Nonlinear Systems
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Related Articles from SNS
Towards Guaranteed Optimal PID Tuning for Uncertain Nonlinear Systems
arXiv:2606.04787v1 Announce Type: new Abstract: Despite the widespread use of PID controllers in engineering practice, designing optimal PID parameters has long been regarded as a challenging problem in both theory and practice, particularly when faced with uncertain nonlinear dynamical systems. Based on the authors' PID control theory established recently for MIMO nonlinear uncertain systems (Zhao and Guo, 2022), which provides a concrete PID parameter set for global stability of PID...
Learning Local Optimal Controller for a Class of Nonlinear Systems via Impulse-Supervised Exploration
arXiv:2606.03107v1 Announce Type: new Abstract: This paper develops an impulse-supervised confined exploration framework for learning local optimal controller for a class of nonlinear systems. The proposed approach combines continuous-time approximate dynamic programming (ADP) with an impulsive supervisory layer, where impulsive braking confines the state within a prescribed region in which a local linear approximation of the nonlinear system is valid.
MPC for nonlinear systems: a comparative review of discretization methods
Electrical Engineering and Systems Science > Systems and Control [Submitted on 4 Jun 2026] Title:MPC for nonlinear systems: a comparative review of discretization methods View PDF HTML (experimental)Abstract:This work provides a comparative review of three different numerical methods generally used to discretize continuous-time non-linear equations appearing in model predictive control problems: direct multiple shooting, direct collocation and successive linearizations. An overview of the...
Polynomial Constraints for Robustness Analysis of Nonlinear Systems
arXiv:2604.01198v2 Announce Type: replace Abstract: This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming, to a broader class of non-polynomial systems. A numerical method for constructing these constraints is proposed.
LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification
arXiv:2412.12036v2 Announce Type: replace Abstract: System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of data-driven discovery in nonlinear dynamical systems, these methods have garnered significant attention. Among them, Sparse Identification of Nonlinear Dynamics (SINDy) has emerged as a transformative approach,...
Risk-Aware Control of Systems with Quasi-Cone-Bounded Nonlinearities
arXiv:2606.08208v1 Announce Type: new Abstract: We develop a tractable, rigorous approach to risk-aware control for a class of nonlinear systems. While many classical control methods reduce uncertainty to a simple average or a worst-case outcome, risk-aware control aims to equip systems with a refined awareness of uncertainty. Efficient methods for risk-aware control of linear systems are available, but there is a paucity of tools for tractable, risk-aware control of nonlinear systems.
A Koopman Set-Membership Approach for Nonlinear Data-Driven Control with Stability Guarantees
arXiv:2606.01378v1 Announce Type: new Abstract: This paper proposes a data-driven controller design method for unknown nonlinear systems based on a Koopman bilinear realization. Using Koopman operator theory, the nonlinear system can be represented as a bilinear discrete-time system with a residual error term. The residual error is proportionally bounded by the norm of the lifted state and input, while the system matrices of the bilinear model are unknown.
Layer-Resolved Nonlinear Optics in Finite-Thickness Two-Dimensional Systems
arXiv:2606.02354v1 Announce Type: cross Abstract: Nonlinear optical (NLO) responses in two-dimensional quantum-confined systems are typically described within bulk-based frameworks as macroscopic spatial averages. In finite-thickness van der Waals multilayers directly relevant to nanoscale devices, this picture substantially breaks down. Here, we establish a general symmetry-based framework for classifying second-order NLO responses in multilayers.
Data-Driven Min-Max MPC with Integral Quadratic Constraints
Announce Type: new Abstract: Data-driven control of nonlinear systems with rigorous guarantees is a challenging control problem. Integral quadratic constraints (IQCs) provide a powerful framework for modeling nonlinearities. This paper presents a data-driven min-max model predictive control (MPC) synthesis method for unknown systems subject to (nonlinear) uncertainties using the IQC framework.
FLASH: Ultrafast beam quality characterization via spatial-to-temporal mapping
Announce Type: new Abstract: Accurate and real-time monitoring of spatial beam quality has emerged as the absolute prerequisite for intelligent optical field regulation and advanced laser applications. However, modern high-power and multimode optical systems exhibit highly complex, nonlinear, and transient behaviors. In these systems, the spatial beam profile undergoes dramatic reorganizations within extremely short timeframes.