localized turing patterns in nonlinear optical cavities abstract the subcritical turing instability is studied in two classes of models for laser driven nonlinear optical cavities in the first class of models the nonlinearity is purely absorptive with arbitrary intensity dependent losses in the second class the refractive index is real and is an arbitrary function of the intracavity intensity through a weakly nonlinear analysis a ginzburg landau equation with quintic nonlinearity is derived thus the maxwell curve which marks the existence of localized patterns in parameter space is determined in the particular case of the lugiato lefever model the analysis is continued to seventh order yielding a refined formula for the maxwell curve and the theoretical curve is compared with recent numerical simulation by gomila et al d gomila a scroggie w firth bifurcation structure of dissipative solitons physica d 227 2007 70 77

spatial structure of time periodic solutions of the ginzburg landau equation abstract we study solutions of the form a x t a x ei t of the complex ginzburg landau equation i a t a xx a a 2 a near those of the integrable limit the nonlinear schrodinger equation i a t a xx a 2 a real we show that spatially periodic and quasiperiodic solutions as well as heteroclinic orbits to them exist in addition to the spatially decaying homoclinic solitions found by hocking and stewartson 1972 we speculate briefly on spatially chaotic solutions

periodic and quasi periodic solutions of degenerate modulation equations abstract in some circumstances degenerations it is essential to add higher order nonlinear coefficients to a ginzburg landau type modulation equation which only has one cubic nonlinearity in this paper we study these degenerate modulation equations we consider the important situation in which the equation has real coefficients and the case of coefficients with small imaginary parts first we determine the stability of periodic solutions the stationary problem is like in the non degenerate case integrable there exist families of quasi periodic and homoclinic solutions this system is perturbed by considering modulation equations with coefficients with small imaginary parts we establish that there exists an unbounded domain in parameter space in which the modulation equation has quasi periodic solutions moreover we show that there is a manifold of codimension 1 in parameter space on which the homoclinic solutions survive the perturbation

brief paper set invariance and performance analysis of linear systems via truncated ellipsoids the objective of this paper is to develop numerically simple and effective methods for system analysis using truncated ellipsoids the paper studies linear time invariant systems subject to persistent disturbance and state constraint the maximal output under a set of initial conditions and the overshoot under a given step input are estimated attempts are also made to detect an invariant set as large as possible within state constraint the results are based on the set invariance condition for the truncated ellipsoid and a characterization of the set where the output possibly reaches a local extrema the analysis problems are converted into optimization problems whose constraints become linear matrix inequalities when a few variables are fixed numerical examples demonstrate the effectiveness of the truncated ellipsoid and the proposed methods

on the transition from the ginzburg landau equation to the extended fisher kolmogorov equation abstract the ginzburg landau gl equation generically describes the behaviour of small perturbations of a marginally unstable basic state in systems on unbounded domains in this paper we consider the transition from this generic situation to a degenerate co dimension 2 case in which the gl approach is no longer valid instead of studying a general underlying model problem we consider a two dimensional system of coupled reaction diffusion equations in one spatial dimension we show that near the degeneration the behaviour of small perturbations is governed by the extended fisher kolmogorov efk equation at leading order the relation between the gl equation and the efk equation is quite subtle but can be analysed in detail the main goal of this paper is to study this relation which we do asymptotically the asymptotic analysis is compared to numerical simulations of the full reaction diffusion system as one approaches the co dimension 2 point we observe that the stable stationary periodic patterns predicted by the gl equation evolve towards various different families of stable stationary but not necessarily periodic so called multi bump solutions in the literature these multi bump patterns are shown to exist as solutions of the efk equation but there is no proof of the asymptotic stability of these solutions our results suggest that these multi bump patterns can also be asymptotically stable in large classes of model problems

a simple method and its applications to nonlinear partial differential equations abstract in this paper a simple method is proposed for constructing more general exact solutions of nonlinear partial differential equations we choose the camassa and holm degasperis and procesi equation and the generalized b family equations to illustrate the validity and advantages of the method as a result many new and more general exact solutions are obtained some previous results are extended

