prescribing the center of mass of a multi soliton solution for a perturbed semilinear wave equation abstract we construct a finite time blow up solution for a class of strongly perturbed semilinear wave equation with an isolated characteristic point in one space dimension given any integer k 2 and 0 r we construct a blow up solution with a characteristic point a such that the asymptotic behavior of the solution near a t a shows a decoupled sum of k solitons with alternate signs whose centers in the hyperbolic geometry have 0 as a center of mass for all times although the result is similar to the unperturbed case in its statement our method is new indeed our perturbed equation is not invariant under the lorentz transform and this requires new ideas in fact the main difficulty in this paper is to prescribe the center of mass 0 r we would like to mention that our method is valid also in the unperturbed case and simplifies the original proof by cote and zaag 9 as far as the center of mass prescription is concerned

profile for the imaginary part of a blowup solution for a complex valued semilinear heat equation abstract in this paper we consider the following complex valued semilinear heat equation t u u u p u c in the whole space r n where p n p 2 we aim at constructing for this equation a complex solution u u 1 i u 2 which blows up in finite time t and only at one blowup point a with the following estimates for the final profile u x t p 1 2 x a 2 8 p ln x a 1 p 1 u 2 x t 2 p p 1 2 p 1 2 x a 2 8 p ln x a 1 p 1 1 ln x a as x a note that the imaginary part is non zero and that it blows up also at point a our method relies on two main arguments the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to get the conclusion up to our knowledge this is the first time where the blowup behavior of the imaginary part is derived in multi dimension

robust adaptive boundary control of a flexible marine riser with vessel dynamics in this paper robust adaptive boundary control for a flexible marine riser with vessel dynamics is developed to suppress the riser s vibration to provide an accurate and concise representation of the riser s dynamic behavior the flexible marine riser with vessel dynamics is described by a distributed parameter system with a partial differential equation pde and four ordinary differential equations odes boundary control is proposed at the top boundary of the riser based on lyapunov s direct method to regulate the riser s vibration adaptive control is designed when the system parametric uncertainty exists with the proposed robust adaptive boundary control uniform boundedness under the ocean current disturbance can be achieved the proposed control is implementable with actual instrumentation since all the required signals in the control can be measured by sensors or calculated by a backward difference algorithm the state of the system is proven to converge to a small neighborhood of zero by appropriately choosing design parameters simulations are provided to illustrate the applicability and effectiveness of the proposed control

probability laws related to the jacobi theta and riemann zeta functions and brownian excursions this paper reviews known results which connect riemann s integral representations of his zeta function involving jacobi s theta function and its derivatives to some particular probability laws governing sums of independent exponential variables these laws are related to one dimensional brownian motion and to higher dimensional bessel processes we present some characterizations of these probability laws and some approximations of riemann s zeta function which are related to these laws

boundary control of an unstable heat equation via measurement of domain averaged temperature in this note a feedback boundary controller for an unstable heat equation is designed the equation can be viewed as a model of a thin rod with not only the heat loss to a surrounding medium stabilizing but also the heat generation inside the rod destabilizing the heat generation adds a destabilizing linear term on the right hand side of the equation the boundary control law designed is in the form of an integral operator with a known continuous kernel function but can be interpreted as a backstepping control law this interpretation provides a lyapunov function for proving stability of the system the control is applied by insulating one end of the rod and applying either dirichlet or neumann boundary actuation on the other

iterative learning control of inhomogeneous distributed parameter systems frequency domain design and analysis abstract this paper aims to construct a design and analysis framework for iterative learning control of linear inhomogeneous distributed parameter systems lidpss which may be hyperbolic parabolic or elliptic and include many important physical processes such as diffusion vibration heat conduction and wave propagation as special cases owing to the system model characteristics lidpss are first reformulated into a matrix form in the laplace transform domain then through the determination of a fundamental matrix the transfer function of lidps is precisely evaluated in a closed form the derived transfer function provides the direct input output relationship of the lidps and thus facilitates the consequent ilc design and convergence analysis in the frequency domain the proposed control design scheme is able to deal with parametric and non parametric uncertainties and make full use of the process repetition while avoid any simplification or discretization for the 3d dynamics of lidps in the time space and iteration domains in the end two illustrative processes are addressed to demonstrate the efficacy of the proposed iterative learning control scheme

