on simple scheme of finite fixed time control design control laws are designed for stabilisation of a chain of integrators of arbitrary degree in finite and fixed time presented control laws are obtained with use of lyapunov function method and homo

strong detectability and observers conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state the concepts of strong detectability and strong observability introduced before in the literature for discrete time systems only are defined and studied for continuous time systems it is shown that there are two different concepts of strong detectability which coincide for discrete time systems algebraic conditions for either concept are given it is shown that these concepts are intimately related to the existence of strong observers i e observers that only use the output of the plant

finite time stabilization of a perturbed double integrator part i continuous sliding mode based output feedback synthesis the twisting and supertwisting algorithms generating important classes of second order sliding modes sosms are well recognized for their finite time stability and robustness properties in the present paper a continuous modification of the twisting algorithm and an inhomogeneous perturbation of the supertwisting algorithm are introduced to extend the class of sosm s that present the afore mentioned attractive features thus modified the twisting and supertwisting algorithms are utilized in the state feedback synthesis and respectively velocity observer design made for the finite time stabilization of a double integrator if only output measurements are available performance and robustness issues of the resulting output feedback synthesis are illustrated by means of numerical simulations

the bishop phelps bollobas theorem for operators we prove the bishop phelps bollobas theorem for operators from an arbitrary banach space x into a banach space y whenever the range space has property of lindenstrauss we also characterize those banach spaces y for which the bishop phelps bollobas theorem holds for operators from 1 into y s everal examples of classes of such spaces are provided for instance the bishop phelps bollobas theorem holds when the range space is finite dimensional an l1 space for a finite measure a c k space for a compact hausdorff space k or a uniformly convex banach space

finite time stability conditions for non autonomous continuous systems finite time stability is defined for continuous non autonomous systems starting with a result from haimo 1986 we then extend this result to n dimensional non autonomous systems through the use of smooth and non smooth lyapunov functions as in perruquetti and drakunov 2000 one obtains two different sufficient conditions and a necessary one for finite time stability of continuous non autonomous systems

stochastic kolmogorov type system with infinite delay abstract the paper considers a stochastic functional kolmogorov type population system with infinite delay under the general probability measures main aim is to show that the environment noise will not only suppress a potential population explosion but also make the solution be stochastically ultimately bounded and asymptotic stable moreover two stochastic functional lotka volterra equations as examples are provided to illustrate the main results

multiple summing operators on banach spaces abstract in this paper we improve some previous results about multiple p summing multilinear operators by showing that every multilinear form from l 1 spaces is multiple p summing for 1 p 2 the proof is based on the existence of a predual for the banach space of multiple p summing multilinear forms we also show the failure of the inclusion theorem in this class of operators and improve some results of y melendez and a tonge about dominated multilinear operators

on an output feedback finite time stabilization problem studies the problem of finite time output feedback stabilization for the double integrator system a class of output feedback controllers that can achieve global finite time stability for the double integrator system are constructed based on a finite time separation principle furthermore it is shown that the closed loop system resulting from our control law can maintain its local finite time stability regardless of some nonlinear perturbations thus our control law actually applies to a large class of nonlinear second order systems

continuous finite time stabilization of the translational and rotational double integrators a class of bounded continuous time invariant finite time stabilizing feedback laws is given for the double integrator lyapunov theory is used to prove finite time convergence for the rotational double integrator these controllers are modified to obtain finite time stabilizing feedback that avoid unwinding

a novel higher order sliding mode control scheme a higher order sliding mode control algorithm is proposed for a class of uncertain multi input multi output nonlinear systems this problem can be viewed as the flnite time stabilization of a higher order input output dynamic system with bounded uncertainties the developed control scheme is based on geometric homogeneity and sliding mode control the proposed procedure provides explicit conditions on the controller parameters and guarantees robustness against uncertainties an illustrative example of a hovercraft vessel control demonstrates the advantages of the strategy

sliding order and sliding accuracy in sliding mode control the synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered usually what is called sliding mode is employed in such synthesis this sliding mode is characterized in practice by a high frequency switching of the control it turns out that the deviation of the system from its prescribed constraints sliding accuracy is proportional to the switching time delay a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced these algorithms feature a bounded control continuously depending on time with discontinuities only in the control derivative it is also shown that the sliding accuracy is proportional to the square of the switching time delay

