Related papers: Gain-Only Neural Operators for PDE Backstepping

We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting the structure of a suitably reduced optimality system, we…

Data-enabled predictive control (DeePC) leverages system measurements in characterizing system dynamics for optimal control. The performance of DeePC relies on optimizing its hyperparameters, especially in noisy systems where the optimal…

We propose a simple, practical and intuitive approach to improve the performance of a conventional controller in uncertain environments using deep reinforcement learning while maintaining safe operation. Our approach is motivated by the…

Performance of model-based feedforward controllers is typically limited by the accuracy of the inverse system dynamics model. Physics-guided neural networks (PGNN), where a known physical model cooperates in parallel with a neural network,…

Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in…

Approximate model-predictive control (AMPC) aims to imitate an MPC's behavior with a neural network, removing the need to solve an expensive optimization problem at runtime. However, during deployment, the parameters of the underlying MPC…

The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…

Spiking neural networks (SNNs) transmit information through discrete spikes, which performs well in processing spatial-temporal information. Due to the non-differentiable characteristic, there still exist difficulties in designing…

Reinforcement learning has been successfully applied to the problem of tuning PID controllers in several applications. The existing methods often utilize function approximation, such as neural networks, to update the controller parameters…

Gaussian Process (GP) Variational Autoencoders (VAEs) extend standard VAEs by replacing the fully factorised Gaussian prior with a GP prior, thereby capturing richer correlations among latent variables. However, performing exact GP…

Inverse problems challenge existing neural operator architectures because ill-posed inverse maps violate continuity, uniqueness, and stability assumptions. We introduce B2B${}^{-1}$, an inverse basis-to-basis neural operator framework that…

Incorporating stochasticity into the training process of deep convolutional networks is a widely used technique to reduce overfitting and improve regularization. Existing techniques often require modifying the architecture of the network by…

This paper investigates reinforcement learning with constraints, which are indispensable in safety-critical environments. To drive the constraint violation monotonically decrease, we take the constraints as Lyapunov functions and impose new…

We employ the recent performance-barrier event-triggered control (P-ETC) for achieving global exponential convergence of a class of reaction-diffusion PDEs via PDE backstepping control. Rather than insisting on a strictly monotonic decrease…

We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forcing or source terms, which commonly arise as pathwise…

As deep neural networks are increasingly deployed in dynamic, real-world environments, relying on a single static model is often insufficient. Changes in input data distributions caused by sensor drift or lighting variations necessitate…

Neural networks can be used to learn the solution of partial differential equations (PDEs) on arbitrary domains without requiring a computational mesh. Common approaches integrate differential operators in training neural networks using a…

Each training step for a variational autoencoder (VAE) requires us to sample from the approximate posterior, so we usually choose simple (e.g. factorised) approximate posteriors in which sampling is an efficient computation that fully…

The representation of the approximate posterior is a critical aspect of effective variational autoencoders (VAEs). Poor choices for the approximate posterior have a detrimental impact on the generative performance of VAEs due to the…

We consider output-feedback stabilization problems for a class of two-component linear parabolic systems with boundary actuation and measurement. The state-feedback control laws are obtained using backstepping method and require measurement…