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This paper addresses the systematic approach to design formation control for kinematic model of unicycle-type nonholonomic mobile robots. These robots are difficult to stabilize and control due to their nonintegrable constraints. The difficulty of control increases when there is a requirement to control a cluster of nonholonomic mobile robots in specific formation. In this paper, the design of the control scheme is presented in a three-step process. First, a robust state-feedback point-to-point stabilization control is designed using sliding mode control. In the second step, the controller is modified so as to address the tracking problem for time-varying reference trajectories. The proposed control scheme is shown to provide the desired robustness properties in the presence of the parameter variation, in the region of interest. Finally, in third step, tracking problem of a single nonholonomic mobile robot extends to formation control for a group of mobile robots in the leader–follower scenario using integral terminal- based sliding mode control augmented with stabilizing control. Starting with the transformation of the mathematical model of robots, the proposed controller ensures that the robots maintain a constant distance between each other to avoid collision. The main problem with the proposed controller is that it requires all states specially velocities. Therefore, the state-feedback control scheme is then extended to output feedback by incorporating a highgain observer. With the help of Lyapunov analysis and appropriate simulations, it is shown that the proposed output-feedback control scheme achieves the required control objectives. Furthermore, the closed loop system trajectories reach to desired equilibrium point in finite time while maintaining the special pattern.
In this paper we are concerned with the well-posedness and the exponential stabilization of the generalized Korteweg–de Vries–Burgers equation, posed on the whole real line, under the effect of a damping term. Both problems are investigated when the exponent p in the nonlinear term ranges over the interval [1, 5). We first prove the global well-posedness in Hs(ℝ) for 0 ≤ s ≤ 3 and 1 ≤ p < 2, and in H3(ℝ) when p ≥ 2. For 2 ≤ p < 5, we prove the existence of global solutions in the L2-setting. Then, by using multiplier techniques and interpolation theory, the exponential stabilization is obtained with an indefinite damping term and 1 ≤ p < 2. Under the effect of a localized damping term the result is obtained when 2 ≤ p < 5. Combining multiplier techniques and compactness arguments, we show that the problem of exponential decay is reduced to proving the unique continuation property of weak solutions. Here, the unique continuation is obtained via the usual Carleman estimate.
We study the C*-algebras associated with upper semi-continuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer–Raeburn ‘stabilization trick’, we construct from each such bundle a groupoid dynamical system whose associated Fell bundle is equivalent to the original bundle. The upshot is that the full and reduced C*-algebras of any saturated upper semi-continuous Fell bundle are stably isomorphic to the full and reduced crossed products of an associated dynamical system. We apply our results to describe the lattice of ideals of the C*-algebra of a continuous Fell bundle by applying Renault's results about the ideals of the C*-algebras of groupoid crossed products. In particular, we discuss simplicity of the Fell-bundle C*-algebra of a bundle over G in terms of an action, described by Ionescu and Williams, of G on the primitive-ideal space of the C*-algebra of the part of the bundle sitting over the unit space. We finish with some applications to twisted k-graph algebras, where the components of our results become more concrete.
The effects of increasing nickel contamination of soil on the update of selected microelements by Brassica juncea L. in the presence of raw halloysite (RH) and halloysite modified by thermal treatment (calcination) at 650°C (MH) were investigated experimentally. Such treatment causes partial dehydroxylation and enhances mineral-adsorption properties towards cations. In a vegetative-pot experiment, four different levels of Ni contamination, i.e. 0 (control), 80, 160, 240 and 320 mg kg−1 were applied in the form of an analytical-grade NiSO4·7H2O solution mixed thoroughly with the soil. Among the minerals which were added to soil to alleviate the negative impact of Ni on plant biomass, MH had a particularly beneficial effect on the growth of B. juncea L. The amount of Ni, Zn, Cu, Mn, Pb and Cr in Indian mustard depended on the Ni dose and type of accompanying mineral structure. The average accumulation of trace elements in B. juncea L. grown in Ni-contaminated soil follow the decreasing order Mn > Zn > Cu > Ni > Pb > Cr.
Initial–boundary-value problems for the two-dimensional Zakharov–Kuznetsov equation posed on bounded rectangles and on a strip are considered. Spectral properties of a linearized operator and critical sizes of domains are studied. An exponential decay rate of regular solutions for the original nonlinear problems is proved.
We present low-dimensional functionalization and characterization of electron density of states using highly correlated/precisely guided proton beam trajectories and a silicon nanocrystal as a target, representing at a same time a versatile nanolaser technique capable for coherent control of atomic quantum states and for scanning the interior of an atom with resolution comparable to 10% of the Bohr radius.