construction of a multisoliton blowup solution to the semilinear wave equation in one space dimension we consider the semilinear wave equation with power nonlinearity in one space dimension given a blow up solution with a characteristic point we refine the blow up behavior first derived by merle and zaag we also refine the geometry of the blow up set near a charac teristic point and show that except may be for one exceptional situation it is never symmetric with the respect to the characteristic point then we show that all blow up modalities predicted by those authors do occur more precisely given any integer k 2 and 0 we construct a blow up solution with a characteristic point a such that the asymptotic behavior of the solution near a t a shows a decoupled sum of k solitons with alternate signs whose centers in the hyperbolic geometry have 0 as a center of mass for all times

construction of type ii blowup solutions for the 1 corotational energy supercritical wave maps abstract we consider the energy supercritical wave maps from r d into the d sphere s d with d 7 under an additional assumption of 1 corotational symmetry the problem reduces to the one dimensional semilinear wave equation t 2 u r 2 u d 1 r r u d 1 2 r 2 sin 2 u we construct for this equation a family of c solutions which blow up in finite time via concentration of the universal profile u r t q r t where q is the stationary solution of the equation and the speed is given by the quantized rates t c u t t l l n l d 1 2 the construction relies on two arguments the reduction of the problem to a finite dimensional one thanks to a robust universal energy method and modulation techniques developed by merle raphael and rodnianski 49 for the energy supercritical nonlinear schrodinger equation then we proceed by contradiction to solve the finite dimensional problem and conclude using the brouwer fixed point theorem

refined asymptotics for the blowup of ut δu up this work is concerned with positive blowing up solutions of the semilinear heat equation ut u up in rn our main contribution is a sort of center manifold analysis for the equation in similarity variables leading to refined asymptotics for u in a backward space time parabola near any blowup point we also explore a connection between the asymptotics of u and the local geometry of the blowup set

two novel iterative learning control schemes for systems with randomly varying trial lengths abstract this paper proposes two novel improved iterative learning control ilc schemes for systems with randomly varying trial lengths different from the existing works on ilc with variable trial lengths that advocate to replace the missing control information by zero the proposed learning algorithms are equipped with a searching mechanism to collect useful but avoid redundant past tracking information which could expedite the learning speed the searching mechanism is realized by the newly defined stochastic variables and an iteratively moving average operator the convergence of the proposed learning schemes is strictly proved based on the contraction mapping methodology two illustrative examples are provided to show the superiorities of the proposed approaches

on initial conditions in iterative learning control initial conditions or initial resetting conditions play a fundamental role in all kinds of iterative learning control methods in this note we study five different initial conditions disclose the inherent relationship between each initial condition and corresponding learning convergence or boundedness property the iterative learning control method under consideration is based on lyapunov theory which is suitable for plants with time varying parametric uncertainties and local lipschitz nonlinearities

brief an iterative learning algorithm for boundary control of a stretched moving string in this paper iterative learning control technique is applied for the first time to a class of flexible systems specifically learning control of a material transport system is considered the system consists of a stretched string and a transporter the motion of transporter is subject to such external disturbances as imperfect wheels and can cause string vibrations the control objective is to damp out any string oscillation during transportation using iterative control applied at the boundaries the control is designed using both discrete and continuous time lyapunov functions the proposed result is new and significant as it demonstrates that iterative learning control methodology is an effective technique for controlling distributed parameter systems

distributed control of a class of flexible mechanical systems with global constraint in this paper the constrained problem is investigated for both flexible string model and euler bernoulli beam model with the tip payload based on an infinite dimensional generalisation of a distributed control method the control objectives are to develop the control law so that the motion of flexible mechanical systems can track a desired reference signal and ensure that the string or beam remain in a constrained space we prove that with the proposed control the tracking error is exponentially stable without violation of the constraint the proof of convergence is based on an integral barrier lyapunov function iblf and extensive simulations are provided to illustrate the performance of the control system

fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems this paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations pdes both distributed measurement form and collocated boundary measurement form are considered a takagi sugeno t s fuzzy pde model is first applied to accurately represent the semilinear parabolic pde system based on the t s fuzzy pde model two types of fuzzy boundary controllers which are easily implemented since only boundary actuators are used are proposed to ensure the exponential stability of the resulting closed loop system sufficient conditions of exponential stabilization are established by employing the lyapunov direct method and the vector valued wirtinger s inequality and presented in terms of standard linear matrix inequalities finally the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples

stable blow up patterns abstract for the semilinear heat equation ut u eu in a convex domain r n given any b we show the existence of solutions which blow up in finite time exactly at b and whose final profile has the form u t x 2 ln x b ln ln x b ln 8 t being the blow up time using a suitable set of rescaled coordinates this asymptotic behavior is proved to be stable with respect to small perturbations of the initial conditions

continuous state feedback tracking of an uncertain heat diffusion process a spatially distributed form of a second order sliding mode control algorithm is suggested for the feedback control of a heat process subject to unmeasurable sufficiently smooth persistent disturbances of arbitrary shape in order to obtain a continuous control input while retaining similar properties of robustness as those usually endowing the discontinuous control systems a dynamic input extension technique is exploited by adding an integrator at the input side and by applying a discontinuous distributed input to the integrator we present a constructive lyapunov analysis of the closed loop performance that yields simple controller tuning conditions guaranteeing the asymptotic tracking of a sufficiently smooth reference trajectory despite the presence of norm bounded persistent disturbances numerical simulations confirm the effectiveness of the proposed approach

new stability and exact observability conditions for semilinear wave equations the problem of estimating the initial state of 1 d wave equations with globally lipschitz nonlinearities from boundary measurements on a finite interval was solved recently by using the sequence of forward and backward observers and deriving the upper bound for exact observability time in terms of linear matrix inequalities lmis fridman 2013 in the present paper we generalize this result to n d wave equations on a hypercube this extension includes new lmi based exponential stability conditions for n d wave equations as well as an upper bound on the minimum exact observability time in terms of lmis for 1 d wave equations with locally lipschitz nonlinearities we find an estimate on the region of initial conditions that are guaranteed to be uniquely recovered from the measurements the efficiency of the results is illustrated by numerical examples

brief iterative learning control with initial rectifying action this paper addresses the initial shift problem in iterative learning control with system relative degree the tracking error caused by nonzero initial shift is detected when applying a conventional learning algorithm finite initial rectifying action is introduced in the learning algorithm and is shown effective in the improvement of tracking performance in particular robustness with respect to variable initial shifts the uniform convergence of the output trajectory to a desired one jointed smoothly with a specified transient trajectory from the starting position is ensured in the presence of fixed initial shift

exponential stabilization for 1 d linear ito type state dependent stochastic parabolic pde systems via static output feedback abstract this paper deals with the problem of exponential stabilization for 1 d linear stochastic parabolic partial differential equation pde systems with state multiplicative noise in the form of ito type a static output feedback sof control scheme is proposed to stabilize the stochastic pde system in a stochastic framework via locally collocated piecewise uniform actuators and sensors the closed loop well posedness analysis is provided by virtue of the semi group theory based on the infinite dimensional infinitesimal operator and lyapunov technique the sof controller design is developed to guarantee the exponential stability of the resulting closed loop system in the mean square sense finally simulation results on a stochastic heat equation are presented to verify the effectiveness of the proposed design method

blowup solutions for a reaction diffusion system with exponential nonlinearities abstract we consider the following parabolic system whose nonlinearity has no gradient structure t u u e p v t v v e q u u 0 u 0 v 0 v 0 p q 0 in the whole space r n we show the existence of a stable blowup solution and obtain a complete description of its singularity formation the construction relies on the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to conclude in particular our analysis uses neither the maximum principle nor the classical methods based on energy type estimates which are not supported in this system the stability is a consequence of the existence proof through a geometrical interpretation of the quantities of blowup parameters whose dimension is equal to the dimension of the finite dimensional problem

