Backstepping Control

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8 papers2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Rapid Fredholm stabilization of the Kuramoto--Sivashinsky equation with unrestricted, spatially-varying anti-diffusion
Oct 6, 2026Luke Bhan, Miroslav Krstic, Yuanyuan ShiBackstepping Control Dynamical Systems
University of California, San Diego, 3180 Voigt Drive, La Jolla, CA 92093, USA.
Admissibility-Preserving Control for Multi-Input Systems with Joint Capacity Constraints
Sep 30, 2026Saurabh Kumar, Lohitvel Gopikannan, Shashi Ranjan Kumar +1Backstepping Control Feedback Control
Intelligent Systems & Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India · Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering, University of Cincinnati, OH 45221, USA
Nonadaptive Learning in Robust Nonlinear Output Regulation
Aug 18, 2026Shimin Wang, Martin Guay, Richard D. BraatzBackstepping Control Robust Control
School of Data Science, Lingnan University, Hong Kong, and Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Department of Chemical Engineering, Queen’s University, Kingston, ON K7L 3N6, Canada · Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Admissibility-Preserving Control for Strict-Feedback Nonlinear Systems with Asymmetric Actuator Constraints
Aug 15, 2026Saurabh Kumar, Shashi Ranjan Kumar, Abhinav SinhaBackstepping Control Safety-Critical Control
Intelligent Systems and Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay, Maharashtra 400076 India · Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, OH 45221, USA
Global Exponential Stabilization of the Kinematic Bicycle Model of a Car in Polar Coordinates
Jul 29, 2026Velimir Todorovski, Kwang Hak Kim, Alessandro Astolfi +1Robotic Control Backstepping Control
Department of Mechanical and Aerospace Engineering, UC San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0411 · Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955, Saudi Arabia
QuadRocket: An Aerial Robotic Testbed for Adaptive Thrust-Vector Control of Rocket-Like Vehicles
Jul 2, 2026Pedro Santos, Joel Reis, Paulo Oliveira +1Backstepping Control Robot Trajectory Tracking
Instituto Superior T´ecnico, Universidade de Lisboa, Lisbon, Portugal · Faculty of Science and Technology, University of Macau, Taipa, Macao, China
Rapid Vibration Suppression and Trajectory Tracking of a Serial Manipulator with Multi-Flexible Links
May 17, 2026Chengyi Wang, Yilong Huang, Ji WangRobotic Control Backstepping Control
School of Aerospace Engineering, Xiamen University, Xiamen 361102, P. R. China
Robust Adaptive Backstepping Impedance Control of Robots in Unknown Environments
Apr 10, 2026Reza Nazmara, Alap Kshirsagar, Jan Peters +1Backstepping Control Impedance Control
Research Center for Systems and Technologies (SYSTEC), ARISE, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal. · Intelligent Autonomous Systems Lab, Department of Computer Science, TU Darmstadt, Germany.

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Rapid Fredholm stabilization of the Kuramoto--Sivashinsky equation with unrestricted, spatially-varying anti-diffusion

Luke Bhan, Miroslav Krstic, Yuanyuan Shi

University of California, San Diego, 3180 Voigt Drive, La Jolla, CA 92093, USA.

Backstepping Control Dynamical Systems Feedback Control

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We develop the first feedback design for rapid stabilization of the Kuramoto--Sivashinsky equation with a spatially varying anti-diffusion coefficient. For constant coefficients, the single-input Fredholm design of Coron and Lü (2015) excludes a discrete set of values at which repeated unstable eigenvalues cause a loss of controllability. We overcome this obstruction by introducing a second boundary input and assigning the two inputs distinct roles. The key idea, inspired by Heymann's Lemma, is to use the boundary value

u(0,t)

entirely for a pre-feedback that renders the modified plant controllable through the curvature input

u_{xx}(0,t)

. The latter input then stabilizes the plant through a Fredholm backstepping transformation. We show that two inputs suffice for controllability and are necessary when the plant has an unstable double eigenvalue. However, the Fredholm kernel still must be approximated for implementation. Hence, to enable kernel and gain approximation, we prove continuity of the coefficient-to-gain design map on compact admissible design classes. Unlike Volterra-based continuity proofs using successive approximations, our proof uses the modal representation to control the spectral data, the inverse coefficient system, and the tails of the kernel and gain series. This yields a single neural operator approximation of the gain to any prescribed

L^2

accuracy across the class. Finally, we establish rapid local stabilization of the nonlinear closed-loop system under both the exact gains and sufficiently accurate approximations. We conclude with numerical results that illustrate prescribed decay rates and the computational cost of the approximations. In particular, we train a Fourier neural operator that achieves typical relative gain errors of approximately

0.1\%

and stabilizes all held-out cases tested, including a plant with an unstable double eigenvalue.