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This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…

This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…

We develop a novel multi-layer predictor-feedback to achieve exact compensation of state-dependent input delay of general nonlinear integro-differential equations. The system of interest is an unconventional mixed Partial Differential…

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 analytically intractable nature of the predictor, we…

This paper presents a control design for the one-phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's…

Spiking neural networks (SNN) are a promising research avenue for building accurate and efficient automatic speech recognition systems. Recent advances in audio-to-spike encoding and training algorithms enable SNN to be applied in practical…

Time delays due to signal latency, computational complexity, and sensor-denied environments, pose a critical challenge in both engineered and biological control systems. In this work, we investigate biologically inspired strategies to…

Unlike ODEs, whose models involve system matrices and whose controllers involve vector or matrix gains, PDE models involve functions in those roles functional coefficients, dependent on the spatial variables, and gain functions dependent on…

This paper proposes an adaptive neural network-based backstepping controller that uses rigid graph theory to address the distance-based formation control problem and target tracking for nonlinear multi-agent systems with bounded time-delay…

Traditional approaches to stabilizing hyperbolic PDEs, such as PDE backstepping, often encounter challenges when dealing with high-dimensional or complex nonlinear problems. Their solutions require high computational and analytical costs.…

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 approximates the gain kernel, which maps the plant coefficient into…

This paper presents a delay-adaptive boundary control scheme for a $2\times 2$ coupled linear hyperbolic PDE-ODE cascade system with an unknown and arbitrarily long input delay. To construct a nominal delay-compensated control law, assuming…

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 -- a function of one variable -- instead of the entire kernel…

The plasticity of the conduction delay between neurons plays a fundamental role in learning. However, the exact underlying mechanisms in the brain for this modulation is still an open problem. Understanding the precise adjustment of…

This study proposes a delay-compensated feedback controller based on proximal policy optimization (PPO) reinforcement learning to stabilize traffic flow in the congested regime by manipulating the time-gap of adaptive cruise…

We solve the global asymptotic stability problem of an unstable reaction-diffusion Partial Differential Equation (PDE) subject to input delay and state quantization developing a switched predictor-feedback law. To deal with the input delay,…

We develop a backstepping control design for a class of continuum systems of linear hyperbolic PDEs, described by a coupled system of an ensemble of rightward transporting PDEs and a (finite) system of $m$ leftward transporting PDEs. The…

A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential…

Spiking Neural Networks (SNNs) are a promising research direction for building power-efficient information processing systems, especially for temporal tasks such as speech recognition. In SNNs, delays refer to the time needed for one spike…