global stabilization of high order nonlinear time delay systems by state feedback abstract we consider the problem of global stabilization by state feedback for a class of high order nonlinear systems with time delay by developing a novel dynamic gain based backstepping approach a state feedback controller independent of the time delay is explicitly constructed with the help of appropriate lyapunov krasovskii functionals the precise knowledge even the upper bound of the time delay is not required it is proved that the states of the nonlinear time delay systems can be regulated to the origin while all the closed loop signals are globally bounded finally both physical and academic examples are given to illustrate the applications of the proposed scheme

adaptive regulation of high order lower triangular systems an adding a power integrator technique abstract in this paper a new adaptive control technique called adding a power integrator is proposed for a class of linearly parametrized high order nonlinear systems that are of a lower triangular structure but neither feedback linearizable nor affine in the control input using the adaptive adding a power integrator technique as a basic design tool we show how to explicitly construct in a recursive manner a smooth adaptive controller that solves the problem of adaptive regulation with global stability the development of the adding a power integrator technique leads to a significant relaxation on the system nonlinearities such as feedback linearizability and affineness which are known to be two standard hypotheses made in the existing nonlinear adaptive control schemes

pseudo transient continuation for nonlinear transient elasticity this paper demonstrates how pseudo transient continuation improves the efficiency and robustness of a newton iteration within a non linear transient elasticity simulation pseudo transient continuation improves efficiency by enabling larger time steps than possible with a newton iteration robustness improves because pseudo transient continuation recovers the convergence of newton s method when the initial iterate is not within the region of local convergence we illustrate the benefits of pseudo transient continuation on a non linear transient simulation of a buckling cylinder including a comparison with a line search based newton iteration

adding one power integrator a tool for global stabilization of high order lower triangular systems a new feedback design tool called adding a power integrator is introduced and used to solve the problem of global robust stabilization for a significant class of uncertain nonlinear systems that are of a lower triangular form but neither necessarily feedback linearizable fully or partially nor affine in the control input and therefore cannot be dealt with via conventional approaches sufficient conditions are presented under which a globally stabilizing smooth state feedback control law can be explicitly constructed using repeatedly the adding one power integrator technique this novel design technique permits removal of the feedback linearizability and linearity of the control input which have been two common assumptions so far in the literature of nonlinear control

robust backstepping control for a class of time delayed systems in this note the problem of robust output feedback control for a class of nonlinear time delayed systems is considered the systems considered are in strict feedback form state observer is first designed then based on the observed states the controller is designed via backstepping method both the designed observer and controller are independent of the time delays based on lyapunov stability theory we prove that the constructed controller can render the closed loop system asymptotically stable simulation results further verify the effectiveness of the proposed approach

influence of mixed boundary conditions in some reaction diffusion systems we analyse global existence of solutions to a system of two reaction diffusion equations for whicha balance law holds the main aim is to make clear the influence of different combinations ofboundary conditions on global existence under the assumption that the nonlinearities satisfy polynomial growth estimates

a novel error compensation control for a class of high order nonlinear systems with input delay a novel tracking error compensation based adaptive neural control scheme is proposed for a class of high order nonlinear systems with completely unknown nonlinearities and input delay in the tracking errors of existing papers there exist the following difficulties first output curve always lags behind the desired trajectory second some big peak errors cause a decrease in tracking precision and third a big initial value of the modified tracking error can make the closed loop system unstable to tackle them three corresponding error compensation terms are constructed including a prediction and compensation term an auxiliary signal produced by the constructed auxiliary system and a damping term however inequality amplification caused by high order will weaken the effectiveness of the proposed error compensation scheme and the control precision will decrease under an assumption that the lower bounds of the unknown control coefficients should be exactly known to overcome aforementioned difficulties in the derivation of the first virtual control law the radial basis function neural network is used to approximate a hybrid term online constructed by unknown nonlinearities a lumped control coefficient achieved by state transformation and the dynamic of the proposed error compensation terms and desired signal meanwhile input delay is coped with a robust compensation signal constructed based on a finite integral of the past control values finally it is proven that all the closed loop signals are semiglobally uniformly ultimately bounded simulation results demonstrate the effectiveness of the proposed method

a point collocation method based on reproducing kernel approximations a reproducing kernel particle method with built in multiresolution features in a very attractive meshfree method for numerical solution of partial differential equations the design and implementation of a galerkin based reproducing kernel particle method however faces several challenges such as the issue of nodal volumes and accurate and efficient implementation of boundary conditions in this paper we present a point collocation method based on reproducing kernel approximations we show that in a point collocation approach the assignment of nodal volumes and implementation of boundary conditions are not critical issues and points can be sprinkled randomly making the point collocation method a true meshless approach the point collocation method based on reproducing kernel approximations however requires the calculation of higher order derivatives that would typically not be required in a galerkin method a correction function and reproducing conditions that enable consistency of the point collocation method are derived the point collocation method is shown to be accurate for several one and two dimensional problems and the convergence rate of the point collocation method is addressed copyright 2000 john wiley sons ltd