fronts pulses sources and sinks in generalized complex ginzberg landau equations an important clement in the long time dynamics of pattern forming systems is a class of solutions we will call coherent structures these are states that are either themselves localized or that consist of domains of regular patterns connected by localized defects or interfaces this paper summarizes and extends recent work on such coherent structures in the one dimensional complex ginzburg landau equation and its generalizations for which rather complete information can be obtained on the existence and competition of fronts pulses sources and sinks for the special subclass of uniformly translating structures the solutions are derived from a set of ordinary differential equations that can be interpreted as a flow in a three dimensional phase space fixed points of the flow correspond to the two basic building blocks of coherent structures uniform amplitude states and evanescent waves whose amplitude decreases smoothly to zero a study of the stability of the fixed points under the flow leads to results on the existence and multiplicity of the different coherent structures the dynamical analysis of the original partial differential equation focusses on the competition between pulses and fronts and is expressed in terms of a set of conjectures for front propagation that generalize the marginal stability and pinch point approaches of earlier authors these rules together with an exact front solution whose dynamics plays an important role in the selection of patterns yield an analytic expression for the upper limit of the range of existence of pulse solutions as well as a determination of the regions of parameter space where uniformly translating fron t solutions can exist extensive numerical simulations show consistency with these rules and conjectures for the existence of fronts and pulses in the parameter ranges where no uniformly translating fronts can exist examples are shown of irregularly spreading fronts that generate strongly chaotic regions as well as nonuniformly translating fronts that lead to uniform amplitude states recent perturbative treatments based on expansions about the nonlinear schr6dinger equation are generalized to perturbations of the cubic quintic and derivative schr idinger equations for which both pulses and fronts exist in the unperturbed system comparison of the results with the exact solutions shows that the perturbation theory only yields a subset of the relevant solutions nevertheless those that are obtained are found to be consistent with the general conjectures and in particular they provide an analytic demonstration of front pulse competition while the discussion of the competition between fronts and pulses focusses on the complex ginzburg landau equation with quintic terms and a subcritical bifurcation a number of results are also presented for the cubic equation in particular the existence of a family of moving source solutions derived by bekki and nozaki for this equation contradicts the naive counting arguments we attribute this contradiction to a hidden symmetry of the solution but have not been able to show explicitly how this symmetry affects the phase space orbits

on the eckhaus instability for spatially periodic patterns abstract the range of stable wavevectors is near the threshold for appearance of periodic patterns in quasi one dimensional systems limited by the long wavelength eckhaus instability at this instability saddle point solutions characterizing the wavelength changing processes inside the stable range merge with the periodic solutions we first analyse this bifurcation near threshold using the amplitude expansion in lowest order then a nonlinear equation for the evolution of slow modulations of the periodic pattern far from threshold but near the eckhaus instability is derived and used to analyse the universal properties of the eckhaus bifurcation more detailed information concerning the spatial symmetry of saddle point solutions is obtained by numerical integration of simple model systems

convergent upper bounds of peak response of lti and polytopic ltv systems through lmis abstract this paper addresses the problem of determining the response peak of dynamical systems a classical problem in control systems the paper starts by considering the impulse response of linear time invariant lti systems a linear matrix inequality lmi condition for establishing upper bounds of the sought peak is proposed by embedding the trajectory onto the level set of a polynomial and by introducing a projection technique for evaluating the extension of this set this condition is sufficient for any degree of the polynomial which has to be chosen a priori and is also necessary whenever this degree is large enough hence the proposed methodology is extended to address the impulse response of polytopic linear time varying ltv systems in particular linear systems affected linearly by structured time varying uncertainty constrained into a polytope lastly generalizations to various responses and specializations to some structures are also presented as shown by several examples which include randomly generated systems and physical systems the proposed conditions may provide significantly less conservative results than the existing lmi methods

