This paper provides a novel framework for the stability analysis of switched linear systems from noisy state measurements, using the indirect approach and quadratic Lyapunov analysis and combines generalization bounds from machine learning and system identification with sensitivity analysis from quadratic Lyapunov analysis.
Abstract
A central methodological question in data-driven control is whether to adopt a direct or indirect approach. Direct methods infer a controller or certificate directly from data, while indirect methods first identify a system model and then apply model-based control techniques. Recent developments of the direct method have led to finite-sample guarantees for the data-driven stability analysis of switched linear systems under various settings. However, for the indirect method, such guarantees remain largely elusive. In this paper, we provide a novel framework for the stability analysis of switched linear systems from noisy state measurements, using the indirect approach and quadratic Lyapunov analysis. Our framework comes with finite-sample guarantees on the convergence rate of the system. For that, we combine generalization bounds from machine learning and system identification with sensitivity analysis from quadratic Lyapunov analysis. To enable comparison, we also extend existing direct data-driven methods to handle measurement noise beyond the bounded noise case currently available in the literature. Finally, we compare the two approaches through numerical experiments, revealing that under moderate-to-high noise levels the indirect approach yields tighter probabilistic guarantees as well as greater robustness to noise and outliers than the direct approach
This paper presents a synergistic control strategy for discrete-time singularly perturbed systems, where data-driven learning is seamlessly combined with LMI-based synthesis, thereby offering an effective new approach for controlling discrete-time singularly perturbed systems in complex engineering environments.
Peng Wang, Wenkai Zhou, Yangyang Wang et al.· Advances in Complex Systems· 0 citations
Nonlinear electrical and electromechanical systems pose significant challenges for observer-based control design. Conventional observer approaches require accurate mathematical models, which often fail under physical irregularities such as sensor noise, measurement delays, and parameter variations. These changes decrease estimation accuracy and degrade control action. This paper proposes a Hybrid ARX– Observer framework to overcome these limitations. It combines the stability of a traditional model-based observer with the flexibility of a data-driven ARX estimator. To guarantee input-to-state stability (ISS), observer gains are computed using a matrix-multiplier technique based on linear matrix inequalities (LMI). The ARX component employs Recursive Least Squares (RLS) adaptation to attenuate measurement noise and capture residual nonlinearities. Both estimates are then fused together using a fusion gain α. This framework is tested on a robotic arm and the results show that the hybrid framework improved the robustness and reduced estimation error up to 4% compared to the conventional observer based estimation, while remaining computationally light compared to fully data-driven alternatives.
Tanmay Wankhade, Saish Pakhare, Aakanksha Mane et al.· International Conference on...· 0 citations
Inspired by recent developments in dissipativity-based control, this work proposes new sufficient conditions for asymptotic stabilization of nonlinear systems using state feedback. We prove that this new framework is well suited for data-driven control of polynomial systems using noisy measurements, a topic that has lately attracted considerable attention. Two iterative procedures for data-based state feedback design are provided using the proposed framework, that use sum-of-squares (SOS) optimization. Typical limitations of conventional SOS methods based on alternating (D-K) procedures for controller design, such as the need to provide an initialization for a control-Lyapunov function (CLF), are overcome in this paper. Numerical examples demonstrate the applicability and the advantages of the new strategies.
D. D. S. Madeira, J. G. N. Silva, W. Correia et al.· 0 citations
In this paper, we address the problem of computing passivity indices-quantitative measures of a system's passivity-due to their significance in controller design. In practical scenarios, the explicit input-output relationship of a system is often unavailable, and only input-output data from simulations or experiments can be accessed. We focus on determining the passivity indices of a discrete linear time-invariant system using optimal input-output samples tailored to the specific property being assessed. Here, passivity indices are formulated as an objective function of an optimization problem. To compute these indices, we introduce prescribed-time gradient flows, which has the property of guaranteed convergence, within a prior chosen time. Notably, the proposed method is data-driven and does not require knowledge of the system's mathematical model, as it relies solely on gradients computed from data. Furthermore, we leverage the feedback interconnection properties of passive systems to ensure both asymptotic and finite-time stability of the discrete-time system, using only the computed passivity indices. Specifically, stabilization is achieved by employing input feedforward passive and output feedback passive systems as controllers, again without requiring the explicit model of the system. Simulation results for the coupled tank system shows the effectiveness of the proposed approach.
Sunidhi Pandey, Shyam Kamal, Devender Singh et al.· International Workshop on Va...· 0 citations
This paper addresses the robust control of uncertain discrete-time switched affine systems subject to a single unitary input delay. The unique feature of this class of systems lies in the fact that the control input is the switching signal, which belongs to a finite set of values. Consequently, the closed-loop trajectories do not converge to an equilibrium point but rather to a limit cycle. To mitigate the impact of the input delay, we propose a min-switching predictive control approach, which is based on the known nominal dynamical characteristics of each mode. The objective of this approach is to ensure the robust stabilization of the uncertain system using this nominal predictor, employing a Lyapunov argument. Our main result provides tractable robust stabilization conditions that guarantee the convergence to a robust limit cycle under system uncertainties and delayed switching. Additionally, an optimization procedure has been incorporated to minimize the size of the attractor, which represents the region where the trajectories asymptotically converge. A numerical example validates the effectiveness of the proposed approach.
Gerson Portilla, Carolina Albea, Alexandre Seuret· International Workshop on Va...· 0 citations
This paper addresses the challenge of observer-based preview control for linear parameter-varying (LPV) networked control systems subject to simultaneous dual-channel packet dropouts in both the measurement output and control input channels. The primary objective is to achieve high-precision reference tracking and robust stability despite random data losses. To this end, two mutually independent Bernoulli-distributed sequences are employed to characterize the dropout phenomena, and an augmented error model is constructed by embedding preview information of the reference signal into the system dynamics. A novel observer-based preview control scheme is then developed. Methodologically, by combining the Lyapunov function approach with a one-step design procedure, and leveraging linear fractional representation (LFR) techniques augmented with slack variables, less conservative sufficient conditions for stochastic stability are derived in terms of linear matrix inequalities (LMIs). Quantitatively, numerical simulations demonstrate that, under specific dropout rates, the proposed method achieves approximately a 61.30% reduction in performance metrics, demonstrating that the preview action effectively minimizes steady-state errors and enhances overall system performance.
Li Li, Xin Zhou, Chen Jia· Journal of Vibration and Con...· 0 citations
