Related papers: Interpolatory $\mathcal{H}_2$-optimality Condition…
We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological…
We consider model reduction of large-scale multi-input, multi-output (MIMO) systems using tangential interpolation in the frequency domain. Our scheme is related to the recently-developed Adaptive Antoulas--Anderson (AAA) algorithm, which…
This paper addresses the problem of the optimal $H_2$ controller design for compartmental systems. In other words, we aim to enhance system robustness while maintaining the law of mass conservation. We perform a novel problem transformation…
This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
This paper investigates stable suboptimal H-infinity controllers for a class of single-input single-output time-delay systems. For a given plant and weighting functions, the optimal controller minimizing the mixed sensitivity (and the…
This paper deals with the distributed $\mathcal{H}_2$ optimal control problem for linear multi-agent systems. In particular, we consider a suboptimal version of the distributed $\mathcal{H}_2$ optimal control problem. Given a linear…
Higher-order topological insulators (HOTIs) have attracted much attention in photonics due to the tightly localized disorder-robust corner and hinge states. Here, we reveal an unconventional HOTI phase with vanishing dipole and quadrupole…
Past research into robotic planning with temporal logic specifications, notably Linear Temporal Logic (LTL), was largely based on a single formula for individual or groups of robots. But with increasing task complexity, LTL formulas…
In this paper, we present a convex formulation of $H_{\infty}$-optimal control problem for coupled linear ODE-PDE systems with one spatial dimension. First, we reformulate the coupled ODE-PDE system as a Partial Integral Equation (PIE)…
We mainly consider the frequency limited $\mathcal{H}_2$ optimal model order reduction of large-scale sparse generalized systems. For this purpose we need to solve two Sylvester equations. This paper proposes efficient algorithm to solve…
Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time $(\mathcal{PT})$ symmetry that are best understood as systems with…
We develop here a computationally effective approach for producing high-quality $\mathcal{H}_\infty$-approximations to large scale linear dynamical systems having multiple inputs and multiple outputs (MIMO). We extend an approach for…
Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…
For a general nonlinear control system, we study the problem of small time local attainability of a target which is the closure of an open set. When the target is smooth and locally the sublevel set of a smooth function, we develop second…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
Linear time-invariant (LTI) systems appear frequently in natural sciences and engineering contexts. Many LTI systems are described by ordinary differential equations (ODEs). For example, biological gene regulation, analog filter circuits,…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian…
Lie-Trotter-Suzuki decompositions are an efficient way to approximate operator exponentials $\exp(t H)$ when $H$ is a sum of $n$ (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution…
Time-optimal control for high-order chain-of-integrators systems with full state constraints and arbitrarily given terminal states remains a challenging problem in the optimal control theory domain, yet to be resolved. To enhance further…