1,721,056 research outputs found
Two abstract approaches in vectorial fixed point theory
No full textIn this paper a fixed point theory is established for operators defined on Cartesian product spaces. Two abstract approaches are presented in terms of closure operators and of general functionals called measures of deviations from zero resembling the measures of noncompactness. In particular, we give vectorial versions to M"{o}nch's fixed point theorems. An application is included to illustrate the theory
Heterogeneous Vectorial Fixed Point Theorems
No full textIn this paper we obtain fixed point theorems for operators defined on Cartesian product spaces under heterogeneous conditions upon the structure of the factor spaces and the operator components. The main results combine Banach-Perov contraction principle with topological fixed point theorems of Monch type in strong and weak topologies. The results make possible a tinted analysis of the operator systems. An application of the vectorial technique to evolution equations with nonlocal Cauchy conditions is included
An H-infinity approach to optimal control of oxygen and carbon dioxide contents in blood
No full textNonlinear Functional Analysis and Its Applications
Full text linkThis book consists of nine papers covering a number of basic ideas, concepts, and methods of nonlinear analysis, as well as some current research problems. Thus, the reader is introduced to the fascinating theory around Brouwer's fixed point theorem, to Granas' theory of topological transversality, and to some advanced techniques of critical point theory and fixed point theory. Other topics include discontinuous differential equations, new results of metric fixed point theory, robust tracker design problems for various classes of nonlinear systems, and periodic solutions in computer virus propagation models
Stochastic Model Predictive Control with Dynamic Chance Constraints
No full textThis work introduces a stochastic model predictive control scheme for dynamic chance constraints. We consider linear discrete-time systems affected by unbounded additive stochastic disturbance. To synthesize an optimal controller, we solve two subsequent stochastic optimization problems. The first problem concerns finding the maximal feasible probabilities of the dynamic chance constraints. After obtaining the probabilities, the second problem concerns finding an optimal controller using stochastic model predictive control. We solve both stochastic optimization problems by reformulating them into deterministic ones using probabilistic reachable tubes and constraint tightening. We prove that the developed algorithm is recursively feasible and yields closed-loop satisfaction of the dynamic chance constraints. In addition, we will introduce a novel implementation using zonotopes to describe the tightening analytically. Finally, we will end with an example illustrating the method's benefits.</p
Data-driven neural feedforward controller design for industrial linear motors
No full text\u3cp\u3eIn this paper we consider the problem of feedforward controller design for industrial linear motors. These motors are safety-critical high-precision mechatronics systems that pose stringent requirements on the feedforward design: safe and predictable behavior for the desired motion profiles, tracking performance within the 10μ m range in the presence of nonlinear friction and real-time implementation within the 1ms range. We investigate and compare several possibilities to design data-driven feedforward controllers using neural networks (NN) and we show that a two-step inverse estimation method is the most suitable approach, due to robustness to noisy data. We also show that basic knowledge about the system dynamics and the friction behavior can be exploited to design neural feedforward controllers with a simple structure, suitable for real-time implementation in industrial linear motors. The developed data-driven neural feedforward controllers are tested and compared with standard mass-acceleration feedforward and iterative learning controllers in realistic simulations.\u3c/p\u3
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Energy-based localization and multiplicity of radially symmetric states for the stationary p-Laplace diffusion
No full textIt is investigated the role of the state-dependent source-term for the localization by means of the kinetic energy of radially symmetric states for the stationary p-Laplace diffusion. It is shown that the oscillatory behavior of the source-term, with respect to the state amplitude, yields multiple possible states, located in disjoint energy bands. The mathematical analysis makes use of critical point theory in conical shells and of a version of Pucci-Serrin three-critical point theorem for the intersection of a cone with a ball. A key ingredient is a Harnack type inequality in terms of the energetic norm
Implicit elliptic equations via Krasnoselskii–Schaefer type theorems
Full text linkExistence of solutions to the Dirichlet problem for implicit elliptic equations is established by using Krasnoselskii–Schaefer type theorems owed to Burton–Kirk and Gao–Li–Zhang. The nonlinearity of the equations splits into two terms: one term depending on the state, its gradient and the elliptic principal part is Lipschitz continuous, and the other one only depending on the state and its gradient has a superlinear growth and satisfies a sign condition. Correspondingly, the associated operator is a sum of a contraction with a completely continuous mapping. The solutions are found in a ball of a Lebesgue space of a sufficiently large radius established by the method of a priori bounds
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