Data-Driven Reachability Analysis from Noisy Data

—We consider the problem of computing reach- able sets directly from noisy data without a given system model. Several reachability algorithms are presented for different type of systems generating the data. First, an algorithm for computing over-approximated reachable sets based on matrix zonotopes is proposed for linear systems. Constrained matrix zonotopes are introduced to provide less conservative reachable sets at the cost of increased computational expenses and utilized to incorporate prior knowledge about the unknown system model. Then we extend the approach to polynomial systems and under the assumption of Lipschitz continuity to nonlinear systems. Theoretical guarantees are given for these algorithms in that they give a proper over-approximate reachable set containing the true reachable set. Multiple numerical examples and real experiments show the applicability of the introduced algorithms, and accuracy comparisons are made between algorithms.

[1]  K. Johansson,et al.  Robust Data-Driven Predictive Control using Reachability Analysis , 2021, Eur. J. Control.

[2]  K. Johansson,et al.  Data-Driven Set-Based Estimation using Matrix Zonotopes with Set Containment Guarantees , 2021, 2022 European Control Conference (ECC).

[3]  Frank Allgöwer,et al.  Combining Prior Knowledge and Data for Robust Controller Design , 2020, IEEE Transactions on Automatic Control.

[4]  Frank Allgöwer,et al.  Provably Robust Verification of Dissipativity Properties from Data , 2020, IEEE Transactions on Automatic Control.

[5]  M. Kanat Camlibel,et al.  From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma , 2020, IEEE Transactions on Automatic Control.

[6]  Laurent El Ghaoui,et al.  Data-Driven Reachability Analysis with Christoffel Functions , 2021, 2021 60th IEEE Conference on Decision and Control (CDC).

[7]  F. Allgöwer,et al.  Data-Driven Reachability Analysis Using Matrix Zonotopes , 2020, L4DC.

[8]  Ufuk Topcu,et al.  On-The-Fly Control of Unknown Smooth Systems from Limited Data , 2020, 2021 American Control Conference (ACC).

[9]  Frank Allgöwer,et al.  Dissipativity verification with guarantees for polynomial systems from noisy input-state data , 2020, 2021 American Control Conference (ACC).

[10]  Matthias Althoff,et al.  Sparse Polynomial Zonotopes: A Novel Set Representation for Reachability Analysis , 2019, IEEE Transactions on Automatic Control.

[11]  Karl H. Johansson,et al.  Ensuring safety for vehicle parking tasks using Hamilton-Jacobi reachability analysis , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[12]  M. Pavone,et al.  Sampling-based Reachability Analysis: A Random Set Theory Approach with Adversarial Sampling , 2020, CoRL.

[13]  Frank Allgöwer,et al.  Verifying dissipativity properties from noise-corrupted input-state data , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[14]  Matthias Althoff,et al.  Establishing Reachset Conformance for the Formal Analysis of Analog Circuits , 2020, 2020 25th Asia and South Pacific Design Automation Conference (ASP-DAC).

[15]  Mark Cannon,et al.  Robust adaptive model predictive control: Performance and parameter estimation , 2019, International Journal of Robust and Nonlinear Control.

[16]  Murat Arcak,et al.  Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods , 2019, 2020 American Control Conference (ACC).

[17]  Frank Allgöwer,et al.  Robust data-driven state-feedback design , 2019, 2020 American Control Conference (ACC).

[18]  M. Kanat Camlibel,et al.  Data Informativity: A New Perspective on Data-Driven Analysis and Control , 2019, IEEE Transactions on Automatic Control.

[19]  Pietro Tesi,et al.  Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness , 2019, IEEE Transactions on Automatic Control.

[20]  Frank Allgöwer,et al.  Linear robust adaptive model predictive control: Computational complexity and conservatism , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[21]  Nikolai Matni,et al.  A Tutorial on Concentration Bounds for System Identification , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[22]  Frank Allgöwer,et al.  Robust MPC with recursive model update , 2019, Autom..

[23]  Jaime F. Fisac,et al.  A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems , 2017, IEEE Transactions on Automatic Control.

[24]  John N. Maidens,et al.  Simulation-based reachability analysis for nonlinear systems using componentwise contraction properties , 2017, Principles of Modeling.

[25]  Martin Berz,et al.  Rigorous Reachability Analysis and Domain Decomposition of Taylor Models , 2017, NSV@CAV.

[26]  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).

[27]  Mahesh Viswanathan,et al.  Parsimonious, Simulation Based Verification of Linear Systems , 2016, CAV.

[28]  Richard D. Braatz,et al.  Constrained zonotopes: A new tool for set-based estimation and fault detection , 2016, Autom..

[29]  Matthias Althoff,et al.  An Introduction to CORA 2015 , 2015, ARCH@CPSWeek.

[30]  John N. Maidens,et al.  Reachability Analysis of Nonlinear Systems Using Matrix Measures , 2015, IEEE Transactions on Automatic Control.

[31]  Mahesh Viswanathan,et al.  Verification of annotated models from executions , 2013, 2013 Proceedings of the International Conference on Embedded Software (EMSOFT).

[32]  Lorenzo Fagiano,et al.  Direct feedback control design for nonlinear systems , 2013, Autom..

[33]  Matthias Althoff,et al.  Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars , 2010 .

[34]  Antoine Girard,et al.  Reachability Analysis of Hybrid Systems Using Support Functions , 2009, CAV.

[35]  T. Söderström,et al.  Estimation of Continuous-time Stochastic System Parameters , 2008 .

[36]  Peter C. Young,et al.  Direct Identification of Continuous-time Models from Sampled Data: Issues, Basic Solutions and Relevance , 2008 .

[37]  Oded Maler,et al.  Systematic Simulation Using Sensitivity Analysis , 2007, HSCC.

[38]  Insup Lee,et al.  Robust Test Generation and Coverage for Hybrid Systems , 2007, HSCC.

[39]  Wolfgang Kuehn,et al.  Rigorously computed orbits of dynamical systems without the wrapping effect , 1998, Computing.

[40]  T. Alamo,et al.  Robust MPC of constrained discrete-time nonlinear systems based on approximated reachable sets , 2006, Autom..

[41]  David Q. Mayne,et al.  Reachability analysis of discrete-time systems with disturbances , 2006, IEEE Transactions on Automatic Control.

[42]  Antoine Girard,et al.  Reachability of Uncertain Linear Systems Using Zonotopes , 2005, HSCC.

[43]  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).

[44]  Hugues Garnier,et al.  Continuous-time model identification from sampled data: Implementation issues and performance evaluation , 2003 .

[45]  P. Varaiya,et al.  Ellipsoidal techniques for reachability analysis: internal approximation , 2000 .

[46]  Pravin Varaiya,et al.  Ellipsoidal Techniques for Reachability Analysis , 2000, HSCC.

[47]  Martin Berz,et al.  Computation and Application of Taylor Polynomials with Interval Remainder Bounds , 1998, Reliab. Comput..

[48]  Bart De Moor,et al.  N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems , 1994, Autom..

[49]  Antonio Vicino,et al.  Optimal estimation theory for dynamic systems with set membership uncertainty: An overview , 1991, Autom..