1,236 research outputs found
Homogeneous Artificial Neural Network
The paper proposes an artificial neural network (ANN) being a global
approximator for a special class of functions, which are known as generalized
homogeneous. The homogeneity means a symmetry of a function with respect to a
group of transformations having topological characterization of a dilation. In
this paper, a class of the so-called linear dilations is considered. A
homogeneous universal approximation theorem is proven. Procedures for an
upgrade of an existing ANN to a homogeneous one are developed. Theoretical
results are supported by examples from the various domains (computer science,
systems theory and automatic control)
Fixed-time Stabilization with a Prescribed Constant Settling Time by Static Feedback for Delay-Free and Input Delay Systems
A static non-linear homogeneous feedback for a fixed-time stabilization of a
linear time-invariant (LTI) system is designed in such a way that the settling
time is assigned exactly to a prescribed constant for all nonzero initial
conditions. The constant convergence time is achieved due to a dependence of
the feedback gain of the initial state of the system. The robustness of the
closed-loop system with respect to measurement noises and exogenous
perturbations is studied using the concept of Input-to-State Stability (ISS).
Both delay-free and input delay systems are studied. Theoretical results are
illustrated by numerical simulations
The Alestle - Vol. 58 No. 22 - 11/08/2005
Vol. 58 No. 2
Generalized Homogeneous Rigid-BodyAttitude Control
The attitude tracking problem for a full-actuated rigid body in 3D is studied
using a impulsive system model based on Lie algebra so(3). A nonlinear
homogeneous controller is designed to globally track a smooth attitude
trajectory in a finite or a (nearly) fixed time. A global settling time
estimate is obtained, which is easily adjustable by tuning the homogeneity
degree. The local input-to-state stability is proven. Simulations illustrating
the performance of the proposed algorithm are presented
On Optimal Control Problems for Generalized Homogeneous Systems
The paper deals with optimal control problems for plants modeled by non-linear ordinary differential equations with homogeneous (in a generalized sense) right hand sides. The classical tools of optimal control theory, namely, Dynamic Programming and Maximum Principle are refined for generalized homogeneous control systems
Input-to-State Stability of Homogeneous Infinite Dimensional Systems with Locally Lipschitz Nonlinearities
International audienceThe Input-to-State Stability (ISS) of homogeneous evolution equations in Banach spaces with unbounded linear operators and locally Lipschitz nonlinearities in the right-hand sides is studied. A new homogeneous converse Lyapunov theorem is presented. Similarly to finite-dimensional models, it is shown that the uniform asymptotic stability of an unperturbed homogeneous evolution equation implies its ISS with respect to homogeneously involved exogenous inputs
On Homogeneous Approximations, Stability and Robustness of Infinite Dimensional Systems
The paper generalizes the concept of homogeneous approximations to a class of unbounded operators satisfying certain regularity assumptions. Stability and robustness of locally homogeneous abstract control systems are studied. The viscous Burgers equation and its nonlinear modifications are considered as illustrative examples
Finite/fixed-time Stabilization of Linear Systems with States Quantization
This paper develops a homogeneity-based approach to finite/fixed-time
stabilization of linear time-invariant (LTI) system with quantized
measurements. A sufficient condition for finite/fixed-time stabilization of
multi-input LTI system under states quantization is derived. It is shown that a
homogeneous quantized state feedback with logarithmic quantizer can guarantee
finite/fixed-time stability of the closed-loop system provided that the
quantization is sufficiently dense. Theoretical results are supported with
numerical simulations
Sliding Mode Control Design Using Canonical Homogeneous Norm
International audienceThe problem of sliding mode control design for nonlinear plant is studied. Necessary and sufficient conditions of quadratic-like stability (stabi-lizability) for nonlinear homogeneous (control) system are obtained. Sufficient conditions of robust stability/stabilizability are deduced. The results are supported with academic examples of sliding mode control design
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