probabilistic output admissible set for systems with time varying uncertainties this paper considers time varying uncertain constrained systems and develops a method for computing a probabilistic output admissible poa set this set consists of the initial states probabilistically assured to satisfy the constraint the time invariant counterpart has already been investigated in hatanaka and takaba computations of probabilistic output admissible set for uncertain constrained systems automatica 44 2 2008 to appear we first define the poa set for time varying uncertainties with finite dimensional probability space then we show that an algorithm similar to hatanaka and takaba computations of probabilistic output admissible set for uncertain constrained systems automatica 44 2 2008 to appear provides the poa set also in the time varying case as long as an upper bound of a what we call future output admissibility foa index is available we moreover present two methods for computing the upper bound of the foa index probabilistic and deterministic methods a numerical simulation demonstrates the effectiveness of our algorithm

on the degenerated soft mode instability we consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems where the character of the bifurcation changes from sub to supercritical behaviour starting from a general equation of motion the full amplitude equation is derived systematically and formulae for the dependence of the coefficients on the system parameters are obtained we emphasize the importance of nonlinear derivative terms in the amplitude equation for the behaviour in the vicinity of the bifurcation point in particular the numerical values of the corresponding coefficients determine the region of coexistence between the stable trivial solution and stable spatially periodic patterns our approach clearly shows that similar considerations fail for the case of oscillatory instabilities

nonquadratic lyapunov functions for robust stability analysis of linear uncertain systems in this note we derive conditions of existence of a homogeneous polynomial lyapunov function of an arbitrary even degree establishing global asymptotic stability of linear system with box bounded uncertainty verification of these conditions is reduced to solving a convex minimization problem we produce numerical examples that demonstrate significant improvement in estimates of admissible uncertainty bounds compared with estimates obtained via the most commonly used quadratic lyapunov functions

on asymptotically equivalent shallow water wave equations abstract the integrable third order korteweg de vries kdv equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves however at quadratic order this asymptotic expansion produces an entire family of shallow water wave equations that are asymptotically equivalent to each other under a group of nonlinear non local normal form transformations introduced by kodama in combination with the application of the helmholtz operator these kodama helmholtz kh transformations are used to present connections between shallow water waves the integrable fifth order kdv equation and a generalization of the camassa holm ch equation that contains an additional integrable case the dispersion relation of the full water wave problem and any equation in this family agree to fifth order the travelling wave solutions of the ch equation are shown to agree to fifth order with the exact solution

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

on the nonlinear stability of plane waves for the ginzburg landau equation i consider the nonlinear stability of plane wave solutions to a ginzburg landau equation with additional fifth order terms and cubic terms containing spatial derivatives i show that under the constraint that the diffusion coefficient be real these waves are stable furthermore it is shown that the radial component of the perturbation decays at a faster rate than the phase component of the perturbation as t the result is also applicable to the classical ginzburg landau equation 1994 john wiley sons inc

breaking the hidden symmetry in the ginzburg landau equation in this paper we study localised traveling solutions to a ginzburg landau equation to which we have added a small o e 0 e 1 quintic term we consider this term as a model for the higher order nonlinearities which appear in the derivation of the ginzburg landau equation by a combination of a geometrical approach and an explicit perturbation analysis we are able to relate the family of bekki nozaki solutions of the cubic equation n bekki and b nozaki 1985 phys lett a 110 133 135 to a curve of co dimension 2 homoclinic bifurcations in parameter space thus we are able to interpret the hidden symmetry which has been conjectured to explain the existence of the bekki nozaki solutions from the point of view of bifurcation theory we show that the quintic term breaks this hidden symmetry and that the one parameter family of bekki nozaki solutions is embedded in a two parameter family of homoclinic solutions which exist at a co dimension 1 homoclinic bifurcation furthermore we show mainly by geometrical arguments that the addition of the small quintic term can create large families of traveling localised structures that cannot exist in the cubic case these solutions exist in open subsets of the parameter space and correspond to structurally stable multi or n circuit heteroclinic orbits in an ode reduction and have a monotonically decreasing increasing amplitude except for a number n of relatively fast jumps