analytical and numerical comparisons of biogeography based optimization and genetic algorithms we show that biogeography based optimization bbo is a generalization of a genetic algorithm with global uniform recombination ga gur based on the common features of bbo and ga gur we use a previously derived bbo markov model to obtain a ga gur markov model one bbo characteristic which makes it distinctive from ga gur is its migration mechanism which affects selection pressure i e the probability of retaining certain features in the population from one generation to the next we compare the bbo and ga gur algorithms using results from analytical markov models and continuous optimization benchmark problems we show that the unique selection pressure provided by bbo generally results in better optimization results for a set of standard benchmark problems we also present comparisons between bbo and ga gur for combinatorial optimization problems include the traveling salesman the graph coloring and the bin packing problems

bishop phelps bollobas property for certain spaces of operators abstract we characterize the banach spaces y for which certain subspaces of operators from l 1 into y have the bishop phelps bollobas property in terms of a geometric property of y namely ahsp this characterization applies to the spaces of compact and weakly compact operators new examples of banach spaces y with ahsp are provided we also obtain that certain ideals of asplund operators satisfy the bishop phelps bollobas property

accuracy of some popular non homogeneous 2 sliding modes asymptotic accuracy of nonsingular terminal sliding modes and 2 sliding modes with prescribed convergence law is calculated in the presence of small sampling periods and measurement errors the controllers are shown to have practically equivalent performance

output tracking control of uncertain nonlinear second order systems abstract the solution of a tracking problem for a secondorder nonlinear system with uncertain dynamics and incomplete state measurement is obtained by means of a procedure directly inspired by the solution of the classical minimum time optimal control problem two different types of uncertainty are considered in the paper in the first case a constant bound on the uncertain dynamics is assumed to be known in the second case the bound is a function of both the measurable and the unmeasurable state variable of the system in both cases the possibility of applying the proposed control algorithms is proved to be determined by a proper choice of the control signal features the resulting system is characterized by a suitable feedback switching logic and the convergence of the system trajectory to the desired one or to a vicinity of this latter is proved also in the uncertain case

the bishop phelps bollobas theorem fails for bilinear forms on l1 l1 abstract in this paper we show that the bishop phelps bollobas theorem fails for bilinear forms on l 1 l 1 while it holds for linear operators from l 1 to l

a lindenstrauss theorem for some classes of multilinear mappings abstract under some natural hypotheses we show that if a multilinear mapping belongs to some banach multilinear ideal then it can be approximated by multilinear mappings belonging to the same ideal all whose arens extensions attain their norms at the same point we prove a similar result for the class of symmetric multilinear mappings we see that the quantitative bollobas type version of these results fails in every multilinear ideal

global and exact hosm differentiator with dynamic gains for output feedback sliding mode control in this paper we introduce a global differentiator based on higher order sliding modes hosm and dynamic gains to solve the problem of trajectory tracking via output feedback for a class of uncertain nonlinear plants with arbitrary relative degree and disturbances norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator since the nonlinearities may be state dependent and time varying uniform global stability and robust exact tracking are guaranteed employing the proposed hosm based exact differentiator the obtained results are not restricted to first order sliding mode control feedback but applies for second order sliding mode algorithms twisting super twisting and variable gain super twisting as well as quasi continuous hosm finite time controllers simulations with an aircraft pitch control application illustrate the claimed properties even in the presence of measurement noise

finite time controllers continuous finite time differential equations are introduced as fast accurate controllers for dynamical systems these have qualities superior to controllers which are currently in use in such appl

higher order sliding mode controllers with optimal reaching higher order sliding mode hosm control design is considered for systems with a known permanent relative degree in this paper we introduce the robust fuller s problem that is a robust generalization of the fuller s problem a standard optimal control problem for a chain of integrators with bounded control by solving the robust fuller s problem it is possible to obtain feedback laws that are hosm algorithms of generic order and in addition provide optimal finite time reaching of the sliding manifold a common difficulty in the use of existing hosm algorithms is the tuning of design parameters our methodology proves useful for the tuning of hosm controller parameters in order to assure desired performances and prevent instabilities the convergence and stability properties of the proposed family of controllers are theoretically analyzed simulation evidence demonstrates their effectiveness

technical communique finite time output stabilization with second order sliding modes in this note a class of discontinuous feedback laws that switch over branches of parabolas in the auxiliary state plane is analyzed conditions are provided under which controllers belonging to this class are second order sliding mode algorithms they ensure uniform global finite time output stability for uncertain systems of relative degree two

homogeneity approach to high order sliding mode design it is shown that a general uncertain single input single output regulation problem is solvable only by means of discontinuous control laws giving rise to the so called high order sliding modes the homogeneity properties of the corresponding controllers yield a number of practically important features in particular finite time convergence is proved and asymptotic accuracy is calculated in a very general way in the presence of input noises discrete measurements and switching delays a robust homogeneous differentiator is included in the control structure thus yielding robust output feedback controllers with finite time convergence it is demonstrated that homogeneity features significantly simplify the design and investigation of a new family of high order sliding mode controllers finally simulation results are presented

