2000 character limit reached
Data-Based Control of Continuous-Time Linear Systems with Performance Specifications
Published 1 Mar 2024 in eess.SY and cs.SY | (2403.00424v2)
Abstract: The design of direct data-based controllers has become a fundamental part of control theory research in the last few years. In this paper, we consider three classes of data-based state feedback control problems for linear systems. These control problems are such that, besides stabilization, some additional performance requirements must be satisfied. First, we formulate and solve a trajectory-reference control problem, on which desired closed-loop trajectories are known and a controller that allows the system to closely follow those trajectories is computed. Then, the solution of the LQR problem for continuous-time systems is presented. Finally, we consider the case in which the precise position of the desired poles of the closed-loop system is known, and introduce a data-based variant of a robust pole-placement procedure. The applicability of the proposed methods is tested using numerical simulations.
- Data-driven model predictive control with stability and robustness guarantees. IEEE Transactions on Automatic Control, 66(4):1702–1717, 2021.
- Data-driven analysis and control of continuous-time systems under aperiodic sampling. IFAC-PapersOnLine, 54(7):210–215, 2021.
- Gianluca Bianchin. Data-driven exact pole placement for linear systems. arXiv:2303.11469, 2023.
- Data-driven control via Petersen’s lemma. Automatica, 145:110537, 2022.
- Learning controllers for performance through LMI regions. IEEE Transactions on Automatic Control, 68(7):4351–4358, 2023.
- Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics, 1994.
- Adaptive linear quadratic control using policy iteration. In Proceedings of 1994 American Control Conference, volume 3, pages 3475–3479, 1994.
- Direct data-driven model-reference control with lyapunov stability guarantees. In 2021 60th IEEE Conference on Decision and Control (CDC), pages 1456–1461, 2021.
- Approaches to robust pole assignment. International Journal of Control, 49(1):97–117, 1989.
- Virtual reference feedback tuning: a direct method for the design of feedback controllers. Automatica, 38(8):1337–1346, 2002.
- Data-enabled predictive control: In the shallows of the DeePC. In 2019 18th European Control Conference (ECC), pages 307–312, 2019.
- Formulas for data-driven control: Stabilization, optimality, and robustness. IEEE Transactions on Automatic Control, 65(3):909–924, 2020.
- On the certainty-equivalence approach to direct data-driven LQR design. IEEE Transactions on Automatic Control, pages 1–8, 2023.
- When sampling works in data-driven control: Informativity for stabilization in continuous time. arXiv:2301.10873, 2023.
- Gene H. Golub and Charles F. van Loan. Matrix Computations. The Johns Hopkins University Press, London, UK, 3 edition, 1996.
- Efficient deep reinforcement learning with imitative expert priors for autonomous driving. IEEE Transactions on Neural Networks and Learning Systems, 34(10):7391–7403, 2023.
- Yu Jiang and Zhong-Ping Jiang. Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics. Automatica, 48:2699–2704, 2012.
- H∞subscript𝐻H_{\infty}italic_H start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT control of linear discrete-time systems: Off-policy reinforcement learning. Automatica, 78:144–152, 2017.
- Efficient off-policy Q-learning for data-based discrete-time LQR problems. IEEE Transactions on Automatic Control, 68(5):2922–2933, 2023.
- On a continuous-time version of Willems’ lemma. In 2022 IEEE 61st Conference on Decision and Control (CDC), pages 2759–2764, 2022.
- An efficient off-policy reinforcement learning algorithm for the continuous-time LQR problem. arXiv:2303.17819, 2023.
- Determination of weighting matrices of a linear quadratic regulator. Journal of Guidance, Control and Dynamics, 18(6):1462–1463, 1995.
- Behavioral systems theory in data-driven analysis, signal processing, and control. Annual Reviews in Control, 52:42–64, 2021.
- Data-driven gain scheduling control of linear parameter-varying systems using quadratic matrix inequalities. IEEE Control Systems Letters, 7:835–840, 2023.
- H∞subscript𝐻H_{\infty}italic_H start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT tracking control of completely unknown continuous-time systems via off-policy reinforcement learning. IEEE Transactions on Neural Networks and Learning Systems, 26(10):2550–2562, 2015.
- Event-triggered control from data. IEEE Transactions on Automatic Control, pages 1–16, 2023.
- Orthogonal polynomial bases for data-driven analysis and control of continuous-time systems. IEEE Transactions on Automatic Control, pages 1–12, 2023.
- Optimal pole placement with Moore’s algorithm. In 2011 Australian Control Conference, pages 124–129, 2011.
- Robust pole placement with Moore’s algorithm. IEEE Transactions on Automatic Control, 59(2):500–505, 2014.
- Data informativity: A new perspective on data-driven analysis and control. IEEE Transactions on Automatic Control, 65(11):4753–4768, 2020.
- Henk J. van Waarde and Mehran Mesbahi. Data-driven parameterizations of suboptimal LQR and H2subscript𝐻2H_{2}italic_H start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT controllers. IFAC-PapersOnLine, 53(2):4234–4239, 2020. 21st IFAC World Congress.
- A. Varga. Robust pole assignment via Sylvester equation based state feedback parametrization. In CACSD. Conference Proceedings. IEEE International Symposium on Computer-Aided Control System Design, pages 13–18, 2000.
- A note on persistency of excitation. Systems & Control Letters, 54(4):325–329, 2005.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.