Showing papers on "Uniform boundedness published in 1991"

Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions

Abstract: Unspecified Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: http://doi.org/10.5167/uzh-22758 Originally published at: Chipot, M; Fila, M; Quittner, P (1991). Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions. Acta Mathematica Universitatis Comenianae. New Series, 60(1):35-103. Acta Math. Univ. Comenianae Vol. LX, 1(1991), pp. 35–103 35 STATIONARY SOLUTIONS, BLOW UP AND CONVERGENCE TO STATIONARY SOLUTIONS FOR SEMILINEAR PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS M. CHIPOT, M. FILA AND P. QUITTNER

Robust control of robotic manipulators without velocity feedback

Abstract: This study concerns the problem of robust control of robotic manipulators without joint velocity feedback. A robust lead + bias controller is studied. The bias signal is intended to compensate the nonlinear dynamics of the robot. The focus of this study is robustness when the nonlinear compensation is not perfect and the external disturbances are not negligible. A conservative polynomial bound is introduced to describe the worst feedback effect of the compensation error and the external disturbances. The polynomial bound covers a class of possible bias signals, synthesized according to the available knowledge about the robot dynamics. Based on the polynomial bound, the tracking errors of a lead + bias controller are proved to be uniformly bounded. They can be minimized by a proper design of the bias signal. In the ideal case where the bias signal compensates the robot dynamics perfectly, the tracking errors will converge to zero.

On subordinated holomorphic semigroups

Abstract: If (e~' ) is a uniformly bounded C0 semigroup on a complex Banach space X, then -A" , 0 < a < 1, generates a holomorphic semigroup on X , and (e ) is subordinated to (e ) through the Levy stable density function. This was proved by Yosida in 1960, by suitably deforming the contour in an inverse Laplace transform representation. Using other methods, we exhibit a large class of probability measures such that the subordinated semigroups are always holomorphic, and obtain a necessary condition on the measure's Laplace transform for that to be the case. We then construct probability measures that do not have this property.

Convergence of Volterra series representation and BIBO stability of bilinear systems

Abstract: Convergence of the Volterra series representation for time-varying bilinear systems is discussed. If the bilinear slate equation martrices are uniformly bounded then, for bounded system inputs, the Volterra series representation converges uniformly on a finite time interval [lo T]. If. in addition, the system's zero-input response is uniformly asymptotically stable, we obtain the class of bounded system inputs for which the Volterra series representation converges uniformly on the infinite lime interval [0, ∞). The results are then used to obtain sufficient conditions for the BIBO stability of bilinear systems.

Transference of strong type maximal inequalities by separation-preserving representations

Abstract: Let X = LP(Ii), where 1 ? p R,, is a uniformly bounded, strongly continuous representation of G in X by separation-preserving operators (for instance, by positivity-pre- serving operators). We show that R transfers to X strong type maximal estimates for sequences of convolution operators defined on LP(G). If R also has a uniformly bounded version in L2(%t), then R will transfer to LP((t) strong type bounds for maximal operators defined by sequences of multipliers which are continuous on the dual group G. These theo- rems, which cease to be valid if the separation-preserving hypothesis is removed, provide strong type maximal operator counterparts for the corresponding single operator theorems of Coifman-Weiss transference theory. One consequence of the second theorem described above is a maximal.theorem counterpart of the Homomorphism Theorem for Sin- gle Multiplier Transforms.

Adaptive force control of single-link mechanism with joint flexibility

Abstract: An adaptive force control, scheme is presented that enables a single-link mechanism with joint flexibility to track a desired force trajectory. A dynamic model of the link system is derived, based on which a two-stage controller is constructed. It is shown that although all the system parameters including environment stiffness are unknown except for some of their bounds, all signals inside the closed-loop system remain uniformly bounded. Moreover, the force tracking error is driven to zero asymptotically. Simulation examples are provided to demonstrate the effectiveness of the proposed controller. >

Rate of approximation of functions of bounded variation by modified Lupas operators

Abstract: This paper discusses the rate of approximation of functions of bounded variation using the Modified Lupas operator. We obtain an approximation theorem and our estimate is essentially the best possible.

Distributional control and generalized analyticity

Abstract: Let S be a strongly continuous, separation-preserving representation of a locally compact abelian group G in Lp(μ), where 1≤p<∞, and μ is an arbitrary measure. We show that S is uniformly bounded with respect to the Lp-and L∞-norms if and only if it satisfies a certain boundedness condition for distribution functions. These equivalent conditions facilitate the transference from Lp(G) to Lp(μ) of the a.e. convergence for a wide class of sequences of convolution operators. The result unifies and generalizes various aspects of ergodic theory--in particular, the ergodic singular integral operators and ergodic Hardy spaces.

Properties of block renormalization group operators for Euclidean Fermions in an external gauge field

Abstract: The basis is laid for a block renormalization analysis of spinor electrodynamics in d=2,3 dimensions in a lattice approximation. The Fermion part of the renormalization group transformation gives rise to a sequence of localized Fermion action, fluctuation covariance, and minimizer operators in a regular external gauge field. It is shown that these operators are uniformly bounded analytic functions of complex‐valued gauge fields with uniform exponentially decaying kernels.