second order sliding mode control for nonlinear affine systems with quantized uncertainty abstract this paper deals with the design of a second order sliding mode sosm control algorithm able to enhance the closed loop performance depending on the current working conditions the novelty of the proposed approach is the design of a nonsmooth switching line based on the quantization of the uncertainties affecting the system the quantized uncertainty levels allow one to define nested box sets in the auxiliary state space i e the space of the sliding variable and its first time derivative and select suitable control amplitudes for each set in order to guarantee the convergence of the sliding variable to the sliding manifold in a finite time the proposed algorithm is theoretically analyzed proving the existence of an upperbound of the reaching time to the origin through the considered quantization levels

multi operator based biogeography based optimization with mutation for global numerical optimization biogeography based optimization bbo is a new evolutionary optimization based on the science of biogeography for global optimization we propose two extensions to bbo first we propose a new migration operation based multi parent crossover called multi parent migration model which is a generalization of the standard bbo migration operator the new migration model can satisfy a balance of exploration and exploitation second the gaussian mutation operator is integrated into multi operator biogeography based optimization mobbo to enhance its exploration ability and to improve the diversity of population experiments have been conducted on 23 benchmark problems of a wide range of dimensions and diverse complexities simulation results and comparisons demonstrate the proposed mobbo algorithm based multi parent crossover model is better or at least comparable to the bbo pbbo and evolutionary algorithms from literature when considering the quality of the solutions obtained

on the polynomial lindenstrauss theorem abstract under certain hypotheses on the banach space x we show that the set of n homogeneous polynomials from x to any dual space whose aron berner extensions are norm attaining is dense in the space of all continuous n homogeneous polynomials to this end we prove an integral formula for the duality between tensor products and polynomials we also exhibit examples of lorentz sequence spaces for which there is no polynomial bishop phelps theorem but our results apply finally we address quantitative versions in the sense of bollobas of these results

universal single input single output siso sliding mode controllers with finite time convergence an universal controller is constructed formulated in input output terms only which causes the output of any uncertain smooth single input single output siso minimum phase dynamic system with known relative degree to vanish in finite time this allows exact tracking of arbitrary real time smooth signals only one parameter is to be adjusted since the approach is based on higher order finite time convergence sliding modes the control can be made arbitrarily smooth providing for the arbitrarily high tracking accuracy order with respect to the sampling step

global finite time stabilisation by output feedback for a class of uncertain nonlinear systems this article considers the problem of global finite time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field to solve the problem we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities then using the homogeneous domination approach we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite time stable due to the use of a reduced order observer the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators

global finite time stabilization by output feedback for planar systems without observable linearization this note considers the problem of global finite time stabilization by output feedback for a class of planar systems without controllable observable linearization a sufficient condition for the solvability of the problem is established by developing a nonsmooth observer and modifying the adding a power integrator technique we show that an output feedback controller can be explicitly constructed to globally stabilize the systems in finite time as a direct application of the main result global output feedback finite time stabilization is achieved for the double linear integrator systems perturbed by some nonlinear functions which are not necessarily homogeneous

a study of particle swarm optimization particle trajectories particle swarm optimization pso has shown to be an efficient robust and simple optimization algorithm most of the pso studies are empirical with only a few theoretical analyses that concentrate on understanding particle trajectories these theoretical studies concentrate mainly on simplified pso systems this paper overviews current theoretical studies and extend these studies to investigate particle trajectories for general swarms to include the influence of the inertia term the paper also provides a formal proof that each particle converges to a stable point an empirical analysis of multi dimensional stochastic particles is also presented experimental results are provided to support the conclusions drawn from the theoretical findings

output feedback finite time stabilization of disturbed feedback linearizable nonlinear systems a novel methodology for designing multivariable high order sliding mode hosm controllers for disturbed feedback linearizable nonlinear systems is introduced it provides for the finite time stabilization of the origin of the state space by using output feedback only the additional assumptions of algebraic strong observability and smooth enough matched disturbances are required the control problem is solved in two consecutive steps firstly designing an observer based on the measured output and secondly designing of a full state controller computed from a new virtual output with vector relative degree the introduced notion of algebraic strong observability allows recovering the state of the system using the measured output and its derivatives by estimating the required derivatives through the hosm differentiator a finite time convergent observer is constructed

