Showing papers on "Bounded function published in 1989"

Smooth stabilization implies coprime factorization

Abstract: It is shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system. It follows that feedback linearizable systems admit such fabrications. In order to establish the result, a Lyapunov-theoretic definition is proposed for bounded-input-bounded-output stability. The notion of stability studied in the state-space nonlinear control literature is related to a notion of stability under bounded control perturbations analogous to those studied in operator-theoretic approaches to systems; in particular it is proved that smooth stabilization implies smooth input-to-state stabilization. >

Computability in analysis and physics

Abstract: This book represents the first treatment of computable analysis at the graduate level within the tradition of classical mathematical reasoning. Among the topics dealt with are: classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The book is self-contained, and yet sufficiently detailed to provide an introduction to research in this area.

Robust stabilization of normalized coprime factor plant descriptions with H/sub infinity /-bounded uncertainty

Abstract: The problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by H/sub infinity / bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system. This problem can be reduced to a Nehari extension problem directly and gives an optimal stability margin. All controllers satisfying a suboptimal stability margin are characterized, and explicit state-space formulas are given. >

Admissibility of unbounded control operators

Abstract: For linear systems described by $\dot x(t) = Ax(t) + Bu(t)$, where A generates a semigroup on the state space X and B is an unbounded operator, some necessary as well as some sufficient conditions are given for B to be admissible, i.e., for any t, the state $x(t)$ should be in X and should depend continuously on the input $u \in L^p $. This approach begins with an axiomatic description of such a system in terms of a functional equation. The results are applied to the wave equation on a bounded interval.

Space Mappings with Bounded Distortion

Abstract: Introduction Some facts from the theory of functions of a real variable Functions with generalized derivatives Mobius transformations Definition of a mapping with bounded distortion Mappings with bounded distortion on Riemannian spaces Main facts in the theory of mappings with boundd distortion Estimates of the moduli of continuity and differentiability almost everywhere of mappings with bounded distortion Some facts about continuous mappings on $R^n$ Conformal capacity The concept of the generalized differential of an exterior form Mappings with bounded distortion and elliptic differential equations Topological properties of mappings with bounded distortion Local structure of mappings with bounded distortion Characterization of mappings with bounded distortion by the property of quasiconformity Sequences of mappings with bounded distortion The set of branch points of a mapping with bounded distortion and locally homeomorphic mappings Extremal properties of mappings with bounded distortion Some further results Some results in the theory of functions of a real variable and the theory of partial differential equations Functions with bounded mean oscillation Harnack's inequality for quasilinear elliptic equations Theorems on semicontinuity and convergence with a functional for functionals of the calculus of variations Some properties of functions with generalized derivatives On the degree of a mapping.

Stable, distributed, real-time scheduling of flexible manufacturing/assembly/diassembly systems

Abstract: The authors consider general flexible manufacturing/assembly/disassembly systems with the following features: (i) there are several types, each with given processing time requirements at a specified sequence of machines; (ii) each part type needs to be produced at a prespecified rate; (iii) parts may incur variable transportation delays when moving from one machine to another; (iv) set-up times are required whenever a machine changes from a production run of parts of one type to a run of another type; (v) some part types may also need assembly or disassembly; and (vi) a proportion of parts of a part type may require separate routing on exiting from a machine, for reasons including, but not limited to, poor quality. The authors exhibit a class of scheduling policies implementable in real time in a distributed way at the various machines, which ensure that the cumulative production of each part type trails the desired production by no more than a specific constant. The buffers of all the machines are guaranteed to be bounded, and the system can thus operate with finite buffer capacities. >

Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one

Abstract: The Fourier algebra A(G) of a locally compact group G is the space of matrix coefficients of the regular representation, and is the predual of the yon Neumann algebra VN(G) generated by the regular representation of G on L 2 (G). A multiplier m of A (G) is a bounded operator on A (G) given by pointwise multiplication by a function on G, also denoted m. We say m is a completely bounded multiplier ofA (G) if the transposed operator on VN(G) is completely bounded (definition below). It may be possible to find a net ofA (G)-functions, (m i : ie I) say, such that mi tends to

Hilbert Modules over Function Algebras

Abstract: Much of the early motivation for the study of operator theory came from integral equations although early in this century both operator theory and functional analysis took on a life of their own. Self-adjoint operators, both bounded and unbounded, occupied center stage for several decades either singly or in algebras. During the last two or three decades various approaches to the non-selfadjoint theory have been introduced with considerable success at least in the case of a single operator. The generalization to several operators, whether commuting or non-commuting, has largely eluded us. In this note we want to outline a different point of view which may assist in guiding developments in this area.