robust distributed control of quasilinear reaction diffusion equations via infinite dimensional sliding modes abstract this paper investigates the problem of robust tracking control for quasilinear reaction diffusion partial differential equations subject to external unknown perturbations the considered class of equations is quite general and includes classical equations such as the heat equation or the fisher kpp equation as special cases global practical stabilization of the tracking error system is established under mild conditions on the disturbance term using a regularized infinite dimensional sliding mode controller extensive simulations support and validate the theoretical results

use of symmetry groups in sliding mode control of nonlinear distributed parameter systems sliding mode control theory is applied to a class of distributed parameter systems the viability of using symmetry groups to aid in feedback control of such systems is discussed a conjecture is presented that leads to the calculation of the control law to support the conjecture the method is applied to the control of a chemical reactor

an inverse heat conduction problem with a nonlinear source term abstract in this paper the nonlinear problem of an inhomogeneous heat equation with linear boundary conditions will be considered the surface heat flux history of a heated conducting body will be identified the approach of the proposed method is to approximate the unknown function using linear polynomial pieces which are determined consecutively from the solution of the minimization problem on the basis of overspecified data some numerical examples will also be presented

adaptive boundary iterative learning control for an euler bernoulli beam system with input constraint this paper addresses the vibration control and the input constraint for an euler bernoulli beam system under aperiodic distributed disturbance and aperiodic boundary disturbance hyperbolic tangent functions and saturation functions are adopted to tackle the input constraint a restrained adaptive boundary iterative learning control abilc law is proposed based on a time weighted lyapunov krasovskii like composite energy function in order to deal with the uncertainty of a system parameter and reject the external disturbances three adaptive laws are designed and learned in the iteration domain all the system states of the closed loop system are proved to be bounded in each iteration along the iteration axis the displacements asymptotically converge toward zero simulation results are provided to illustrate the effectiveness of the proposed abilc scheme

iterative learning control for discrete time systems with event triggered transmission strategy and quantization this paper investigates the iterative learning problem for discrete time systems with event triggered scheme and quantization the event triggered scheme is firstly considered in the iterative learning controllers to reduce the number of iteration steps to be updated here the event triggered scheme is designed depending on time t and iterative learning step k quantization is then introduced in the event triggered controllers and some relaxed conditions are presented to guarantee the tracking problem by using some interval matrix properties finally simulation results are given to illustrate the usefulness of the developed criteria

blow up profile for the complex ginzburg landau equation abstract we construct a solution to the complex ginzburg landau equation which blows up in finite time t only at one blow up point we also give a sharp description of its blow up profile the proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude two major difficulties arise in the proof the linearized operator around the profile is not self adjoint and it has a second neutral mode in the last section the interpretation of the parameters of the finite dimensional problem in terms of the blow up time and the blow up point gives the stability of the constructed solution with respect to perturbations in the initial data

observers and initial state recovering for a class of hyperbolic systems via lyapunov method a b s t r a c t recently the problem of estimating the initial state of some linear infinite dimensional systems from measurements on a finite interval was solved by using the sequence of forward and backward observers ramdani tucsnak and weiss 2010 in the present paper we introduce a direct lyapunov approach to the problem and extend the results to the class of semilinear systems governed by wave and beam equations with boundary measurements from a finite interval we first design forward observers and derive linear matrix inequalities lmis for the exponential stability of the estimation errors further we obtain simple finite dimensional conditions in terms of lmis for an upper bound t on the minimal time that guarantees the convergence of the sequence of forward and backward observers on 0 t for the initial state recovering this t represents also an upper bound on the observability time for observation times bigger than t these lmis give upper bounds on the convergence rate of the iterative algorithm in the norm defined by the lyapunov functions in our approach t is found as the minimal dwelling time for the switched exponentially stable forward and backward estimation error systems with the different lyapunov functions liberzon 2003 the efficiency of the results is illustrated by numerical examples 2013 elsevier ltd all rights reserved

