Approximation of stability radii for largescale dissipative Hamiltonian systems A linear timeinvariant dissipative Hamiltonian (DH) system dot x  (JR)Q x, with a skewHermitian J, a Hermitian positive semidefinite R, and a Hermitian positive definite Q, is always Lyapunov stable and under further weak conditions even asymptotically stable. By exploiting the characterizations from Mehl et al. (SIAM J. Matrix Anal. Appl. 37(4), 1625xe2x80x931654, 2016), we focus on the estimation of two stability radii for largescale DH systems, one with respect to nonHermitian perturbations of R in the form R  Bxcex94CH for given matrices B, C, and another with respect to Hermitian perturbations in the form R  Bxcex94BH,xcex94  xcex94H. We propose subspace frameworks for both stability radii that converge at a superlinear rate in theory. The one for the nonHermitian stability radius benefits from the DH structurepreserving model order reduction techniques, whereas for the Hermitian stability radius we derive subspaces yielding a Hermite interpolation property between the full and projected problems. With the proposed frameworks, we are able to estimate the two stability radii accurately and efficiently for largescale systems which include a finiteelement model of an industrial disk brake.

Dissipativity properties in constrained optimal control: A computational approach Abstract   In this paper, we consider discretetime nonlinear optimal control problems with possibly nonconvex cost subject to constraints on states and inputs. For these problems, we present a computational approach for the verification of strict dissipativity properties, which have recently been employed to study optimal system operation, turnpike phenomena, and closedloop properties of economic model predictive control schemes. Based on a nonstrict dissipation inequality, we provide necessary and sufficient conditions for strict dissipativity by explicitly computing the set w.r.t. which the system is strictly dissipative as well as the corresponding storage function. We focus on strict dissipativity w.r.t. periodic orbits and steadystates, being the most relevant cases of strict dissipativity, although our approach can be directly extended to strict dissipativity w.r.t. more general sets. For polynomial optimal control problems, the presented approach leads to a polynomial optimization problem, which is solved via sumofsquares programming. The optimal periodic orbit can then be constructed, without a priori knowledge of its period length, as the set of points for which a suitable nonstrict dissipation inequality holds with equality. In addition, we consider the important special case of indefinite linear quadratic optimal control problems subject to quadratic constraints, for which an optimal periodic orbit resulting from our construction is always located on the boundary of the constraint set.