Related papers: Error bounds for model reduction of feedback-contr…
Depending on the frequency range of interest, finite element-based modeling of acoustic problems leads to dynamical systems with very high dimensional state spaces. As these models can mostly be described with second order linear dynamical…
Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…
The problem of suboptimality under bounded disturbances for the adaptive systems based on speed-graadient approach is discussed. A formulation of the estimated optimality of nonlinear nonlinearly parametrized adaptive control systems is…
We study optimal bilinear control problems for stochastic nonlinear Schr\"odinger equations in both the mass subcritical and critical case. For general initial data of the minimal L2 regularity, we prove the existence and first order…
Unsteady aerodynamic models are necessary to accurately simulate forces and develop feedback controllers for wings in agile motion; however, these models are often high dimensional or incompatible with modern control techniques. Recently,…
We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions. In contrast to classical control, the a priori determination of an…
We develop resonance-based low-regularity numerical integrators for stochastic Schr"odinger equations with additive $Q$-Wiener noise, covering both the linear equation with rough potential and the cubic nonlinear case. For the linear…
For linear time-invariant (LTI) systems, the design of an optimal controller is a commonly encountered problem in many applications. Among all the optimization approaches available, the linear quadratic regulator (LQR) methodology certainly…
We consider distributionally robust optimal control of stochastic linear systems under signal temporal logic (STL) chance constraints when the disturbance distribution is unknown. By assuming that the underlying predicate functions are…
Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality…
Model Predictive Control is an extremely effective control method for systems with input and state constraints. Model Predictive Control performance heavily depends on the accuracy of the open-loop prediction. For systems with uncertainty…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…
We present a methodology for bounding the error term of an asymptotic solution to a singularly perturbed optimal control (SPOC) problem whose exact solution is known to be computationally intractable. In previous works, reduced or…
We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…
In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…
The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a…
This paper studies the linear quadratic regulation (LQR) problem of unknown discrete-time systems via dynamic output feedback learning control. In contrast to the state feedback, the optimality of the dynamic output feedback control for…
In this paper, we establish new strategies to reduce the dimension of large-scale controlled stochastic differential equations with non-zero initial states. The first approach transforms the original setting into a stochastic system with…