adaptive boundary control for unstable parabolic pdes part i lyapunov design we develop adaptive controllers for parabolic partial differential equations pdes controlled from a boundary and containing unknown destabilizing parameters affecting the interior of the domain these are the first adaptive controllers for unstable pdes without relative degree limitations open loop stability assumptions or domain wide actuation it is the first necessary step towards developing adaptive controllers for physical systems such as fluid thermal and chemical dynamics where actuation can be only applied non intrusively the dynamics are unstable and the parameters such as the reynolds rayleigh prandtl or peclet numbers are unknown because they vary with operating conditions our method builds upon our explicitly parametrized control formulae to avoid solving riccati or bezout equations at each time step most of the designs we present are state feedback but we present two benchmark designs with output feedback which have infinite relative degree

exponential stabilization of conservation systems with interior disturbance abstract in this paper we consider the stabilization problem of the conservation systems with interior disturbance employing the idea of sliding mode control we design a nonlinear distributed feedback controller we prove the solvability of the resulted closed loop system by the maximal monotone operator theory further we prove the exponential stability of the closed loop system in particular we prove that the requirement of a classical solution in the lyapunov approach is unnecessary

a blowup solution of a complex semi linear heat equation with an irrational power abstract in this paper we consider the following semi linear complex heat equation t u u u p u c in r n with an arbitrary power p p 1 we construct for this equation a complex solution u u 1 i u 2 which blows up in finite time t and only at one blowup point a moreover we also describe the asymptotics of the solution by the following final profiles u x t p 1 2 x a 2 8 p ln x a 1 p 1 u 2 x t 2 p p 1 2 p 1 2 x a 2 8 p ln x a 1 p 1 1 ln x a 0 as x a in addition to that since we also have u 1 0 t and u 2 0 t as t t the blowup in the imaginary part shows a new phenomenon unknown for the standard heat equation in the real case a non constant sign near the singularity with the existence of a vanishing surface for the imaginary part shrinking to the origin in our work we have succeeded to extend for any power p where the non linear term u p is not continuous if p is not integer in particular the solution which we have constructed has a positive real part we study our equation as a system of the real part and the imaginary part u 1 and u 2 our work relies on two main arguments the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to get the conclusion

data driven h_ infty control for nonlinear distributed parameter systems the data driven h infty control problem of nonlinear distributed parameter systems is considered in this paper an off policy learning method is developed to learn the h infty control policy from real system data rather than the mathematical model first karhunen loeve decomposition is used to compute the empirical eigenfunctions which are then employed to derive a reduced order model rom of slow subsystem based on the singular perturbation theory the h infty control problem is reformulated based on the rom which can be transformed to solve the hamilton jacobi isaacs hji equation theoretically to learn the solution of the hji equation from real system data a data driven off policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved for implementation purpose a neural network nn based action critic structure is developed where a critic nn and two action nns are employed to approximate the value function control and disturbance policies respectively subsequently a least square nn weight tuning rule is derived with the method of weighted residuals finally the developed data driven off policy learning approach is applied to a nonlinear diffusion reaction process and the obtained results demonstrate its effectiveness

linear boundary control for a class of nonlinear pde processes abstract this paper studies the problem of output regulation via boundary feedback control for a class of nonlinear pde processes including important industrial bio chemical reactors under physically reasonable smoothness stability and steady state assumptions it is proven that a linear stable controller with integral action yields global exponential regulation of the process output

d type anticipatory iterative learning control for a class of inhomogeneous heat equations in this paper a d type anticipatory iterative learning control ilc scheme is applied to the boundary control of a class of inhomogeneous heat equations where the heat flux at one side is the control input while the temperature measurement at the other side is the control output by transforming the inhomogeneous heat equation into its integral form and exploiting the properties of the embedded jacobi theta functions the learning convergence of ilc is guaranteed through rigorous analysis without any simplification or discretization of the 3d dynamics in the time space as well as iteration domains the adopted ilc scheme makes full use of the process repetition and deals with state independent or state dependent uncertainties meanwhile due to the feedforward characteristic of ilc the proposed scheme not only makes anticipatory compensation possible to overcome the heat conduction delay in boundary output tracking but also eliminates the gain margin limitation encountered in feedback control in the end an illustrative example is presented to demonstrate the performance of the proposed ilc scheme

