H(infinity) filtering for rectangular discrete-time descriptor systems

This paper deals with the H(infinity) recursive estimation problem for general rectangular time-variant descriptor systems in discrete time. Riccati-equation based recursions for filtered and predicted estimates are developed based on a data fitting approach and game theory. In this approach, the nature determines a state sequence seeking to maximize the estimation cost, whereas the estimator tries to find an estimate that brings the estimation cost to a minimum. A solution exists for a specified gamma-level if the resulting cost is positive. In order to present some computational alternatives to the H(infinity) filters developed, they are rewritten in information form along with the respective array algorithms. (C) 2009 Elsevier Ltd. All rights reserved.

Experimental results on the nonlinear H(infinity) control via quasi-LPV representation and game theory for wheeled mobile robots

In this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear H(infinity) approaches. Two nonlinear H(infinity) controllers that guarantee induced L(2)-norm, between input (disturbances) and output signals, bounded by an attenuation level gamma, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.

A Fault-Tolerant Manipulator Robot Based on H(2), H(infinity), and Mixed H(2)/H(infinity) Markovian Controls

This paper develops a Markovian jump model to describe the fault occurrence in a manipulator robot of three joints. This model includes the changes of operation points and the probability that a fault occurs in an actuator. After a fault, the robot works as a manipulator with free joints. Based on the developed model, a comparative study among three Markovian controllers, H(2), H(infinity), and mixed H(2)/H(infinity) is presented, applied in an actual manipulator robot subject to one and two consecutive faults.

Neural network-based H(infinity) control for fully actuated and underactuated cooperative manipulators

This paper develops H(infinity) control designs based on neural networks for fully actuated and underactuated cooperative manipulators. The neural networks proposed in this paper only adapt the uncertain dynamics of the robot manipulators. They work as a complement of the nominal model. The H(infinity) performance index includes the position errors as well the squeeze force errors between the manipulator end-effectors and the object, which represents a complete disturbance rejection scenario. For the underactuated case, the squeeze force control problem is more difficult to solve due to the loss of some degrees of manipulator actuation. Results obtained from an actual cooperative manipulator, which is able to work as a fully actuated and an underactuated manipulator, are presented. (C) 2008 Elsevier Ltd. All rights reserved.

Galerkin Method and Weighting Functions Applied to Nonlinear H(infinity) Control with Output Feedback

This paper considers two aspects of the nonlinear H(infinity) control problem: the use of weighting functions for performance and robustness improvement, as in the linear case, and the development of a successive Galerkin approximation method for the solution of the Hamilton-Jacobi-Isaacs equation that arises in the output-feedback case. Design of nonlinear H(infinity) controllers obtained by the well-established Taylor approximation and by the proposed Galerkin approximation method applied to a magnetic levitation system are presented for comparison purposes.

On the convergence of successive Galerkin approximation for nonlinear output feedback H(infinity) control

Although the formulation of the nonlinear theory of H(infinity) control has been well developed, solving the Hamilton-Jacobi-Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H(infinity) control via output feedback are presented. An example is presented illustrating the application of the algorithm.

Fixed-point DSP implementation of nonlinear H(infinity) controller for large gap electromagnetic suspension system

Electromagnetic suspension systems are inherently nonlinear and often face hardware limitation when digitally controlled. The main contributions of this paper are: the design of a nonlinear H(infinity) controller. including dynamic weighting functions, applied to a large gap electromagnetic suspension system and the presentation of a procedure to implement this controller on a fixed-point DSP, through a methodology able to translate a floating-point algorithm into a fixed-point algorithm by using l(infinity) norm minimization due to conversion error. Experimental results are also presented, in which the performance of the nonlinear controller is evaluated specifically in the initial suspension phase. (C) 2009 Elsevier Ltd. All rights reserved.

Eigenvalues of Casimir operators for gl(m/infinity)

A full set of Casimir operators for the Lie superalgebra gl(m/infinity) is constructed and shown to be well defined in the category O-FS generated by the highest-weight irreducible representations with only a finite number of non-zero weight components. The eigenvalues of these Casimir operators are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(m/infinity) are also determined.

Casimir invariants and characteristic identities for gl(infinity)

A full set of (higher-order) Casimir invariants for the Lie algebra gl(infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American Institute of Physics.

On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

One, two, (three), infinity: Newspaper and lab beauty-contest experiments

"Beauty-contest" is a game in which participants have to choose, typically, a number in [0,100], the winner being the person whose number is closest to a proportion of the average of all chosen numbers. We describe and analyze Beauty-contest experiments run in newspapers in UK, Spain, and Germany and find stable patterns of behavior across them, despite the uncontrollability of these experiments. These results are then compared with lab experiments involving undergraduates and game theorists as subjects, in what must be one of the largest empirical corroborations of interactive behavior ever tried. We claim that all observed behavior, across a wide variety of treatments and subject pools, can be interpretedas iterative reasoning. Level-1 reasoning, Level-2 reasoning and Level-3 reasoning are commonly observed in all the samples, while the equilibrium choice (Level-Maximum reasoning) is only prominently chosen by newspaper readers and theorists. The results show the empirical power of experiments run with large subject-pools, and open the door for more experimental work performed on the rich platform offered by newspapers and magazines.

Symmetric periodic orbits near heteroclinic loops at infinity for a class of polynomial vector fields

For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.

A(-infinity)-interpolation in the ball

We give a necessary and sufficient condition for a sequence [ak}k in the unit ball of C° to be interpolating for the class A~°° of holomorphic functions with polynomial growth. The condition, which goes along the lines of the ones given by Berenstein and Li for some weighted spaces of entire functions and by Amar for H°° functions in the ball, is given in terms of the derivatives of m > n functions F Fm e A~°° vanishing on {ak)k.

Wittgenstein And Labyrinth Of ‘Actual Infinity’: The Critique Of Transfinite Set Theory

In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory (including the Diagonal Argument, the Continuum Hypothesis and Cantor’s Theorem) and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing (completed) infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of the concept of ‘denumerability’ as it is presented in set theory as well as his philosophic refutation of Cantor’s Diagonal Argument and the implications of such a refutation onto the problems of the Continuum Hypothesis and Cantor’s Theorem. Throughout, the discussion will be placed within the historical and philosophical framework of the Grundlagenkrise der Mathematik and Hilbert’s problems.