2000 character limit reached
Adaptive Robust Control Contraction Metrics: Transient Bounds in Adaptive Control with Unmatched Uncertainties (2310.13655v1)
Published 20 Oct 2023 in eess.SY, cs.SY, and math.OC
Abstract: This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The approach utilizes contraction theory and addresses fundamental limitations of existing approaches by allowing the contraction metric to depend on the unknown model parameters. This allows the controller to incorporate new model estimates generated online without sacrificing its strong convergence and bounded transients guarantees. The approach is specifically designed for trajectory tracking so the approach is more broadly applicable to adaptive model predictive control as well. Simulation results on a nonlinear system with unmatched uncertainties demonstrates the approach.
- D. Angeli, “A lyapunov approach to incremental stability properties,” IEEE Transactions on Automatic Control, vol. 47, no. 3, pp. 410–421, 2002.
- M. Zamani, N. van de Wouw, and R. Majumdar, “Backstepping controller synthesis and characterizations of incremental stability,” Systems & Control Letters, vol. 62, no. 10, pp. 949–962, 2013.
- W. Lohmiller and J.-J. E. Slotine, “On contraction analysis for non-linear systems,” Automatica, vol. 34, no. 6, pp. 683–696, 1998.
- I. R. Manchester and J.-J. E. Slotine, “Control contraction metrics: Convex and intrinsic criteria for nonlinear feedback design,” IEEE Transactions on Automatic Control, vol. 62, no. 6, pp. 3046–3053, 2017.
- S. Singh, A. Majumdar, J.-J. Slotine, and M. Pavone, “Robust online motion planning via contraction theory and convex optimization,” in 2017 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2017, pp. 5883–5890.
- I. R. Manchester and J.-J. E. Slotine, “Robust control contraction metrics: A convex approach to nonlinear state-feedback H∞superscript𝐻{H}^{\infty}italic_H start_POSTSUPERSCRIPT ∞ end_POSTSUPERSCRIPT control,” IEEE Control Systems Letters, vol. 2, no. 3, pp. 333–338, 2018.
- P. Zhao, A. Lakshmanan, K. Ackerman, A. Gahlawat, M. Pavone, and N. Hovakimyan, “Tube-certified trajectory tracking for nonlinear systems with robust control contraction metrics,” IEEE Robotics and Automation Letters, vol. 7, no. 2, pp. 5528–5535, 2022.
- B. T. Lopez and J.-J. E. Slotine, “Adaptive nonlinear control with contraction metrics,” IEEE Control Systems Letters, vol. 5, no. 1, pp. 205–210, 2020.
- ——, “Universal adaptive control of nonlinear systems,” IEEE Control Systems Letters, vol. 6, pp. 1826–1830, 2021.
- H. K. Khalil, “Adaptive output feedback control of nonlinear systems represented by input-output models,” IEEE transactions on Automatic Control, vol. 41, no. 2, pp. 177–188, 1996.
- J. Köhler, P. Kötting, R. Soloperto, F. Allgöwer, and M. A. Müller, “A robust adaptive model predictive control framework for nonlinear uncertain systems,” International Journal of Robust and Nonlinear Control, vol. 31, no. 18, pp. 8725–8749, 2021.
- G. Chowdhary, T. Yucelen, M. Mühlegg, and E. N. Johnson, “Concurrent learning adaptive control of linear systems with exponentially convergent bounds,” International Journal of Adaptive Control and Signal Processing, vol. 27, no. 4, pp. 280–301, 2013.
- R. L. Kosut, M. K. Lau, and S. P. Boyd, “Set-membership identification of systems with parametric and nonparametric uncertainty,” IEEE Transactions on Automatic Control, vol. 37, no. 7, pp. 929–941, 1992.
- E. D. Sontag and Y. Wang, “On characterizations of the input-to-state stability property,” Systems & Control Letters, vol. 24, no. 5, pp. 351–359, 1995.
- B. S. Rüffer, N. Van De Wouw, and M. Mueller, “Convergent systems vs. incremental stability,” Systems & Control Letters, vol. 62, no. 3, pp. 277–285, 2013.
- M. Zamani and P. Tabuada, “Backstepping design for incremental stability,” IEEE Transactions on Automatic Control, vol. 56, no. 9, pp. 2184–2189, 2011.
- K. Leung and I. R. Manchester, “Nonlinear stabilization via control contraction metrics: A pseudospectral approach for computing geodesics,” in 2017 American Control Conference (ACC). IEEE, 2017, pp. 1284–1289.
- J. Lofberg, “Yalmip: A toolbox for modeling and optimization in matlab,” in 2004 IEEE international conference on robotics and automation (IEEE Cat. No. 04CH37508). IEEE, 2004, pp. 284–289.