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For a wide class of chemical reaction networks, including all those governed by detailed balanced mass-action kinetics, we examine the robustness of equilibrium species concentrations against fluctuations in the overall reactant supply. In particular, we present lower bounds on the individual species-concentration sensitivities that derive from reaction network structure alone, independent of kinetic parameters or even of the particular equilibrium state at which sensitivities are calculated. These bounds suggest that, in the class of reaction networks considered here, very high robustness (i.e., very low sensitivities) should be expected only when the various molecules are constructed from a large number of distinct elemental building blocks that appear in high multiplicity or that combine gregariously. This situation is often encountered in biology. [ABSTRACT FROM AUTHOR]

It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we argue that a comprehensive probabilistic robustness analysis requires a detailed evaluation of the robustness function, and we show that such an evaluation can be performed with essentially any desired accuracy and confidence using algorithms with complexity that is linear in the dimension of the uncertainty space. Moreover, we show that the average memory requirements of such algorithms are absolutely bounded and well within the capabilities of today's computers. In addition to efficiency, our approach permits control over statistical sampling error and the error due to discretization of the uncertainty radius. For a specific level of tolerance of the discretization error, our techniques provide an efficiency improvement upon conventional methods which is inversely proportional to the accuracy level; i.e., our algorithms get better as the demands for accuracy increase. [ABSTRACT FROM AUTHOR]

We consider constrained finite-time optimal control problems for discrete-time linear time-invariant systems with constraints on inputs and outputs based on linear and quadratic performance indices. The solution to such problems is a time-varying piecewise affine (PWA) statefeedback law and can be computed by means of multiparametric programming. By exploiting the properties of the value function and the piecewise affine optimal control law of the constrained finitetime optimal control (CFTOC), we propose two new algorithms that avoid storing the polyhedral regions. The new algorithms significantly reduce the on-line storage demands and computational complexity during evaluation of the PWA feedback control law resulting from the CFTOC. [ABSTRACT FROM AUTHOR]

In a recent paper, the authors introduced the recovery method (local energy matching principle) for solving large systems of lattice equations. The idea is to construct a partial differential equation along with a finite element discretization such that the arising system of linear equations has equivalent energy as the original system of lattice equations. Since a vast variety of efficient solvers is available for solving large systems of finite element discretizations of elliptic PDEs, these solvers may serve as preconditioners for the system of lattice equations. In this paper, we will focus on both the theoretical and the numerical dependence of the method on various mesh-dependent parameters, which can be easily computed and monitored during the solution process. Systematic parameter tests have been performed which underline (a) the robustness and the efficiency of the recovery method and (b) the reliability of the control parameters, which are computed in a preprocessing step to predict the performance of the preconditioner based on the recovery method. [ABSTRACT FROM AUTHOR]