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We propose an alternative implementation of preconditioning techniques for the solution of non-linear problems. Within the framework of Newton-Krylov methods, preconditioning techniques are needed to improve the performance of the solvers.…
We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). These systems are typically…
A typical bottleneck of model predictive control algorithms is the computational burden in order to compute the receding horizon feedback law which is predominantly determined by the length of the prediction horizon. Based on a relaxed…
Hybrid model predictive control with both continuous and discrete variables is widely applicable to robotic control tasks, especially those involving contacts with the environment. Due to combinatorial complexity, the solving speed of…
An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring…
This paper focuses on unconditionally optimal error analysis of an uncoupled and linearized Crank--Nicolson Galerkin finite element method for the time-dependent nonlinear thermistor equations in $d$-dimensional space, $d=2,3$. We split the…
We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…
We use one-step conditional risk mappings to formulate a risk averse version of a total cost problem on a controlled Markov process in discrete time infinite horizon. The nonnegative one step costs are assumed to be lower semi-continuous…
We consider Tikhonov regularization of control-constrained optimal control problems. We present new a-priori estimates for the regularization error assuming measure and source-measure conditions. In the special case of bang-bang solutions,…
We examine the problem of two-point boundary optimal control of nonlinear systems over finite-horizon time periods with unknown model dynamics by employing reinforcement learning. We use techniques from singular perturbation theory to…
Nonlinear receding horizon model predictive control is a powerful approach to controlling nonlinear dynamical systems. However, typical approaches that use the Jacobian, adjoint, and forward-backward passes may lose fidelity and efficacy…
In this work, we develop a novel data-driven model predictive controller using advanced techniques in the field of machine learning. The objective is to regulate control signals to adjust the desired internal room setpoint temperature,…
This article presents a method for solving large-scale linear inverse problems regular- ized with a nonlinear, edge-preserving penalty term such as the total variation or Perona-Malik. In the proposed scheme, the nonlinearity is handled…
We consider the solution of linear saddle-point problems, using the alternating direction method-of-multipliers (ADMM) as a preconditioner for the generalized minimum residual method (GMRES). We show, using theoretical bounds and empirical…
We present an approach for accelerating nonlinear model predictive control. If the current optimal input signal is saturated, also the optimal signals in subsequent time steps often are. We propose to use the open-loop optimal input signals…
Most of the real-time implementations of the stabilizing optimal control actions suffer from the necessity to provide high computational effort. This paper presents a cutting-edge approach for real-time evaluation of linear-quadratic model…
Model Predictive Control (MPC) is a well-established approach to solve infinite horizon optimal control problems. Since optimization over an infinite time horizon is generally infeasible, MPC determines a suboptimal feedback control by…
This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use…
The expansion in automation of increasingly fast applications and low-power edge devices poses a particular challenge for optimization based control algorithms, like model predictive control. Our proposed machine-learning supported approach…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…