A simple characterization of uniform boundedness for a class for recursions

Abstract: Detecting bounded recursions is a powerful optimization technique for recursive database query languages, as bounded recursions can be replaced by equivalent nonrecursive definitions. The problem is also of theoretical interest in that varying the class of recursions considered generates problem instances that vary from linearly decidable to NP-hard to undecidable. In this paper we review and clarify the existing definitions of boundedness. We then specify a class of recursions C such that membership in C guarantees that a certain simple condition is necessary and sufficient for boundedness. We use the notion of membership in C to unify and extend previous work on determining decidable classes of bounded recursions.

Weighted Lp boundedness of Fourier series with respect to generalized Jacobi weights

Abstract: Let w be a generalized Jacobi weight on the interval [-1,1] and, for each function f, let Snf denote the n-th partial sum of the Fourier series of f in the orthogonal polynomials associated to w. We prove a result about uniform boundedness of the operators Sn in some weighted Lp spaces. The study of the norms of the kernels Kn related to the operators Sn allows us to obtain a relation between the Fourier series with respect to different generalized Jacobi weights.

The Lorentz reciprocity in random media—The derivation from Maxwell's equations

Abstract: The Lorentz reciprocity in random media is mathematically derived from Maxwell's equations on the assumption that the media are isotropic and that the material parameters e and μ are uniformly bounded random functions and exist in a finite region. It should be emphasized that the assumption is sufficiently satisfied in physics and that other conditions for e and μ are not assumed. The Lorentz reciprocity is valid in the sense that the reciprocal relation holds for any order moment of electromagnetic fields. The result and the derivation process presented here are useful for analyzing the wave propagation and scattering in random media.

Feedback codes with uniformly bounded codeword lengths and zero-error capacities

Abstract: A certain class of variable-length codes with feedback whose codeword lengths are uniformly upper bounded is considered. For this class of variable-length codes, it is shown that the zero-error capacity region for the, single-user and multiuser channels with feedback can be extended up to the ordinary average-error capacity under some conditions, if variable-length codes (semiblock codes) are used in place of fixed-length codes. This condition is different from that of M.V. Burnashev (1976) for variable-length codes with feedback but without any uniform bound on the codeword lengths. It is also shown that the capacity region for variable-length feedback codes coincides with that for fixed-length feedback codes. >

Searching in the Presence of Linearly Bounded Errors (Extended Abstract)

Abstract: We consider the problem of determining an unknown quantity x by asking “yes-no” questions, where some of the answers may be erroneous. In particular, we focus on a linearly bounded model of errors where for some known constant r, 0 < r < 1 2 , each initial sequence of i answers is guaranteed to have no more than ri errors. This model allows the errors to occur in a somewhat malicious way: for example, we must deal with a scenario where all errors occur in the last few answers. The problem is examined under the following variations: kinds of questions allowed (comparison or membership), nature of the domain of the searched quantity (bounded [x ∈ {1, . . . , n}, for some fixed n] or unbounded [x is any positive integer]). In the bounded domain, the only previous bound on the number of questions which works for the entire range 0 < r < 1 2 (with either comparison or membership questions) is O(n2 1 1−2r ). We improve this significantly by showing that O(log n) membership questions are enough. The upper bound on number of comparison questions needed is improved to O(n2 1 1−r ), which is o(n) even when r gets arbitrarily close to 12 . In the unbounded domain, where now n is the number being searched, we show that O(log n) membership questions or O([n log n]2 1 1−r ) comparison questions are enough. The problem is solved using the framework of chip games. Author was supported by DARPA Contract N00014-87-K-825 and National Science Foundation Grant CCR-8914428. Author’s net address: jaa@theory.lcs.mit.edu Author was supported by DARPA Contract N00014-87-K825, National Science Foundation Grant CCR-8912586, and Air Force Contract AFOSR-89-0271. Author’s net address: aditi@theory.lcs.mit.edu

On the existence of weak solutions of the stationary semiconductor equations with velocity saturation

Abstract: In the present paper we prove the existence and differentiability of weak solutions to the stationary semiconductor equations where the mobility coefficients model the effect of saturation of drift velocity The proof of existence relies on approximation by uniformly bounded mobility coefficients

A note on the condition for convergence of nonlinear ABS method

Abstract: This paper is concerned with the assumptions in the convergence theorem of the nonlinear ABS algorithm. In the published papers, it has been assumed that the condition number of the scaling matrices is uniformly bounded above. In this paper it is shown that the above condition can be replaced by the following simpler condition: the orthogonality measure of scaling vector sets is uniformly bounded from below. It is also shown that the latter condition is weaker than the original one.