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

the group finite element formulation abstract the introduction of trial solutions for groups of variables within a finite element formulation is shown to provide a significant economy with no loss of accuracy for steady solutions of the two dimensional burgers equations with linear rectangular elements the application of the group finite element to the convective term produces a threefold reduction in execution time with a small improvement in accuracy operation count estimates indicate even larger economies in three dimensions or if higher order nonlinearities occur or if higher order shape functions are used applications of the group formulation are described for inviscid and viscous laminar and turbulent separated and unseparated and incompressible and compressible flows

nonsmooth feedback control of time delay nonlinear systems a dynamic gain based approach this technical note addresses the problem of global control for a class of time delay nonlinear systems under a smoothness condition on the system nonlinearities a delay independent non smooth dynamic state compensator is constructed by developing a dynamic gain based design method with the help of appropriate lyapunov krasovskii functionals it is shown that all the states of the time delay nonlinear system can be regulated to the origin while maintaining boundedness of the closed loop system a benchmark example is given to illustrate the effectiveness of the proposed non smooth feedback controller

nonlinear h almost disturbance decoupling the l2 gain almost disturbance decoupling problem for siso nonlinear systems is formulated sufficient conditions are identified for the existence of a parametrized state feedback controller such that the l2 gain from disturbances to output can be made arbitrarily small by increasing its gain the controller is explicity constructed using a lyapunov based recursive scheme sufficient conditions for the solvability of the h almost disturbance decoupling problem and the explicit construction of teh controller are given for a more restrictive class of nonlinear systems

asymptotic stabilization of a class of smooth two dimensional systems this paper studies the asymptotic stabilizability of two dimensional control systems the class under consideration includes c infty systems that satisfy a certain genericity assumption and all real analytic systems necessary and sufficient conditions for feedback stabilization using continuous feedback and a sufficient condition for c 1 feedback stabilization are given this latter condition is given in terms of an inequality involving two indices if the direction of the inequality is changed an obstruction to c infty feedback stabilizability is obtained a subclass of polynomial systems is also studied and given complete necessary and sufficient conditions for global asymptotic stabilization using c 1 feedback

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

adaptive approximation based regulation control for a class of uncertain nonlinear systems without feedback linearizability in this paper for a general class of uncertain nonlinear cascade systems including unknown dynamics which are not feedback linearizable and cannot be solved by existing approaches an innovative adaptive approximation based regulation control aarc scheme is developed within the framework of adding a power integrator api by deriving adaptive laws for output weights and prediction error compensation pertaining to single hidden layer feedforward network slfn from the lyapunov synthesis a series of slfn based approximators are explicitly constructed to exactly dominate completely unknown dynamics by the virtue of significant advancements on the api technique an adaptive api methodology is eventually established in combination with slfn based adaptive approximators and it contributes to a recursive mechanism for the aarc scheme as a consequence the output regulation error can asymptotically converge to the origin and all other signals of the closed loop system are uniformly ultimately bounded simulation studies and comprehensive comparisons with backstepping and api based approaches demonstrate that the proposed aarc scheme achieves remarkable performance and superiority in dealing with unknown dynamics

nilpotent approximations of control systems and distributions a constructive method is given to approximate the vector fields in a nonlinear control system which is linear in the controls by a system of similar form and on the same state space with the describing vector fields of the approximating system generating a lie algebra which has a certain relevant sub algebra nilpotent given a k dimensional distribution on r n say locally defined near zero the method leads to an approximating k distribution which has nilpotent basis agrees with the original distribution at zero and each derived distribution of the approximating distribution and original distribution also agree at zero

a point collocation method for geometrically nonlinear membranes abstract this paper describes the development of a numerical model for geometrically nonlinear membranes and evaluates its performance for membranes at static equilibrium the scheme has several features not commonly seen in structural finite element analysis the point collocation method group formulation and a staggered mesh in the point collocation finite element method the partial differential equations are solved at each node instead of by integrating over elements the group formulation simplifies the handling of nonlinearities by interpolating the nonlinear products of variables as opposed to seeking the product of independently interpolated variables the domain is discretized with a staggered mesh of linear triangles and associated polygons two sequential gradient recovery operations are performed first the gradients of the linear triangles are calculated and converted to stresses then polygon derivative shape functions derived in this paper are used to determine the internal forces from the stress gradients the resulting system of nonlinear equations is solved with a jacobian free newton krylov solver the code is first verified using the patch test and the method of manufactured solutions then the results are validated using experimental data and benchmark code results in the literature for the hencky problem a circular membrane with a fixed perimeter and uniform inflation pressure the observed rates of convergence for both displacement and radial strain were two for the configurations and grids used in this investigation the scheme was suitable for accurately predicting sub hyperelastic deformations