finite time output feedback position and attitude tracking of a rigid body the position and attitude tracking of a rigid body without velocity measurements is addressed dual quaternions are used to describe the coupled rotational and translational motions of the rigid body yielding compact forms of the kinematics and dynamics suitable for control law synthesis an output feedback pose position and attitude tracking controller is then designed by integrating techniques from passivity and homogeneity more precisely a passivity enabling auxiliary system is proposed to provide necessary damping instead of velocity feedback and a homogeneous method is used to ensure finite time convergence the proposed controller guarantees uniform almost global finite time stability of the closed loop system and produces a well defined vector field on the attitude configuration manifold thus avoiding the unwinding phenomenon moreover it can be split to obtain velocity free controllers with finite time convergence for the cases of translation only or rotation only control numerical examples verify the effectiveness of the proposed method

robust finite time output feedback control of perturbed double integrator this paper addresses the problem of finite time output feedback stabilization for the perturbed double integrator system a simple output feedback proportional derivative pd controller is proposed global finite time stability is proven based on lyapunov stability theory and geometric homogeneity technique furthermore it is proven that the proposed controller can maintain local finite time stability regardless of some nonlinear perturbations thus the proposed controller actually can be applied to a large class of uncertain second order nonlinear systems simulations demonstrate the effectiveness of the proposed approach

two sided polynomial ideals on banach spaces abstract classes of homogeneous polynomials between banach spaces have been studied in the last three decades from the perspective of the stability with respect to the composition of a homogeneous polynomial with linear operators in an attempt to explore the underlying nonlinearity in a more consistent way and to bring the subject closer to its roots in complex analysis and also taking into account recent results in the field in this paper we propose the study of classes of homogeneous polynomials that are stable under the composition with homogeneous polynomials

hypercyclic convolution operators on frechet spaces of analytic functions a result of godefroy and shapiro states that the convolution operators on the space of entire functions on c n which are not multiples of identity are hypercyclic analogues of this result have appeared for some spaces of holomorphic functions on a banach space in this work we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators some known results come out as particular cases of this setting we also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the schatten von neumann class

finite time stability and robust control synthesis of uncertain switched systems stability analysis is developed for uncertain nonlinear switched systems while being asymptotically stable and homogeneous of degree q 0 these systems are shown to approach the equilibrium point in finite time restricted to second order systems this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations based on this fundamental property switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m vector relative degree 2 2 t the controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts the proposed synthesis procedure is illustrated via application to a friction servo motor

finite time stabilization of nonlinear systems with parametric and dynamic uncertainties in this note non smooth finite time stabilization of nonlinear systems with parametric and dynamic uncertainties is investigated to solve this problem the input to state stability property is used to characterize unmeasured dynamic uncertainties a constructive partial state control design is proposed on the basis of involved combined use of lyapunov backstepping and input to state stability techniques under small gain type local conditions a solution for the finite time regulation of a class of uncertain nonlinear systems is obtained

adaptive differential evolution algorithm for multiobjective optimization problems in this paper a new adaptive differential evolution algorithm adea is proposed for multiobjective optimization problems in adea the variable parameter f based on the number of the current pareto front and the diversity of the current solutions is given for adjusting search size in every generation to find pareto solutions in mutation operator and the select operator combines the advantages of de with the mechanisms of pareto based ranking and crowding distance sorting adea is implemented on five classical multiobjective problems the results illustrate that adea efficiently achieves two goals of multiobjective optimization problems find the solutions converge to the true pareto front and uniform spread along the front

norm attaining bilinear forms onl1 0 1 abstract we show that the set of norm attaining bilinear forms onl1 0 1 is not dense in the space of all continuous bilinear forms

technical communique input output finite time stabilization of linear systems bounded input bounded output bibo stability is usually studied when only the input output behavior of a dynamical system is of concern the present paper investigates the analogous concept in the framework of finite time stability fts namely the input output fts io fts fts has been already investigated in several papers in terms of state boundedness whereas in this work we deal with the characterization of the input output behavior sufficient conditions are given concerning the class of l 2 and l input signals for the analysis of io fts and for the design of a static state feedback controller guaranteeing io fts of the closed loop system the effectiveness of the proposed results is eventually illustrated by means of some numerical examples

output input stability and minimum phase nonlinear systems this paper introduces and studies the notion of output input stability which represents a variant of the minimum phase property for general smooth nonlinear control systems the definition of output input stability does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics in the spirit of the input to state stability philosophy it requires the state and input of the system to be bounded by a suitable function of the output and derivatives of the output modulo a decaying term depending on initial conditions the class of output input stable systems thus defined includes all affine systems in global normal form whose internal dynamics are input to state stable and also all left invertible linear systems whose transmission zeros have negative real parts as an application we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control

a multilinear lindenstrauss theorem abstract we show that the set of n linear mappings on a product of n banach spaces such that all their arens extensions attain their norms at the same element is norm dense in the space of all bounded n linear mappings