blowup solutions for a nonlinear heat equation involving a critical power nonlinear gradient term abstract we consider the following exponential reaction diffusion equation involving a nonlinear gradient term t u u u 2 e u x t r n 0 t 1 we construct for this equation a solution which blows up in finite time t 0 and satisfies some prescribed asymptotic behavior we also show that the constructed solution and its gradient blow up in finite time t simultaneously at the origin and find precisely a description of its final blowup profile it happens that the quadratic gradient term is critical in some sense resulting in the change of the final blowup profile in comparison with the case 0 the proof of the construction is inspired by the method of merle and zaag in 1997 it relies on the reduction of the problem to a finite dimensional one and uses the index theory to conclude one of the major difficulties arising in the proof is that outside the blowup region the spectrum of the linearized operator around the profile can never be made negative truly new ideas are needed to achieve the control of the outer part of the solution thanks to a geometrical interpretation of the parameters of the finite dimensional problem in terms of the blowup time and the blowup point we obtain the stability of the constructed solution with respect to perturbations in the initial data

stability analysis of linear partial differential equations with generalized energy functions we present a method for the stability analysis of a large class of linear partial differential equations pdes in one spatial dimension we rely on lyapunov analysis to establish the exponential stability of the systems under consideration the proposed test for the verification of the underlying lyapunov inequalities relies on the existence of solutions of a system of coupled differential equations we illustrate the application of this method using a pde actuated by a backstepping computed feedback law furthermore for the case of pdes defined by polynomial data we formulate a numerical methodology in the form of a convex optimization problem which can be solved algorithmically we show the effectiveness of the proposed numerical methodology using examples of different types of pdes

exponential stabilization of the uncertain wave equation via distributed dynamic input extension the wave equation is studied under the effect of a persistent external perturbation a dynamical distributed controller is suggested based on an infinite dimensional generalization of second order sliding mode control techniques that provides the exponential attainment of a sufficiently smooth arbitrary reference of the state trajectory the control system comprises of both feedforward and feedback parts the latter being a discontinuous term directly connected to the plant input through a dynamical filter that augments the system state smoothing out the discontinuity of the feedback control loop as a result a continuous input is applied to the plant a constructive lyapunov based proof of convergence of the proposed control algorithm is carried out and supporting numerical results are presented

exponential stabilization for a class of nonlinear parabolic pde systems via fuzzy control approach this paper deals with the exponential stabilization problem for a class of nonlinear spatially distributed processes that are modeled by semilinear parabolic partial differential equations pdes for which a finite number of actuators are used a fuzzy control design methodology is developed for these systems by combining the pde theory and the takagi sugeno t s fuzzy model based control technique initially a t s fuzzy parabolic pde model is proposed to accurately represent a semilinear parabolic pde system then based on the t s fuzzy model a lyapunov technique is used to design a continuous fuzzy state feedback controller such that the closed loop pde system is exponentially stable with a given decay rate the stabilization condition is presented in terms of a set of spatial differential linear matrix inequalities sdlmis furthermore a recursive algorithm is presented to solve the sdlmis via the existing linear matrix inequality optimization techniques finally numerical simulations on the temperature profile control of a catalytic rod are given to verify the effectiveness of the proposed design method

determination of the weyl invariants and calculation of the coupling coefficients for unitary groups the author presents a new approach for determining the weyl invariants of unitary groups such an approach is based on the generating function of the basis of the representation for unitary groups built in an earlier work hage hassan 1983 the author obtains two expressions for the weyl invariants both including the parameters involved in the generating function coupling coefficients appear in one of the expressions the comparison of the development of the two expressions allows the calculation of the coupling coefficients the application of this approach to the calculation of the coupling coefficients for the direct product lambda 10 x lambda 2 mu 2 of su 3 leads to an expression of the isoscalar factor where no summation occurs in contradistinction with the known expression for the coupling coefficients which involve five summations

brief paper an lmi approach to h boundary control of semilinear parabolic and hyperbolic systems exponential stability analysis and l 2 gain analysis are developed for scalar uncertain distributed parameter systems governed by semilinear partial differential equations of parabolic and hyperbolic types sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities lmis for both systems these conditions are then utilized to synthesize h static output feedback boundary controllers of the systems in question

