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In this paper we present a convex optimization problem for solving the rational covariance extension problem. Given a partial covariance sequence and the desired zeros of the modeling filter, the poles are uniquely determined from the unique minimum of the corresponding optimization problem. In this way we obtain an algorithm for solving the covariance(More)
In this paper we formalize the observation that filtering and interpolation induce complementary, or " dual, " decompositions of the space of positive real rational functions of degree less than or equal to n. From this basic result about the geometry of the space of positive real functions, we are able to deduce two complementary sets of conclusions about(More)
The trigonometric moment problem is a classical moment problem with numerous applications in mathematics, physics, and engineering. The rational covariance extension problem is a constrained version of this problem, with the constraints arising from the physical re-alizability of the corresponding solutions. Although the maximum entropy method gives one(More)
Efficient and robust numerical methods for solving the periodic Riccati differential equation (PRDE) are addressed. Such methods are essential, for example, when deriving feedback controllers for orbital stabilization of underactuated mechanical systems. Two recently proposed methods for solving the PRDE are presented and evaluated on artificial systems and(More)
We consider a benchmark example of a three-link planar biped walker with torso, which is actuated in between the legs. The torso is thought to be kept upright by two identical torsional springs. The mathematical model reflects a three-degree-of-freedom mechanical system with impulse effects, which describe the impacts of the swing leg with the ground, and(More)
We approach a problem of motion planning and stabilization for a benchmark example, known as the “Butterfly” robot. It was proposed as a benchmark challenge for developing systematic techniques for nonprehensile rolling manipulation. A dynamical model of the underactuated system with a non-unilateral contact is derived. The recently proposed(More)