Related papers: Data-driven balanced truncation for linear systems…
In this contribution, we propose a data-driven procedure to fit quadratic-bilinear surrogate models from data. Although the dynamics characterizing the original model are strongly nonlinear, we rely on lifting techniques to embed the…
The purpose of this paper is to develop a model reduction theory for linear quantum stochastic systems that are commonly encountered in quantum optics and related fields, modeling devices such as optical cavities and optical parametric…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…
We investigate model order reduction (MOR) for linear dynamical systems, where a quadratic output is defined as a quantity of interest. The system can be transformed into a linear dynamical system with many linear outputs. MOR is feasible…
We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that…
Strongly driven nonlinear systems are frequently encountered in physics, yet their accurate control is generally challenging due to the intricate dynamics. In this work, we present a non-perturbative, semi-analytical framework for tailoring…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting…
Predictive design and optimization methods for controlled quantum systems depend on the accuracy of the system model. Any distortion of the input fields in an experimental platform alters the model accuracy and eventually disturbs the…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…
When solving partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce…
This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear…
We present a midpoint policy iteration algorithm to solve linear quadratic optimal control problems in both model-based and model-free settings. The algorithm is a variation of Newton's method, and we show that in the model-based setting it…
In this paper we consider a recently developed distributed optimization algorithm based on gradient tracking. We propose a system theory framework to analyze its structural properties on a preliminary, quadratic optimization set-up.…
Recent literature has shown how linear time-invariant (LTI) systems can be represented by trajectories features, that is relying on a single input-output (IO) data dictionary to span all possible system trajectories, as long as the input is…
We present a data-driven nonintrusive model order reduction method for dynamical systems with moving boundaries. The proposed method draws on the proper orthogonal decomposition, Gaussian process regression, and moving least squares…
Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper…
Fluctuation dissipation theorems connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many…
We develop a pivot-shifted Carleman linearization framework for quantum algorithms solving quadratic nonlinear ordinary differential equations. By shifting the dynamics by a pivot state prior to Carleman lifting, and combining this with a…