We consider a damped abstract second order evolution equation with an additional
vanishing damping of Kelvin–Voigt type. Unlike the earlier work by Zuazua and Ervedoza, we
do not assume the operator defining the main damping to be bounded. First, using a
constructive frequency domain method coupled with a decomposition of frequencies and the
introduction of a new variable, we show that if the limit system is exponentially stable,
then this evolutionary system is uniformly − with respect to the calibration parameter −
exponentially stable. Afterwards, we prove uniform polynomial and logarithmic decay
estimates of the underlying semigroup provided such decay estimates hold for the limit
system. Finally, we discuss some applications of our results; in particular, the case of
boundary damping mechanisms is accounted for, which was not possible in the earlier work
We develop in this paper efficient and robust numerical methods for solving anisotropic Cahn-Hilliard systems. We construct energy stable schemes for the time discretization of the highly nonlinear anisotropic Cahn-Hilliard systems by using a stabilization technique. At each time step, these schemes lead to a sequence of linear coupled elliptic equations with constant coefficients that can be efficiently solved by using a spectral-Galerkin method. We present numerical results that are consistent with earlier work on this topic, and also carry out various simulations, such as the linear bi-Laplacian regularization and the nonlinear Willmore regularization, to demonstrate the efficiency and robustness of the new schemes.
In this paper we propose and analyze stable variational formulations for convection diffusion problems starting from concepts introduced by Sangalli. We derive efficient and reliable a posteriori error estimators that are based on these formulations. The analysis of resulting adaptive solution concepts, when specialized to the setting suggested by Sangalli’s work, reveals partly unexpected phenomena related to the specific nature of the norms induced by the variational formulation. Several remedies, based on other specifications, are explored and illustrated by numerical experiments.
For the locally symmetric space X attached to an arithmetic subgroup of an algebraic group G of ℚ-rank r, we construct a compact manifold by gluing together 2r copies of the Borel–Serre compactification of X. We apply the classical Lefschetz fixed point formula to and get formulas for the traces of Hecke operators ℋ acting on the cohomology of X. We allow twistings of ℋ by outer automorphisms η of G. We stabilize this topological trace formula and compare it with the corresponding formula for an endoscopic group of the pair (G,η) . As an application, we deduce a weak lifting theorem for the lifting of automorphic representations from Siegel modular groups to general linear groups.
We study in an abstract setting the indirect stabilization of systems of two wave-like
equations coupled by a localized zero order term. Only one of the two equations is
directly damped. The main novelty in this paper is that the coupling operator is not
assumed to be coercive in the underlying space. We show that the energy of smooth
solutions of these systems decays polynomially at infinity, whereas it is known that
exponential stability does not hold (see [F. Alabau, P. Cannarsa and V. Komornik,
J. Evol. Equ. 2 (2002) 127–150]). We give applications of
our result to locally or boundary damped wave or plate systems. In any space dimension, we
prove polynomial stability under geometric conditions on both the coupling and the damping
regions. In one space dimension, the result holds for arbitrary non-empty open damping and
coupling regions, and in particular when these two regions have an empty intersection.
Hence, indirect polynomial stability holds even though the feedback is active in a region
in which the coupling vanishes and vice versa.
In this paper we study a one dimensional model of ferromagnetic nano-wires of finite
length. First we justify the model by Γ-convergence arguments.
Furthermore we prove the existence of wall profiles. These walls being unstable, we
stabilize them by the mean of an applied magnetic field.
This paper deals with feedback stabilization of second order equations of
ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[,
where A0 is a densely defined positive selfadjoint linear operator on a
real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is
proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and
Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the
strong stabilization. This result is derived from a general compactness
theorem for semigroup with compact resolvent and solves several open problems.
We derive a residual a posteriori error estimates for the subscales stabilization of
convection diffusion equation. The estimator yields upper bound on the error which is
global and lower bound that is local
We study the stabilization of global solutions of the
Kawahara (K) equation in a bounded interval, under the effect of
a localized damping mechanism. The Kawahara equation is a model
for small amplitude long waves. Using multiplier techniques and
compactness arguments we prove the
exponential decay of the solutions of the (K) model. The proof
requires of a unique continuation theorem and the smoothing effect
of the (K) equation on the real line, which are proved in this work.
In this work, we propose a methodology for the expression of necessary and
sufficient Lyapunov-like conditions for the existence of stabilizing
feedback laws. The methodology is an extension of the well-known Control
Lyapunov Function (CLF) method and can be applied to very general nonlinear
time-varying systems with disturbance and control inputs, including both
finite and infinite-dimensional systems. The generality of the proposed
methodology is also reflected upon by the fact that partial stability with
respect to output variables is addressed. In addition, it is shown that the
generalized CLF method can lead to a novel tool for the explicit design of
robust nonlinear controllers for a class of time-delay nonlinear systems
with a triangular structure.
In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls.
In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of the two-dimensional Burgers equation. We end this paper with a few numerical simulations, comparing the performance of the nonlinear law with the linear one.
We prove global internal controllability in large time for the nonlinear Schrödinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near 0. We use Bourgain spaces to prove this result on L2. We also get a regularity result about the control if the data are assumed smoother.
In this work we consider a stabilized Lagrange multiplier method in order to
approximate the Coulomb frictional contact model in linear elastostatics. The
particularity of the method is that no discrete inf-sup condition is needed. We
study the existence and the uniqueness of solution of the discrete problem.
This paper analyzes the stabilization problem from the energy point of view. Perturbations are detected by the gyros and categorized according to the constraints on the zero-moment point, energy, and walking pattern. Ankle torque is exerted to extend the linear inverted pendulum mode (LIPM). Compensation movement is computed according to the analysis on the energy of LIPM and the influence of disturbance to the energy. The experimental results from both the simulation and the physical robot not only proved effective but also explain various human reactions to disturbance in locomotion.