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T-optimal designs formulti-factor polynomial regressionmodelsvia a semidefinite relaxation method
We consider T-optimal experiment design problems for discriminating multi-factor polynomial regression models wherethe design space is defined by polynomial inequalities and the regression parameters are constrained to given convex sets.Our proposed optimality criterion is formulated as a convex optimization problem with a moment cone constraint. When theregression models have one factor, an exact semidefinite representation of the moment cone constraint can be applied to obtainan equivalent semidefinite program.When there are two or more factors in the models, we apply a moment relaxation techniqueand approximate the moment cone constraint by a hierarchy of semidefinite-representable outer approximations. When therelaxation hierarchy converges, an optimal discrimination design can be recovered from the optimal moment matrix, and itsoptimality can be additionally confirmed by an equivalence theorem. The methodology is illustrated with several examples
Nonparametric estimation of concave production technologies by entropic methods
An econometric methodology is developed for nonparametric estimation of concave production technologies. The methodology, bases on the priciple of maximum likelihood, uses entropic distance and concvex programming techniques to estimate production functions.convex programming, production functions, entropy
Distributed Control of Positive Systems
A system is called positive if the set of non-negative states is left
invariant by the dynamics. Stability analysis and controller optimization are
greatly simplified for such systems. For example, linear Lyapunov functions and
storage functions can be used instead of quadratic ones. This paper shows how
such methods can be used for synthesis of distributed controllers. It also
shows that stability and performance of such control systems can be verified
with a complexity that scales linearly with the number of interconnections.
Several results regarding scalable synthesis and verfication are derived,
including a new stronger version of the Kalman-Yakubovich-Popov lemma for
positive systems. Some main results are stated for frequency domain models
using the notion of positively dominated system. The analysis is illustrated
with applications to transportation networks, vehicle formations and power
systems
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