vibration control for a nonlinear three dimensional flexible manipulator trajectory tracking abstractthis paper proposes an innovative approach to the trajectory tracking in three dimensional space and vibration control problems in the presence of a nonlinear three dimensional flexible manipulator based on the partial differential equation model unlike two dimensional plane we select spherical coordinates to describe the position of the end point in three dimensional space this novel approach makes it possible to realise the trajectory tracking by controlling the two angles in spherical coordinates meanwhile a vibration control scheme is proposed to restrain vibrations in addition the existence and uniqueness of solutions are demonstrated finally the performance of the desired trajectory tracking the proposed vibration control scheme and their convergence properties are demonstrated by numerical simulations

boundary control of a timoshenko beam system with input dead zone in this paper boundary control is designed for a timoshenko beam system with the input dead zone by the hamilton s principle the dynamics of the timoshenko beam system is represented by a distributed parameter model with two partial differential equations and four ordinary differential equations the bounded part is separated from the input dead zone and then forms the disturbance like term together with the boundary disturbance which finally acts on the timoshenko beam system boundary control based on the lyapunov s direct method is proposed to ensure the timoshenko beam converge into a small neighbourhood of zero where stability of the system is also analysed besides the existence and uniqueness of the solution of the timoshenko beam system are proved simulations are provided to reveal the applicability and effectiveness of the proposed control scheme

pointwise exponential stabilization of a linear parabolic pde system using non collocated pointwise observation this paper deals with the problem of exponential stabilization for a linear distributed parameter system dps using pointwise control and non collocated pointwise observation where the system is modeled by a parabolic partial differential equation pde the main objective of this paper is to construct an output feedback controller for pointwise exponential stabilization of the linear parabolic pde system using the non collocated pointwise observation the observer based output feedback control technique is utilized to overcome the design difficulty caused by the non collocation pointwise observation we construct a luenberger type pde state observer to exponentially track the state of the pde system a collocated pointwise feedback controller is proposed based on the estimated state a variation of poincare wirtinger inequality is derived and the spatial domain is decomposed into multiple sub domains according to the number of the actuators and sensors by using lyapunov s direct method integration by parts and the variation of poincare wirtinger inequality at each sub domain sufficient conditions for the existence of the observer based out feedback controller are developed such that the resulting closed loop system is exponentially stable and presented in terms of standard linear matrix inequalities lmis furthermore the closed loop well posedness analysis is also provided by the semigroup approach extensive numerical simulation results are presented to show the performance of the proposed output feedback controller

guaranteed cost design for controlling semilinear parabolic pde systems with mobile collocated actuators and sensors this paper investigates the guaranteed cost design problem for controlling a class of semilinear parabolic partial differential equation pde systems using mobile collocated actuators and sensors

an iterative learning control approach for linear systems with randomly varying trial lengths this technical note addresses an iterative learning control ilc design problem for discrete time linear systems where the trial lengths could be randomly varying in the iteration domain an ilc scheme with an iteration average operator is introduced for tracking tasks with non uniform trial lengths which thus mitigates the requirement on classic ilc that all trial lengths must be identical in addition the identical initialization condition can be absolutely removed the learning convergence condition of ilc in mathematical expectation is derived through rigorous analysis as a result the proposed ilc scheme is applicable to more practical systems in the end two illustrative examples are presented to demonstrate the performance and the effectiveness of the averaging ilc scheme for both time invariant and time varying linear systems

a new boson calculus for su 3 it is shown that the gelfand weyl pattern for su 3 can be uniquely expressed in terms of four non negative and one positive or negative free integers this provides an optimal albeit non linear boson calculus for su 3 in terms of four harmonic oscillators and one planar rotor by optimal it is meant that every irreducible representation is obtained once and once only our techniques can be generalized to other groups

wigner s d matrix elements for su 3 a generating function approach using our calculus for su 3 a generating function for wigner d matrix elements is derived for the first time from this an explicit expression for the individual matrix elements in an arbitrary irreducible representation is obtained also for the first time in terms of polynomials in the matrix elements of the defining representation of su 3 this expression does not depend on any particular parametrization of the group