Diffusive logistic equations with indefinite weights: population models in disrupted environments

Abstract: The dynamics of a population inhabiting a strongly heterogeneous environment are modelledby diffusive logistic equations of the form ut = d Δu + [m(x) — cu]u in Ω × (0, ∞), where u represents the population density, c, d > 0 are constants describing the limiting effects of crowding and the diffusion rate of the population, respectively, and m(x) describes the local growth rate of the population. If the environment ∞ is bounded and is surrounded by uninhabitable regions, then u = 0 on ∂∞× (0, ∞). The growth rate m(x) is positive on favourablehabitats and negative on unfavourable ones. The object of the analysis is to determine how the spatial arrangement of favourable and unfavourable habitats affects the population being modelled. The models are shown to possess a unique, stable, positive steady state (implying persistence for the population) provided l/d> where is the principle positive eigenvalue for the problem — Δϕ=λm(x)ϕ in Χ,ϕ=0 on ∂Ω. Analysis of how depends on m indicates that environments with favourable and unfavourable habitats closely intermingled are worse for the population than those containing large regions of uniformly favourable habitat. In the limit as the diffusion rate d ↓ 0, the solutions tend toward the positive part of m(x)/c, and if m is discontinuous develop interior transition layers. The analysis uses bifurcation and continuation methods, the variational characterisation of eigenvalues, upper and lower solution techniques, and singular perturbation theory.

Biological growth and spread modeled by systems of recursions. I. Mathematical theory.

Abstract: We study the asymptotic behavior of solutions to a system of recursions u in+1 = Qi[mu n], i = 1, ..., k. The vector operator Q has the origin theta and a positive vector beta as fixed points and is defined for vector-valued functions bounded between theta and gamma where gamma greater than or equal to beta. In addition, Q is order-preserving, commutes with translation, and is continuous in the topology of uniform convergence on compact subsets. Let theta less than or equal to pi much less than beta, and suppose that for all pi much less than alpha much less than beta, Q(n) alpha]----beta as n----infinity. If u0 much greater than pi on a sufficiently large ball and has bounded support, then un propagates with a speed c*(xi) in the direction of the unit vector xi as n----infinity. In certain cases, c*(xi) can be calculated explicitly. The results generalize those of a scalar equation studied by Weinberger.

Instability analysis and robust adaptive control of robotic manipulators

Abstract: The robustness of adaptive controllers with respect to uncertainty is examined. The uncertainties include bounded input disturbances, unknown and time-varying plant parameters, and unmodeled dynamics. A simple example shows instability of a recent manipulator control scheme in the presence of bounded disturbances. The adaptive laws for updating the controller parameters are modified so that instabilities are counteracted and robustness is guaranteed. >

Filtering and smoothing in an H/sup infinity / setting

Abstract: Consideration is given to the problems of filtering and smoothing for linear systems in an H/sup infinity / setting, i.e. the plant and measurement noises have bounded energies (are in L/sub 2/), but are otherwise arbitrary. Two distinct situations for the initial condition of the system are considered: in one case the initial condition is assumed known; in the other case it is not known, but the initial condition, the plant, and the measurement noise are in some weighted ball of R/sup n/*L/sub 2/. Both finite-horizon and infinite-horizon cases are considered. The authors present necessary and sufficient conditions for the existence of estimators (both filters and smoothers) that achieved a prescribed performance bound and develop algorithms that result in performance within the bounds. They also present the optimal smoother. The approach uses basic quadratic optimization theory in a time-domain setting, as a consequence of which time-varying and time-invariant linear systems can be considered with equal ease. >