global robust stabilization of minimum phase nonlinear systems with uncertainty the problem of global stabilization via state feedback is studied for a class of minimum phase nonlinear systems with unknown unmodelled time varying parameters or disturbances belonging to a given compact set sufficient conditions are presented for the existence of a robust stabilizing state feedback controller the controller is constructed explicitly by using a lyapunov based recursive design procedure the proposed feedback control law is a smooth function of the state and requires information of bounding functions on the size of uncertainties in the case where the disturbance signals represent only an unknown constant vector parameter and appear linearly in the system an adaptive controller is developed based on similar arguments achieving global stability with state regulation the main results of this paper incorporate and generalize a number of robust and adaptive control schemes for global stabilization of uncertain feedback linearizable systems without zero dynamics

brief paper observer based control of a class of time delay nonlinear systems having triangular structure time delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering it has been shown in the literature that the existence of a stabilizing observer based controller is related to delay dependent conditions that are generally satisfied for a small time delay motivating works towards reducing the conservatism of the results are among the on going research topics especially when partial state measurements are imposed this paper investigates the problem of observer based stabilization of a class of time delay nonlinear systems written in triangular form first we show that a delay nonlinear observer is globally convergent under the global lipschitz condition of the system nonlinearity then it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay an illustrative example is provided to approve the theoretical results

analysis of thin shells by the element free galerkin method a meshless approach to the analysis of arbitrary kirchhoff shells by the element free galerkin efg method is presented the shell theory used is geometrically exact and can be applied to deep shells the method is based on moving least squares approximant the method is meshless which means that the discretization is independent of the geometric subdivision into finite elements the satisfaction of the c1 continuity requirements is easily met by efg since it requires only c1 weights therefore it is not necessary to resort to mindlin reissner theory or to devices such as discrete kirchhoff theory the requirements of consistency are met by the use of a polynomial basis of quadratic or higher order a subdivision similar to finite elements is used to provide a background mesh for numerical integration the essential boundary conditions are enforced by lagrange multipliers membrane locking which is due to different approximation order for transverse and membrane displacements is removed by using larger domains of influence with the quadratic basis and by using quartic polynomial basis which can prevent membrane locking completely it is shown on the obstacle course for shells that the present technique performs well

adaptive control of nonlinearly parameterized systems the smooth feedback case studies global adaptive control of nonlinearly parameterized systems with uncontrollable linearization using a parameter separation technique and the tool of adding a power integrator we develop a feedback domination design approach for the explicit construction of a smooth adaptive controller that solves the problem of global state regulation in contrast to the existing results in the literature a key feature of our adaptive regulator is its minimum order property namely no matter how big the number of unknown parameters is the order of the dynamic compensator is identical to one and is therefore minimal as a consequence global state regulation of feedback linearizable systems with nonlinear parameterization is achieved by one dimensional adaptive controllers without imposing any extra e g convex concave conditions on the unknown parameters

adaptive fuzzy control of switched nonlinear time varying delay systems with prescribed performance and unmodeled dynamics abstract this paper considers the problem of adaptive prescribed performance control for a class of switched nonlinear systems with time varying delays and unmodeled dynamics fuzzy logic systems are introduced to deal with the unknown nonlinear terms utilizing dynamic surface control and convex combination method a state feedback controller is constructed it is proven that all signals of the closed loop system are bounded finally simulation results are given to show that the proposed scheme is effective

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

reaction diffusion systems with initial data of low regularity abstract models issued from ecology chemical reactions and several other application fields lead to semi linear parabolic equations with super linear growth even if in general blow up can occur these models share the property that mass control is essential in many circumstances it is known that this l 1 control is enough to prove the global existence of weak solutions the theory is based on basic estimates initiated by m pierre and collaborators who have introduced methods to prove l 2 a priori estimates for the solution here we establish such a key estimate with initial data in l 1 while the usual theory uses l 2 this allows us to greatly simplify the proof of some results we also establish new existence results of semilinearity which are super quadratic as they occur in complex chemical reactions our method can be extended to semi linear porous medium equations