Adaptive Control of Linear Time Varying Plants: The Case of "Jump" Parameter Variations

Abstract: In this note we consider the adaptive control problem of linear, time varying, single-input singl-output plants with parameter discontinuities ("jump" parameter variations). In our formulation, the plant parameters are assumed to be uniformly bounded and piecewise continuous functions of time. Inside the intervals of continuity, the plant is assumed to satisfy some general conditions on observability, controllability and zero dynamics and the parameters are assumed to be smooth (or at least Lipschitz) but their speed of variation is not necessarily small. Under these, quite general, conditions it is established that a control law of the model reference type [5] which, in the case of know parameters, guarantees exponential and therefore internal stability of the closed loop, provided that in any time interval the average number of parameter discontinuities is small enough. In the case of partially unknown plant parameters, this control law is combined with an estimator. The resulting adaptive controller guarantees boundedness of the closed loop for bounded reference signals provided that: 1. in any time interval, the average number of parameter discontinuities is small enough and 2. inside the intervals of continuity, the functional dependence on time (or structure) of the fast time varying parameters is known up to a slowly varying component. The currently available results on the adaptive control problem of time-varying plants have been derived under stronger assumptions, typically requiring that the plant parameters are smooth and slowly time-varying [1,2,3] or piecewise continuous and slowly varying in the mean [4].

Bounded Fixed Point Iteration

Abstract: In the context of abstract interpretation for languages without higher-order features we study the number of times a functional need to be unfolded in order to give the least fixed point. For the cases of total or monotone functions we obtain an exponential bound and in the case of strict and additive (or distributive) functions we obtain a quadratic bound. These bounds are shown to be tight in that sufficiently long chains of functions can be shown to exist. Specializing the case of strict and additive functions to functionals of a form that would correspond to iterative programs we show that a linear bound is tight. This is related to several analyses studied in the literature (including strictness analysis).

Finite-dimensional decentralized adaptive control for interconnected distributed parameter systems

Abstract: A method for the design of a finite–dimensional decentralized adaptive controller for an interconnected distributed parameter system is presented. We first state the system description and construct a finite–dimensional decentralized adaptive controller. Next we show that all the signals in the closed loop system are uniformly bounded, the state and parameter errors converge exponentially to a residual set in the case of tracking, and regulation is achieved perfectly. Finally we show the effectiveness of the proposed method using a simple numerical example.

Stability analysis for a two-time-scale neural tracking controller

Abstract: The stability of a two-time scale neural tracking controller is analyzed using Lyapunov stability theory. The results show that the tracking error of the system is uniformly bounded and converges to a bounded region if the two-time-scale neural tracking controller is used. Moreover, the region depends only on the accuracy of the slow learning rule is a switching leakage term is used in the fast learning rule. >

Preventing infinite looping in Prolog

Abstract: A method is proposed to modify Prolog compilers so that infinite looping can often be avoided in recursive Prolog programs. The study is carried out in the context of deductive databases. Termination of recursive query processing here is related to boundedness: uniform boundedness and extensional boundedness. Limitations of this method are briefly discussed. >

On Uniform Boundedness of Solutions to Discrete Velocity Models in Several Dimensions

Abstract: The global existence question for discrete velocity models in more than one space dimension remains unsolved, except for initial values which are small in some sense ([2], [6], [7]). The crucial difficulty is that we do not seem to have the tools to obtain uniform L∞ — bounds in time on the local solution in terms of the initial values (this, of course, would entail global existence of a mild solution). The purpose of this article is to compare the situation with the better understood one-dimensional case, spell out some crucial differences, and point out a possible way to progress.

The trace theorem $W^{2,1}_p(\Omega_T) \ni f \mapsto \nabla_{\!x} f \in W^{1-1/p,1/2-1/2p}_p(\partial \Omega_T)$ revisited

Abstract: Filling a possible gap in the literature, we give a complete and readable proof of this trace theorem, which also shows that the imbedding constant is uniformly bounded for $T \downarrow 0$. The proof is based on a version of Hardy's inequality (cp. Appendix).

A Fast Time & Order Recursive Algorithm for Parameter Estimation of a Set of ARX Systems

Abstract: It would be useful in control system design and signal processing to be able to determine a family of least squares (LS) ARX models of different order (p,q) for a physical system (p: AR order, q: order of the exogenous input part), and then select the best model according to some criterion for evaluating the resulting models. A practical problem is how to obtain such a family of models efficiently. To solve this, a time and order recursive algorithm (TORA) is developed in this paper. For uniformly bounded input and output processes, the strong consistency of the parameter estimates generated by the recursive LS algorithm guarantees that the TORA produces strongly consistent parameter estimates. The TORA can be useful, by combining it with other relevant techniques, in stochastic modeling, adaptive IIR filtering, quantification of unmodeled dynamics, and self-tuning control.

Robustness of extended least squares based adaptive control

Abstract: The authors show that the popular extended least-squares-based one-step ahead adaptive tracking algorithm is robust to both the presence of small unmodeled dynamics and violation of the stochasticity assumption on the noise. Specifically, the noise is allowed to be any bounded sequence. The only modification used is a projection of the parameter estimates. The adaptive control algorithm is a weighted extended least-squares type noninterlaced adaptation law with projection. Assuming the nominal plant to be minimum-phase, without the small unmodeled dynamics, it is proved that all the signals in the closed-loop system are uniformly bounded. >