Exact recursive polyhedral description of the feasible parameter set for bounded-error models

Abstract: A method is described which exactly characterizes the set of all the values of the parameter vector of a linear model that are consistent with bounded errors on the measurements. It provides a parameterized expression of this set, which can be used for robust control design or for optimizing any criterion over the set. This approach is based on a new variant of the double description method for determining the edges of a polyhedral cone. It can be used in real time and provides a suitable context for implementation on a computer. Whenever a new measurement modifies the set, the characterization is updated. The technique is illustrated with a simple example. >

Instance-based prediction of real-valued attributes

Abstract: Instance-based representations have been applied to numerous classification tasks with some success Most of these applications involved predicting a symbolic class based on observed attributes This paper presents an instance-based method for predicting a numeric value based on observed attributes We prove that, given enough instances, if the numeric values are generated by continuous functions with bounded slope, then the predicted values are accurate approximations of the actual values We demonstrate the utility of this approach by comparing it with a standard approach for value prediction The instance-based approach requires neither ad hoc parameters nor background knowledge

Existence of solutions for all Deborah numbers for a non-Newtonian model modified to include diffusion

Abstract: We consider the existence of solutions for a non-Newtonian fluid that is based upon a nonlinear dumb-bell model. It is shown that a rigorous existence proof can be obtained for solutions on a bounded domain at arbitrary values of Deborah number provided the model includes a spatial diffusion term that is usually neglected in the derivation of the model by assuming that the structure is spatially homogeneous. Although this diffusion term is critical to the existence proof, it is expected to be numerically small compared to other terms in the constitutive model, except possibly in the vicinity of very large stress gradients, which it will tend to smooth out. The proof also requires that the stress always remain bounded. Although it is likely that this will be true for a model with a nonlinear (FENE) spring, it is difficult to prove rigorously. Hence, in the existence proof we resort to an ad hoc assumption that is equivalent to asserting that the polymer breaks (degrades) if the end-to-end distance exceeds some prescribed values that is less than the full cotour length but is otherwise arbitrary.

On the Cauchy problem and initial traces for a degenerate parabolic equation

Abstract: The authors study the Cauchy problem for the degenerate parabolic equation ut = div(|Du| p−2 Du)(p<2), and find sufficient conditions on the initial trace u0 (and in particular on its behaviour as |x|→∞) for existence of a solution in some strip RN × (0,T). Using a Harnack type inequality they show that these conditions are optimal in the case of nonnegative solutions. Uniqueness of solutions is shown if u0 belongs to L1loc(RN), but is left open in the case that u0 is merely a locally bounded measure. The results are closely related to papers by Aronson-Caffarelli, Benilan-Crandall-Pierre, and Dahlberg-Kenig about the porous medium equation ut = Δum. The proofs are different and allow one to generalize some of the above results to equations with variable coefficients.

The nonlinear geometry of linear programming. II. Legendre transform coordinates and central trajectories

