEE.

[12]  Zhuo Wang,et al.  From model-based control to data-driven control: Survey, classification and perspective , 2013, Inf. Sci..

[13]  Frank Allgöwer,et al.  Sampling strategies for data-driven inference of passivity properties , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[14]  Stephen Tu,et al.  On the Approximation of Toeplitz Operators for Nonparametric $\mathcal{H}_{\infty}$-norm Estimation , 2017, American Control Conference.

[15]  Bart De Moor,et al.  A note on persistency of excitation , 2005, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).