We propose an approach for the L-infinity model reduction of descriptor systems based on smooth optimization techniques. A direct application of smooth optimization techniques for L-infinity model reduction does not seem suitable, as they converge linearly at best for this highly nonsmooth problem, and require the computation of the costly L-infinity norm objective too many times. Instead, we...
In this talk, we will discuss the perturbation of a Hermitian matrix pair (H, M), where H is non-singular and M is a positive definite matrix. The corresponding perturbed pair (\widetilde{H}, \widetilde{M}) = (H + \delta H, M + \delta M) is assumed to satisfy the conditions that \widetilde{H} remains non-singular and \widetilde{M} remains positive definite. We derive an upper bound for the...
Over the past years, there has been extensive research in the control systems community on data-based approaches for the analysis and synthesis of dynamical systems. A distinguishing feature of this “new wave” of data-driven methods is the emphasis on solutions and techniques with provable guarantees regarding the (robust) stability and performance of the considered (closed-loop) systems. In...
Partial differential equations (PDEs) are extensively utilized for modeling various physical phenomena. These equations often depend on certain parameters, necessitating either the identification of optimal parameters or solving the equation across multiple parameters to understand how a structure might react under different conditions. Performing an exhaustive search over the parameter space...
The talk presents the latest results in the field of viscosity optimization. The first result is the development of an efficient algorithm that leverages new formulas for calculating the trace, as well as the first and second derivatives of the trace, of the associated Lyapunov equation. This approach enhances the precision and computational efficiency of viscosity optimization. The second...
Recently, data-enabled predictive control (DeePC) schemes based on Willems' fundamental lemma have attracted considerable attention. At the core are computations using Hankel-like matrices and their connection to the concept of persistency of excitation. We propose an iterative solver for the underlying data-driven optimal control problems resulting from linear discrete-time systems. To this...
In this talk, we will discuss a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as (port-)Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or with dissipation and hence plays a crucial role in the description of the physical properties of the system. We propose to combine...
Linear quadratic Gaussian (LQG) balanced truncation is a model reduction technique for possibly unstable linear time-invariant systems which are to be controlled by an LQG controller. In contrast to the classical balanced truncation approach, the LQG balancing procedure is based on the closed-loop system behavior rather than on the transfer function of the open-loop system. Furthermore, LQG...
We develop and present a range of feedback control laws for the fluidic pinball control problem. This control problem seeks to control the vortex shedding behind three cylinders where cylinder rotation is the actuation mechanism. This benchmark problem has been used to demonstrate several machine learning control strategies. In this talk, we present an approach that uses interpolatory model...
Optimizing complex processes is crucial in industries like food production and materials science, where improving product quality and efficiency can drive innovation. Achieving optimal control in these systems requires advanced techniques to handle nonlinearity, uncertainty, and high-dimensionality.
In this talk, we will navigate a diverse landscape of approaches encompassing physical...
Vibrational structures are susceptible to catastrophic failure or structural damage when external forces induce resonances or repeated unwanted oscillations. One common mitigation strategy to address this challenge is using dampers to suppress the effect of these disturbances. This leads to the question of how to find optimal damper viscosities and positions for a given vibrational structure....
Dynamical systems can be used to model a broad class of physical processes, and conservation laws give rise to system properties like passivity or port-Hamiltonian structure. An important problem in practical applications is to steer dynamical systems to prescribed target states, and feedback controllers provide a powerful tool to do so. However, controllers designed using classical methods do...
In this talk we will present eigenvalue estimates for the solutions of operator Lyapunov equations with a noncompact (but relatively Hilbert Schmidt) control operator. We compute eigenvalue estimates from Galerkin discretizations of Lyapunov equations and discuss the appearance of spurious (non convergent) discrete eigenvalues. This phenomenon is called the spectral pollution. Our main tools,...
Polytopic autoencoders provide low-dimensional parametrizations of states in a polytope. For nonlinear PDEs, this is readily applied to low-dimensional linear parameter-varying (LPV) approximations as they have been exploited for efficient nonlinear controller design via series expansions of the solution to the state-dependent Riccati equation. In this work, we develop a polytopic autoencoder...
A novel method to identify the transfer functions of single-input-single-output linear time invariant (SISO-LTI) dynamical systems is proposed. The proposed approach uses an operator based generalization of Prony’s classical parameter estimation method. In this work, generalized Prony schemes are used to reconstruct the transfer function of the system as a linear combination of rational basis...
We introduce a novel procedure for computing an SVD-type approximation of a matrix $\mathbf{A}\in\mathbb{R}^{m\times n}$, $m\geq n$. Specifically, we propose a randomization-based algorithm that improves over the standard Randomized Singular Value Decomposition (RSVD). Most significantly, our approach, the Row-aware RSVD (R-RSVD), explicitly constructs information from the row space of...
In this talk, we will consider a linear gyroscopic mechanical systems of the form
\begin{equation}\displaystyle M \ddot x(t) + G\dot x(t) + K x(t) = 0,
\end{equation}
where the mass matrix $M\in\mathbb{R}^{n\times n}$ and the stiffness matrix $K\in\mathbb{R}^{n\times n}$ are symmetric positive definite matrices, while the gyroscopic matrix $G \in\mathbb{R}^{n\times n}$ is skew-symmetric,...
The Koopman linearization enables the use of the linear operator theory in the study of nonlinear dynamical systems by switching from a topological dynamical system $(K, \varphi)$ to a Koopman system $(C(K), T_{\varphi})$ consisting of the space $C(K)$ of continuous complex-valued functions on $K$ and the composition operator $T_{\varphi} \colon f \mapsto f \circ \varphi$ on $C(K).$
Let...
We present a two-level trust-region (TLTR) method for solving unconstrained nonlinear optimization problems. The TLTR method employs a composite iteration step based on two distinct search directions: a fine-level direction, derived from minimization in the full high-resolution space, and a coarse-level direction, obtained through minimization in a subspace generated via random projection,...
