18 citations · 35 across the 17 of their papers we have counts for
20 papers
Rapid Fredholm stabilization of the Kuramoto--Sivashinsky equation with unrestricted, spatially-varying anti-diffusion
Luke Bhan, Miroslav Krstic, Yuanyuan Shi
We develop the first feedback design for rapid stabilization of the Kuramoto--Sivashinsky equation with a spatially varying anti-diffusion coefficient. For constant coefficients, t…
Fredholm Backstepping with Heymann Pre-Feedback for Linearized Navier--Stokes 2D Channel
Miroslav Krstic
We stabilize the linearized 2-D Poiseuille channel flow at arbitrary Reynolds numbers, and assign the decay of every wavenumber to any user-prescribed rate. The actuation is as in…
The Heavy Chain PDE: Rapid Stabilization by Backstepping
Miroslav Krstic
We consider boundary stabilization of a heavy chain hanging from a moving trolley with no tip load. Because the tension vanishes at the free end, the wave speed vanishes there; in…
Approximate Feedback Linearization for a Nonlinear Hyperbolic PDE Class -- Part I: Volterra Truncation
Miroslav Krstic
Backstepping for nonlinear PDEs yields exact feedback linearizing laws in the form of infinite Volterra series -- elegant in theory, but with challenges for implementation. This pa…
Stabilization of nonlinear systems with unknown delays via delay-adaptive neural operator approximate predictors
Luke Bhan, Miroslav Krstic, Yuanyuan Shi
This work establishes the first rigorous stability guarantees for approximate predictors in delay-adaptive control of nonlinear systems, addressing a key challenge in practical imp…
Delay compensation of multi-input distinct delay nonlinear systems via neural operators
Filip Bajraktari, Luke Bhan, Miroslav Krstic +1
In this work, we present the first stability results for approximate predictors in multi-input non-linear systems with distinct actuation delays. We show that if the predictor appr…
Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors
Luke Bhan, Miroslav Krstic, Yuanyuan Shi
In this work, we propose a rigorous method for implementing predictor feedback controllers in nonlinear systems with unknown and arbitrarily long actuator delays. To address the an…
Neural Operator Feedback for a First-Order PIDE with Spatially-Varying State Delay
Jie Qi, Jiaqi Hu, Jing Zhang +1
A transport PDE with a spatial integral and recirculation with constant delay has been a benchmark for neural operator approximations of PDE backstepping controllers. Introducing a…
Neural Operators for Predictor Feedback Control of Nonlinear Delay Systems
Luke Bhan, Peijia Qin, Miroslav Krstic +1
Predictor feedback designs are critical for delay-compensating controllers in nonlinear systems. However, these designs are limited in practical applications as predictors cannot b…
Backstepping for Partial Differential Equations:A Survey
Rafael Vazquez, Jean Auriol, Federico Bribiesca-Argomedo +1
Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as systems that are by nature finite-dimensional and modeled by ordinary differential equations…
Adaptive control of reaction-diffusion PDEs via neural operator-approximated gain kernels
Luke Bhan, Yuanyuan Shi, Miroslav Krstic
Neural operator approximations of the gain kernels in PDE backstepping has emerged as a viable method for implementing controllers in real time. With such an approach, one approxim…
PDE Control Gym: A Benchmark for Data-Driven Boundary Control of Partial Differential Equations
Luke Bhan, Yuexin Bian, Miroslav Krstic +1
Over the last decade, data-driven methods have surged in popularity, emerging as valuable tools for control theory. As such, neural network approximations of control feedback laws,…
Towards a MATLAB Toolbox to compute backstepping kernels using the power series method
Xin Lin, Rafael Vazquez, Miroslav Krstic
In this paper, we extend our previous work on the power series method for computing backstepping kernels. Our first contribution is the development of initial steps towards a MATLA…
Gain-Only Neural Operators for PDE Backstepping
Rafael Vazquez, Miroslav Krstic
In this work we advance the recently-introduced deep learning-powered approach to PDE backstepping control by proposing a method that approximates only the control gain function --…
Adaptive Neural-Operator Backstepping Control of a Benchmark Hyperbolic PDE
Maxence Lamarque, Luke Bhan, Yuanyuan Shi +1
To stabilize PDEs, feedback controllers require gain kernel functions, which are themselves governed by PDEs. Furthermore, these gain-kernel PDEs depend on the PDE plants' function…
Gain Scheduling with a Neural Operator for a Transport PDE with Nonlinear Recirculation
Maxence Lamarque, Luke Bhan, Rafael Vazquez +1
To stabilize PDE models, control laws require space-dependent functional gains mapped by nonlinear operators from the PDE functional coefficients. When a PDE is nonlinear and its "…
Moving-Horizon Estimators for Hyperbolic and Parabolic PDEs in 1-D
Luke Bhan, Yuanyuan Shi, Iasson Karafyllis +2
Observers for PDEs are themselves PDEs. Therefore, producing real time estimates with such observers is computationally burdensome. For both finite-dimensional and ODE systems, mov…
Exponential and Prescribed-Time Extremum Seeking with Unbiased Convergence
Cemal Tugrul Yilmaz, Mamadou Diagne, Miroslav Krstic
We present multivariable extremum seeking (ES) designs that achieve unbiased convergence to the optimum. Two designs are introduced: one with exponential unbiased convergence (unbi…
Block Backstepping for Isotachic Hyperbolic PDEs and Multilayer Timoshenko Beams
Guangwei Chen, Rafael Vazquez, Junfei Qiao +1
In this paper, we investigate the rapid stabilization of N-layer Timoshenko composite beams with anti-damping and anti-stiffness at the uncontrolled boundaries. The problem of stab…
Semi-Global Practical Extremum Seeking with Practical Safety
Alan Williams, Miroslav Krstic, Alexander Scheinker
We introduce a type of safe extremum seeking (ES) controller, which minimizes an unknown objective function while also maintaining practical positivity of an unknown barrier functi…