weakly subcritical stationary patterns eckhaus instability and homoclinic snaking the transition from subcritical to supercritical stationary periodic patterns is described by the one dimensional cubic quintic ginzburg landau equation at a axx i a1 a 2 ax a2a 2 a b a 2 a a 4 a w here a x t represents the pattern amplitude and the coefficients a1 a2 a ndb are real the conditions for eckhaus instability of periodic solutions are determined and the resulting spatially modulated states are computed some of these evolve into spatially localized structures in the vicinity of a maxwell point while others resemble defect states the results are used to shed light on the behavior of localized structures in systems exhibiting homoclinic snaking during the transition from subcriticality to supercriticality

global well posedness for the generalized 2d ginzburg landau equation abstract the local well posedness for the generalized two dimensional 2d ginzburg landau equation is obtained for initial data in h s r 2 s 1 2 the global result is also obtained in h s r 2 s 1 2 under some conditions the results on local and global well posedness are sharp except the endpoint s 1 2 we mainly use the tao s k z multiplier method to obtain the trilinear and multilinear estimates

the integral bifurcation method and its application for solving a family of third order dispersive pdes abstract in this paper an improved method named the integral bifurcation method is introduced in order to demonstrate its effectiveness for obtaining travelling wave solutions of the nonlinear wave equations a family of third order dispersive partial differential equations which were given by a degasperis d holm and a hone are studied many integral bifurcations are obtained for different parameter conditions by using these integral bifurcations many travelling wave solutions such as loop soliton solutions solitary wave solutions cusp soliton solutions and periodic wave solutions are obtained in particular under the conditions c 1 0 c 2 c 3 1 a very peculiar periodic wave solution is obtained

robust performance with fixed and worst case signals for uncertain time varying systems in this paper we focus our attention on the determination of upper bounds of the l norm of the output of a linear discrete time dynamic system driven by a step input in the presence of both persistent unknown but l bounded disturbances and memoryless time varying model uncertainty for the same type of systems we also analyze the transient behavior of the step response in terms of its overshoot the problem is solved in a constructive way by determining appropriate invariant sets contained in a given convex region finally we show how to extend these results to continuous time systems

nonlinear instability in plane poiseuille flow a quantitative comparison between the methods of amplitude expansions and the method of multiple scales this paper shows that two different expansion procedures for hydrodynamical stability problems are equivalent the method of multiple scales of stewartson stuart 1971 is extended to calculate the stream function up to order epsilon 2 watson s 1960 rigorous amplitude expansion of the solution of the navier stokes equations is also used to calculate the stream function up to the same order of magnitude and a complete equivalence between the two results is found an analysis of the eckhaus model equations has been made and the results are equivalent

slow time periodic solutions of the ginzburg landau equation in this paper we study the behaviour of solutions of the form if z t q z e i wt e 1 of the rescaled ginzburg landau equation k 1 1 ib l kl2 k 1 ia kzz for a ca b eb w plays the role of free parameter this leads to a perturbation analysis on a complex duffing equation similar to the analysis of holmes physica d 23 1986 84 we show that the spatial quasiperiodic solutions of the unperturbed e 0 case disappear due to the perturbation and prove the existence of degenerated periodic solutions which oscillate through the origin we also establish the existence of several types of heteroclinic orbits connecting counterrotating periodic patterns

ultimate boundedness control for uncertain discrete time systems via set induced lyapunov functions in this note linear discrete time systems affected by both parameter and input uncertainties are considered the problem of the synthesis of a feedback control assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence is investigated it is shown that the problem has a solution if and only if there exists a certain lyapunov function which does not belong to a preassigned class of functions e g the quadratic ones but it is determined by the target set in which ultimate boundedness is desired one of the advantages of this approach is that we may handle systems with control constraints no matching assumptions are made for systems with linearly constrained uncertainties it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets the resulting compensator may be implemented as a linear variable structure control