event based control of linear hyperbolic systems of conservation laws in this article we introduce event based boundary controls for 1 dimensional linear hyperbolic systems of conservation laws inspired by event triggered controls developed for finite dimensional systems an extension to the infinite dimensional case by means of lyapunov techniques is studied the main contribution of the paper lies in the definition of two event triggering conditions by which global exponential stability and well posedness of the system under investigation is achieved some numerical simulations are performed for the control of a system describing traffic flow on a roundabout

boundary second order sliding mode control of an uncertain heat process with unbounded matched perturbation the primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and actuation the underlying heat process is governed by an uncertain parabolic partial differential equation pde with neumann boundary conditions it exhibits an unknown constant diffusivity parameter and it is affected by a smooth boundary disturbance which is not available for measurements and which is possibly unbounded in magnitude the proposed robust synthesis is formed by the linear feedback design and by the twisting second order sliding mode control algorithm suitably combined and re worked in the infinite dimensional setting a non standard lyapunov functional is invoked to establish the global asymptotic stability in a sobolev space involving spatial state derivatives of the same order as that of the plant equation the stability proof is accompanied by a set of simple tuning rules for the controller parameters the effectiveness of the developed control scheme is supported by simulation results

an iterative learning control law for dynamical systems abstract this paper is concerned with an iterative learning control law which enables us to find a control input that generates the desired output exactly over a finite time interval through the repetition of trials we derive a sufficient condition for nonlinear systems to achieve the desired output by the iterative learning control based on this result we show that the direct transmission term of the plant plays a crucial role in the error convergence of the learning process further we identify the class of plants to which the learning control law is applicable

blow up for quasilinear heat equations described by means of nonlinear hamilton jacobi equations it is well known that the nonnegative solutions of the semilinear heat equation formula blow up in a finite timet depending on the initial data assumed to be large enough this equation is interesting because it exhibits in different ranges the three most typical blow up behaviours for solutions of nonlinear parabolic equations indeed we consider radialy symmetric solutions and show that for 2 single point blow up occurs for 2 blow up is global and for 2 we have regional blow up moreover the analysis shows that the precise asymptotic behaviour is described by a nonconstant self similar blow up solution of the first order hamilton jacobi equation formula this means that both equations are asymptotically equivalent near blow up this type of asymptotic degeneracy of a parabolic equation into a first order equation is actually proved for a more general class of quasilinear heat equations

classification of singularities for blowing up solutions in higher dimensions consider the cauchy problem p u t u u p when x r n t 0 n 1 u x 0 u 0 x when x r n where p 1 and u 0 x is a continuous nonnegative and bounded function it is known that under fairly general assumptions on u 0 x the unique solution of p u x t blows up in a finite time by which we mean that lim sup sup u x t t t x r n in this paper we shall assume that u x t blows up at x 0 t t and derive the possible asymptotic behaviours of u x t as x t 0 t under general assumptions on the blow up rate

solution of a nonlinear heat equation with arbitrarily given blow up points we consider the equation where i u is scalar valued and p 1 it has been proven that if u t blows up at time t the blow up points are finite in number and located in i our aim is to prove that this result is optimal that is for any given points x1 xk in i there is a solution u such that its blow up points are exactly x1 xk

a convex sum of squares approach to analysis state feedback and output feedback control of parabolic pdes we present an optimization based framework for analysis and control of linear parabolic partial differential equations pdes with spatially varying coefficients without discretization or numerical approximation for controller synthesis we consider both full state feedback and point observation output feedback the input occurs at the boundary point actuation we use positive definite matrices to parameterize positive lyapunov functions and polynomials to parameterize controller and observer gains we use duality and an invertible state variable transformation to convexify the controller synthesis problem finally we combine our synthesis condition with the luenberger observer framework to express the output feedback controller synthesis problem as a set of lmi sdp constraints we perform an extensive set of numerical experiments to demonstrate the accuracy of the conditions and to prove the necessity of the lyapunov structures chosen we provide numerical and analytical comparisons with alternative approaches to control including sturm liouville theory and backstepping finally we use numerical tests to show that the method retains its accuracy for alternative boundary conditions