Inexact Newton method with backtracking is one of the most popular techniques for solving large sparse nonlinear systems of equations. The method is easy to implement, and converges well for many practical problems. However, the method is not robust. More precisely speaking, the convergence may stagnate for no obvious reason. In this paper, we extend the recent work of Tuminaro, Walker and Shad...

Robust linear and nonlinear control is a continuing requirement for automotive powertrain controls. Newton iteration techniques have been proposed for both nonparametric linear and recently nonlinear control. Such nonparametric methods may eventually allow benefits of both low-order controllers and more rapid calibration time. This paper evaluates the feasibility of such Newton iteration techni...

Parallel manipulators have been proposed to overcome accuracy problem in the end effector positioning, exhibited by serial manipulators(Stewart, 1965)(Reboulet, 1988)(Merlet, 2000). These parallel robots are primarly used in the applications for which the considered processes require a high degree of accuracy, high speeds or accelerations. Aircraft simulator (Stewart, 1965), machining tools (Ne...

We study the problem of learning a kernel matrix from an apriori kernel and training data. An unconstrained convex optimization formulation is proposed, with an arbitrary convex smooth loss function on kernel entries and a LogDet divergence for regularization. Since the number of variables is of order O(n), standard Newton and quasi-Newton methods are too time-consuming. An operator form Hessia...

In this paper the dynamic analysis of a macro–micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of the Large Adaptive Reflector (LAR), the Canadian design of next-generation giant radio telescopes. In this structure it is proposed to use two parallel redundant manipulators at the macro and micro level, both ac...

We perform a covariant $1+3$ split of the Newton-Cartan equations. The resulting 3-dimensional system equations, called $1+3$-Newton-Cartan is structurally equivalent to $1+3$-Einstein In particular it features momentum constraint, and choice adapted coordinates corresponds shift vector. show that these equations reduce classical Newton without need for special Galilean coordinates. solutions a...

Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of bounded regions in the corresponding arrangement of hypersurfaces, and to the Euler characteristic of the complexified complement. Under suitable hypotheses...

Autonomous Underwater Vehicles (AUVs) are presenting an ever expanding range of applications that enhance human capabilities and mitigate human risk. Development of a successful subsurface autonomous launch and recovery system would expand the functional use of AUVs in many fields, e.g., year-round Canadian Arctic exploration and sovereignty missions. This paper provides an overview of the desi...

To provide COSMOS, a dynamic model baaed manipulator control system, with an improved dynamic model, a PUMA 560 arm waa diaaaaembled; the inertial propertiea of the individual links were meaaured; and an ezplicit model incorporating all ofthe non-zero meaaured parametera waa deriued. The ezplicit model of the PUMA arm has been obtained with a derivation procedure comprised of aeveral heuristic...

We provide methods of computing multivalued solutions to the Euler-Poisson system and test them in the context of a klystron amplifier. An Eulerian formulation capable of computing multivalued solutions is derived from a kinetic description of the Euler-Poisson system and a moment closure. The system of the moment equations may be closed due to the special structure of the solution in phase spa...