on the well posedness problem and the scattering problem for the dullin gottwald holm equation in this paper we study the well posedness of the cauchy problem and the scattering problem for a new nonlinear dispersive shallow water wave equation the so called dgh equation which was derived by dullin gottwald and holm the issue of passing to the limit as the dispersive parameter tends to zero for the solution of the dgh equation is investigated and the convergence of solutions to the dgh equation as 2 0 is studied and the scattering data of the scattering problem for the equation can be explicitly expressed the new exact peaked solitary wave solutions are obtained in the dgh equation after giving the condition of existing peakon in the dgh equation it turns out to be nonlinearly stable for the peakon in the dgh equation

global existence and blow up solutions for a nonlinear shallow water equation considered herein are the problems of the existence of global solutions and the formation of singularities for a new nonlinear shallow water wave equation derived by dullin gottward and holm blow up can occur only in the form of wave breaking a wave breaking mechanism for solutions with certain initial profiles is described in detail and the exact blow up rate is established the blow up set for a class of initial profiles and lower bounds of the existence time of the solution are also determined

new exact periodic wave solutions for the dullin gottwald holm equation abstract in this paper the dullin gottwald holm equation is studied using semi inverse method and integral bifurcation method new periodic waves such as peakon like periodic wave compacton like periodic wave and singular periodic wave are found and their dynamical behaviors and certain strange phenomena are explained using the proposed criterion the exact parametric representations of these waves are also presented

a set induced norm approach to the robust control of constrained systems most realistic control problems involve both some type of time domain constraints and model uncertainty however the majority of controller design procedures currently available focus only on one aspect of the problem with only a handful of methods capable of simultaneously addressing both issues recently it has been proposed to address this class of problems by using a constrained robustness measure generated by a constraint set induced operator norm to assess the stability properties of a family of systems in this paper the properties of this constrained robustness measure are explored and the theoretical framework is extended to include control as well as state constraints these results are applied to the problem of designing fixed order stabilizing feedback controllers for systems subject to structured parametric model uncertainty and time domain constraints

performance robustness of discrete time systems with structured uncertainty given an interconnection of a nominal discrete time plant and a stabilizing controller together with structured norm bounded nonlinear time varying perturbations necessary and sufficient conditions for robust stability and performance of the system are provided it is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem the resulting stability robustness problem is shown to be equivalent to a simple algebraic one the solution of which provides the desired necessary and sufficient conditions for performance stability robustness these conditions provide an effective tool for robustness analysis and can be applied to a large class of problems in particular it is shown that some known results can be obtained immediately as special cases of these conditions

exact peaked wave solution of ch γ equation by the first integral method abstract by using the first integral method which is based on the ring theory of commutative algebra an exact peaked wave solution to ch equation has been obtained directly the obtained solution agrees well with the previously known one in the literature however the first integral method is easier and quicker than other traditional techniques this indicates that the validity and great potential of the first integral method in solving complicated solitary wave problems

strong selection or rejection of spatially periodic patterns in degenerate bifurcations abstract when studying bifurcating space periodic solutions one often has a situation common in many problems of fluid dynamics in which in the r k plane r a control parameter such as reynolds number k wave number the passage from linear stability to instability is characterized by a parabola like curve having a minimum at r c k c we analyse classes of problems in which the coefficients of nonlinear terms in the amplitude equation go through zero near k c various examples of such degenerate problems can be found in the literature but have not been studied yet we give an extensive classification of bifurcation pictures which display rather unusual behaviour we further study the stability of these periodic solutions subject to quite general perturbation we find as a general result that all bifurcating solutions are unstable except for a small neighbourhood of a curve in the r k plane there is hence a strong selection mechanism of periodic patterns which fixes for each value of r with a very small uncertainty the wave number of the stable bifurcating periodic solution for one class of problems the curve continues to exist for all values of r for which our theory is consistent for another class the curve stops at a value r r c for r r all bifurcating periodic solutions are unstable in this case instability provides a mechanism of rejection of all periodic patterns in the last section we analyse the particular case of the blasius boundary layer flow