Abstract: Karmarkar's projective scaling algorithm for solving linear programming problems associates to each objective function a vector field defined in the interior of the polytope of feasible solutions of the problem. This paper studies the set of trajectories obtained by integrating this vector field, called P-trajectories, as well as a related set of trajectories, called A-trajectories. The A-trajectories arise from another linear programming algorithm, the affine scaling algorithm. The affine and projective scaling vector fields are each defined for linear programs of a special form, called standard form and canonical form, respectively. These trajectories are studied using a nonlinear change of variables called Legendre transform coordinates, which is a projection of the gradient of a logarithmic barrier function. The Legendre transform coordinate mapping is given by rational functions, and its inverse mapping is algebraic. It depends only on the constraints of the linear program, and is a one-to-one mapping for canonical form linear programs. When the polytope of feasible solutions is bounded, there is a unique point mapping to zero, called the center. The A-trajectories of standard form linear programs are linearized by the Legendre transform coordinate mapping. When the polytope of feasible solutions is bounded, they are the complete set of geodesics of a Riemannian geometry isometric to Euclidean geometry. Each A-trajectory is part of a real algebraic curve. Each P-trajectory for a canonical form linear program lies in a plane in Legendre transform coordinates. The P-trajectory through 0 in Legendre transform coordinates, called the central P-trajectory, is part of a straight line, and is contained in the A-trajectory through 0, called the central A-trajectory. Each P-trajectory is part of a real algebraic curve. The central A-trajectory is the locus of centers of a family of linear programs obtained by adding an extra equality constraint of the form (c, x) = ,u . It is also the set of minima of a parametrized family of logarithmic barrier functions. Power-series expansions are derived for the central A-trajectory, which is also the central P-trajectory. These power-series have a simple recursive form and are useful in developing "higher-order" analogues of Karmarkar's algorithm. A-trajectories are defined for a general linear program. Using this definition, it is shown that the limit point x,0 of a central A-trajectory on the boundary of the feasible solution polytope P is the center of the unique face of P containing x,0 in its relative interior. Received by the editors October 8, 1986 and, in revised form, June 9, 1987 and March 25, 1988. 1980 Mathematics Subject Classification (1985 Revision). Primary 90C05; Secondary 52A40, 34A34. The first author was partially supported by ONR contract N00014-87-K0214. ( 1989 American Mathematical Society 0002-9947/89 $1.00 + $.25 per page

The construction of analytic diffeomorphisms for exact robot navigation on star worlds

Abstract: The authors consider the construction of navigation functions on configuration spaces whose geometric expressiveness is rich enough for navigation amidst real-world obstacles. They describe a general methodology which extends the construction of navigation functions on sphere worlds to any smoothly deformable space. According to this methodology, the problem of constructing a navigation function is reduced to the construction of a transformation mapping a given space into its model sphere world. The transformation must satisfy certain regularity conditions guaranteeing invariance of the navigation function properties. The authors demonstrate this idea by constructing navigation functions on star worlds: n-dimensional star shaped subsets of E/sup n/ punctured by any finite number of smaller disjoint n-dimensional stars. This construction yields automatically a bounded torque feedback control law which is guaranteed to guide the robot to destination point from almost every initial position without hitting any obstacle. >

Direct and inverse scattering transforms with arbitrary spectral singularities

Abstract: In this paper, we find a way to overcome the deficiency by dropping the boundedness requirement for m. In our method, The bounded solutions of (1.1) are only required in a neighborhood of z=∞ (which is the only pole of zJ)

Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups

Abstract: Supported by the National Science Foundation during 1986–1988 at the Mathematical Sciences Research Institute, Berkeley, and at the Institute for Advanced Study, Princeton.

Feedback stabilization of a linear control system in hilbert space with an a priori bounded control

Abstract: This paper derives a feedback controlf(t), ‖f(t)‖E≦r,r>0, which forces the infinite-dimensional control systemdu/dt=Au+Bf, u(0)=u o ≠H to have the asymptotic behavioru(t)→0 ast→∞ inH. HereA is the infinitesimal generator of aC o semigroup of contractionse At on a real Hilbert spaceH andB is a bounded linear operator mapping a Hilbert space of controlsE intoH. An application to the boundary feedback control of a vibrating beam is provided in detail and an application to the stabilization of the NASA Spacecraft Control Laboratory is sketched.

Global existence for semilinear parabolic systems

Abstract: Global existence results are obtained for semilinear parabolic systems of partial differential equations of the form \[ u_t = D\Delta u + (fu)\quad {\text{on }}\Omega \times (0,T)\] with bounded initial data and various boundary conditions, where D is an $m \times m$ diagonal matrix with positive entries on the diagonal, $\Omega $ is a smooth bounded domain in $R^n $, and $f:R^m \to R^m $ is locally Lipschitz. These results are based on f satisfying a Lyapunov-type condition, and generalize a previous result of l Iollis, Martin, and Pierre [SIAM J. Math. Anal., 18 (1987), pp. 744–761]. This theory is applied to some specific reaction-diffusion and nerve conduction problems.