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Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, in practice, organizations are not able to be fully flexible, as decisions…
We propose and analyze a reliable and efficient a posteriori error estimator for the pointwise tracking optimal control problem of the Stokes equations. This linear-quadratic optimal control problem entails the minimization of a cost…
The periodic signal tracking and the unknown disturbance rejection under limited communication resources are main important issues in many physical systems and practical applications. The control of such systems has some challenges such as…
Based on the method of FGD, we apply the method of adaptive gradient descent which uses different step length at different epoch. Adaptive gradient descent performs much better than FGD in the tests and keeps the guarantee of convergence…
We propose an experimental study of adaptive time-stepping methods for efficient modeling of the aggregation-fragmentation kinetics. Precise modeling of this phenomena usually requires utilization of the large systems of nonlinear ordinary…
The convergence behavior of Stochastic Gradient Descent (SGD) crucially depends on the stepsize configuration. When using a constant stepsize, the SGD iterates form a Markov chain, enjoying fast convergence during the initial transient…
We address the weak numerical solution of stochastic differential equations driven by independent Brownian motions (SDEs for short). This paper develops a new methodology to design adaptive strategies for determining automatically the…
Convergence of classical parallel iterations is detected by performing a reduction operation at each iteration in order to compute a residual error relative to a potential solution vector. To efficiently run asynchronous iterations,…
Differential Dynamic Programming (DDP) is one of the indirect methods for solving an optimal control problem. Several extensions to DDP have been proposed to add stagewise state and control constraints, which can mainly be classified as…
Iterative Learning Control (ILC) schemes can guarantee properties such as asymptotic stability and monotonic error convergence, but do not, in general, ensure adherence to output constraints. The topic of this paper is the design of a…
In this paper, we first propose a method that can efficiently compute the maximal robust controlled invariant set for discrete-time linear systems with pure delay in input. The key to this method is to construct an auxiliary linear system…
The alternating direction method of multipliers (ADMM) is a flexible method to solve a large class of convex minimization problems. Particular features are its unconditional convergence with respect to the involved step size and its direct…
Online feedback-based optimization has become a promising framework for real-time optimization and control of complex engineering systems. This tutorial paper surveys the recent advances in the field as well as provides novel convergence…
The challenge of constructing feedback control laws for risk-averse optimal control of partial differential equations (PDEs) with random coefficients is addressed. The control objective composes a tracking-type cost with the nonlinear…
Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the…
We present a numerical method for convergence acceleration for multifidelity models of parameterized ordinary differential equations. The hierarchy of models is defined as trajectories computed using different timesteps in a time…
In this work we present two new families of multirate time step adaptivity controllers, that are designed to work with embedded multirate infinitesimal (MRI) time integration methods for adapting time steps when solving problems with…
Time integration of ODEs or time-dependent PDEs with required resolution of the fastest time scales of the system, can be very costly if the system exhibits multiple time scales of different magnitudes. If the different time scales are…
We introduce a novel data-driven method to mitigate the risk of cascading failures in delayed discrete-time Linear Time-Invariant (LTI) systems. Our approach involves formulating a distributionally robust finite-horizon optimal control…
This paper addresses the numerical optimization of proportional-integral-derivative (PID) controllers for linear time-invariant systems with delays, where the derivative action is implemented using a low-pass filter. While performance…