1 soliton solution and conservation laws of the generalizeddullin gottwald holm equation abstract this paper obtains the 1 soliton solution of the generalized dullin gottwald holm equation by the aid of solitary wave ansatz subsequently the conserved quantities are obtained by utilising the interplay between the multipliers and underlying lie point symmetry generators of the equation

application of exp function method to dullin gottwald holm equation in this paper we adopt the exp function method and the traveling wave transformation to study the so called dgh equation as a result a number of exact solutions of this equation have been found the family of solution including some exact solutions such as solitary wave pattern periodic traveling wave solution kink wave solution and new bounded wave solutions and explained some of the solutions physical meaning

optimal persistent disturbance attenuation control for linear hybrid systems abstract in this paper the disturbance attenuation properties for a class of linear hybrid systems are investigated and a hybrid optimal persistent disturbance attenuation control problem is studied first a procedure is developed to determine the minimal l induced gain of linear hybrid systems however for general hybrid systems the termination of the procedure is not guaranteed then the decidability issues are discussed the termination of the procedure in a finite number of steps is shown for a subclass of hybrid systems with simplified discrete event dynamics called switched linear systems finally the optimal persistent disturbance attenuation controller synthesis problem is studied it is shown that the optimal performance level can be achieved by a piecewise linear state feedback control law and a systematic approach is proposed to design such feedback control

on nonlinear amplitude evolution under stochastic forcing the complex ginzburg landau amplitude equation with or without random forcing arises as approximate reductions of complicated physical systems on extended spatial domains near bifurcation points unlike the deterministic ginzburg landau equation whose well posedness is well known there seems no rigorous result on global existence and uniqueness of the randomly forced ginzburg landau equation our work provides such a rigorous result on global existence and uniqueness under very mild conditions

stability criterion for bright solitary waves of the perturbed cubic quintic schro dinger equation abstract the stability of the bright solitary wave solution to the perturbed cubic quintic schrodinger equation is considered it is shown that in a certain region of parameter space these solutions are unstable with the instability being manifested as a small positive eignevalue furthermore it is shown that in the complimentary region of parameter space there are no small unstable eigenvalues the proof involves a novel calculation of the evans function which is of interest in its own right as a consequence of the eigenvalue calculation it is additionally shown that n bump bright solitary waves bifurcate from the primary wave

nonquadratic lyapunov functions for robust control abstract this paper deals with the problem of controlling a linear continuous time system with structured time varying parameter uncertainties and input disturbances with a lyapunov function approach in contrast with most of the previous results in the literature we do not confine our attention to the class of quadratic lyapunov functions conversely the basic motivation of this paper is to determine whether there exist other functions that can be conveniently used as candidate lyapunov functions this question has a positive answer the proposed class is that of polyhedral norms or more generally of polyhedral minkowski functionals we show that the class of these functions is universal in the sense that if the problem of ultimately bounding the state in an assigned convex set via state feedback control can be solved via a lyapunov function and a continuous state feedback compensator then it can be solved via a polyhedral lyapunov function and a possibly different continuous control moreover we show that the control can be piecewise linear a numerical technique for constructing the controller is presented for the case in which the uncertainty constraint sets are polyhedral

singular heteroclinic orbits for degenerate modulation equations the problem of finding heteroclinic orbits for the quintic ginzburg landau equation in the case that the imaginary parts of the coefficients are o with 0 1 is considered when c where is a distinguished parameter in the equation and 0 there exists a singular heteroclinic orbit connecting a stable finite amplitude state to the stable zero state it is shown that for a certain region of parameter space this orbit persists for small with a wave speed c which is o furthermore using an approach reminiscent of the melnikov method the sign of c 0 is calculated this calculation is crucial in settling the persistence question finally it is shown that for this wave speed it is possible for additional heteroclinic orbits to exist these additional orbits connect two finite amplitude states

