Data-Driven Control Methods for Linear Discrete-Time Singularly Perturbed Systems

Data-Driven Hybrid Framework for Dynamic System Control

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.

Memory DOF Control for Discrete-time LPV Systems: Two Iterative LMI-based Approaches

Adaptive Predefined-Time Stabilization: An Integrated Approach

This paper proposes an “adaptive + time-varying” control scheme for nonlinear systems with uncertainties and high system nonlinearities, realizing the convergence before the arbitrarily predefined time. By incorporating the low-power terms into predefined-time stabilization and integrating dynamic high gains with time-varying gains, an “adaptive + time-varying” continuous controller is constructed. This continuous controller enables the system states to converge to zero before the predefined time, while effectively avoiding the singularity caused by unbounded time-varying gains in traditional control schemes. In addition, note that the system admits generic nonlinearities characterized by low-order growth rate functions. By introducing a set of different power-type parameters in the design and stability analysis, predefined-time convergence under more general system nonlinearities is achieved. A simulation example is presented to demonstrate the effectiveness of the proposed control strategy. Note to Practitioners—This work is motivated by the time-critical control in practical nonlinear systems. In practical applications, completing the tasks within a predefined time is essential. However, prescribed-time control entails unbounded time-varying gains that tend toward infinity as time $t$ approaches the predefined time $T_{p}$ . In view of this, we propose an “adaptive + time-varying” control scheme that ensures the system converges to zero within an arbitrarily prescribed time while avoiding the singularity issue. By monitoring the convergence progress online and switching the time-varying gain to a constant, the proposed method provides a more reliable implementation. Furthermore, the scheme relaxes the assumptions on system nonlinearities, making it suitable for a wider range of engineering applications subject to uncertainties and nonlinearities.

Control Of Uncertain Nonlinear Systems Using Non-parametric Machine Learning

Accurately modeling nonlinear dynamical systems is challenging due to model inaccuracies and uncertainties, which can significantly degrade controller performance. Designing stabilizing controllers for nonlinear systems under such uncertainties remains a challenging problem. A wide range of stabilizing control algorithms have been proposed in the existing literature; however, their effectiveness relies on the accuracy of system dynamics. This manuscript addresses the issue of stabilizing controller design for nonlinear systems, particularly when the drift vector field is uncertain, by integrating non-parametric machine learning techniques to estimate the unknown component. In this work, a framework is proposed in which Gaussian process regression (GPR) is employed to estimate the unknown drift vector field and integrate it into the control synthesis. Moreover, an event-triggered condition is employed to collect data online as needed. The proposed approach enables the construction of control laws that practically stabilize the system, despite incomplete system knowledge. Rigorous theoretical guarantees for the proposed method are provided, and the effectiveness of the framework is demonstrated through numerical simulation studies.

A Backstepping-Free Framework for Adaptive Prescribed-Time Stabilization of Uncertain Nonlinear Systems

This article investigates the problem of global adaptive prescribed-time (PT) stabilization for a class of nonlinear systems subject to parametric uncertainties. Unlike prevalent adaptive control strategies that rely on recursive backstepping procedures, this work proposes a novel backstepping-free control framework. By leveraging the solution to a time-varying parametric Lyapunov equation (TV-PLE), we construct an adaptive time-varying gain feedback controller. A distinguishing feature of this approach is the utilization of a logarithmic Lyapunov function instead of the conventional quadratic form, which not only simplifies the stability analysis but also effectively characterizes the nonlinear coupling between the singular control gain and the adaptation dynamics. Rigorous theoretical analysis establishes that the proposed controller guarantees global PT stability, ensuring that all closed-loop signals—particularly the control input—remain bounded despite the singularity of the time-varying gain at the terminal time. Furthermore, the proposed method accommodates unknown linear growth conditions, offering a less restrictive design compared to existing linear time-varying feedback schemes. Comparative simulation results are presented to validate the effectiveness and superiority of the developed approach. Note to Practitioners—This paper is motivated by the practical challenges in controlling strict-feedback uncertain nonlinear systems, such as robotic manipulators and electromechanical devices, where precise task completion within a strict deadline is critical. Traditional adaptive control methods often rely on the “backstepping” technique. While theoretically sound, backstepping requires complex recursive calculations and repeated differentiations, leading to the “explosion of complexity” and making real-time implementation on embedded processors difficult. To address these issues, this paper presents a backstepping-free adaptive control framework. The primary contribution is a simplified controller design that guarantees the system stabilizes globally within a user-defined preset time, regardless of the initial conditions or unknown physical parameters.

Koopman-based model predictive control for nonlinear systems with bounded model uncertainty