peakons kinks compactons and solitary patterns solutions for a family of camassa holm equations by using new hyperbolic schemes in this paper a family of camassa holm equations with distinct parameters is investigated new solitary wave solutions that include peakons kinks compactons solitary patterns solutions and plane periodic solutions are formally derived new schemes that rest mainly on hyperbolic functions are employed to achieve our goal the work highlights the qualitative change in the physical structures of the obtained solutions

global existence of solutions to the derivative 2d ginzburg landau equation abstract in this paper we study a complex derivative ginzburg landau equation with two spatial variables 2d we obtain sufficient conditions for the existence and uniqueness of global solutions for the initial boundary value problem of the derivative 2d ginzburg landau equation and improve the known results

multipulse like orbits for a singularly perturbed nearly integrable system abstract we use topological shooting arguments to study the existence of multipulse like orbits for a singularly perturbed 3 dimensional dynamical system established as a model problem for the 1 dimensional complex ginzburg landau equations our main result improves an earlier result obtained by doelman and hek

brief paper computations of probabilistic output admissible set for uncertain constrained systems this paper considers uncertain constrained systems and develops two algorithms for computing a probabilistic output admissible poa set which is a set of initial states probabilistically assured to satisfy the constraint the first algorithm is inspired by an existing randomized sequential technique the second algorithm alleviates the computational effort based on heuristics the present algorithms terminate in a finite number of iterations and provide a poa set additionally we can obtain information on the size of the resulting set a posteriori a numerical simulation demonstrates the applicability of the poa set to a control system design scheme

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

invariant painleve analysis and coherent structures of two families of reaction diffusion equations exact closed form coherent structures pulses fronts domain walls having the form of complicated traveling waves are constructed for two families of reaction diffusion equations by the use of invariant painleve analysis these analytical solutions which are derived directly from the underlying pde s are investigated in the light of restrictions imposed by the ode that any traveling wave reduction of the corresponding pde must satisfy in particular it is shown that the coherent structures a asymptotically satisfy the ode governing traveling wave reductions and b are accessible to the pde from compact support initial conditions the solutions are compared with each other and with previously known solutions of the equations

h sub 2 control with time domain constraints theory and an application in this paper we study the problem of minimizing the h sub 2 norm of a given transfer function subject to time domain constraints on the time response of a different transfer function to a given test signal the main result of this paper shows that this problem admits a minimizing solution in r h sub 2 moreover rational solutions with performance arbitrarily close to optimal can be found by constructing families of approximating problems each one of these problems entails solving a finite dimensional quadratic programming problem whose dimension can be determined before hand these results are illustrated and experimentally validated by designing a controller for an active vision application

classification of bounded travelling wave solutions for the dullin gottwald holm equation abstract in this paper we classify all bounded travelling wave solutions for the integrable dullin gottwald holm equation it is shown that it decomposes in two known cases the camassa holm and the korteweg de vries equation for the former the classification is similar to the one presented in 2005 12 while for the latter it is only possible to obtain smooth solutions

homoclinic saddle node bifurcations and subshifts in a three dimensional flow we study a two parameter family of three dimensional vector fields that are small perturbations of an integrable system possessing a line of degenerate saddle points connected by a manifold of homoclinic loops under perturbation this manifold splits and undergoes a quadratic homoclinic tangency perturbation methods followed by geometrical analyses reveal the presence of countably infinite sets of homoclinic orbits to and a non wandering set topologically conjugate to a shift on two symbols a smale horseshoe we use the symbolic description to identify and partially order bifurcation sequences in which the homoclinic orbits appear and we formally derive an explicit two dimensional poincare return map to further illustrate our results the problem was motivated by the search for travelling structures such as fronts and domain walls in partial differential equations