a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

fuzzy wavelet neural network models for prediction and identification of dynamical systems this paper presents fuzzy wavelet neural network fwnn models for prediction and identification of nonlinear dynamical systems the proposed fwnn models are obtained from the traditional takagi sugeno kang fuzzy system by replacing the then part of fuzzy rules with wavelet basis functions that have the ability to localize both in time and frequency domains the first and last model use summation and multiplication of dilated and translated versions of single dimensional wavelet basis functions respectively and in the second model then parts of the rules consist of radial function of wavelets gaussian type of activation functions are used in if part of the fuzzy rules a fast gradient based training algorithm i e the broyden fletcher goldfarb shanno method is used to find the optimal values for unknown parameters of the fwnn models simulation examples are also given to compare the effectiveness of the models with the other known methods in the literature according to simulation results we see that the proposed fwnn models have impressive generalization ability

a scaled feedback stabilization of power integrator triangular systems using unbounded time varying scaling of the states we design c1 feedback laws for power integrator triangular systems which globally asymptotically stabilize gas the origin despite the uncontrollability of the linearization with bounded scaling the feedback laws achieve global practical stability gps for a trade off between gas gps of the origin and unboundedness boundedness of the scaling we construct a dynamic version of these feedback laws

regression modeling in back propagation and projection pursuit learning we study and compare two types of connectionist learning methods for model free regression problems 1 the backpropagation learning bpl and 2 the projection pursuit learning ppl emerged in recent years in the statistical estimation literature both the bpl and the ppl are based on projections of the data in directions determined from interconnection weights however unlike the use of fixed nonlinear activations usually sigmoidal for the hidden neurons in bpl the ppl systematically approximates the unknown nonlinear activations moreover the bpl estimates all the weights simultaneously at each iteration while the ppl estimates the weights cyclically neuron by neuron and layer by layer at each iteration although the bpl and the ppl have comparable training speed when based on a gauss newton optimization algorithm the ppl proves more parsimonious in that the ppl requires a fewer hidden neurons to approximate the true function to further improve the statistical performance of the ppl an orthogonal polynomial approximation is used in place of the supersmoother method originally proposed for nonlinear activation approximation in the ppl

an adaptive orthogonal search algorithm for model subset selection and non linear system identification a new adaptive orthogonal search aos algorithm is proposed for model subset selection and non linear system identification model structure detection is a key step in any system identification problem this consists of selecting significant model terms from a redundant dictionary of candidate model terms and determining the model complexity model length or model size the final objective is to produce a parsimonious model that can well capture the inherent dynamics of the underlying system in the new aos algorithm a modified generalized cross validation criterion called the adjustable prediction error sum of squares apress is introduced and incorporated into a forward orthogonal search procedure the main advantage of the new aos algorithm is that the mechanism is simple and the implementation is direct and easy and more importantly it can produce efficient model subsets for most non linear identification problems

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

stability margins of nonlinear optimal regulators with nonquadratic performance criteria involving cross weighting terms abstract in this paper we derive guaranteed gain sector and disk margins for nonlinear optimal and inverse optimal regulators that minimize a nonlinear nonquadratic performance criterion involving cross weighting terms specifically sufficient conditions that guarantee gain sector and disk margins are given in terms of the state control and cross weighting nonlinear nonquadratic weighting functions the proposed results provide a generalization of the meaningful inverse optimal nonlinear regulator stability margins as well as the classical linear quadratic optimal regulator gain and phase margins

uniform stabilization of nonlinear systems with arbitrary switchings and dynamic uncertainties we solve the problem of global uniform input to state stabilization of nonlinear switched systems with time varying and periodic dynamics with dynamic uncertainties and with external disturbances the switching signal is assumed to be unknown and the dynamics of the known components of the state vector is equivalent to the general triangular form gtf with non invertible input output maps in our first and most general result we prove that if the dynamic uncertainty is treated as external disturbance then the general triangular form system can be stabilized with arbitrarily small gain w r t the dynamic uncertainty by means of a switching independent smooth and periodic feedback hence using a suitable extension of the well known small gain theorem to our case of switched systems with arbitrary switchings we obtain the uniform input to state stabilization of the entire interconnected system the second part of the paper addresses a more special case of triangular form tf switched systems with right invertible input output i o maps with unknown switchings and with dynamic uncertainties we show that the design becomes simpler and more constructive and the controllers become time invariant if the dynamics is autonomous in this special case finally we consider an example with explicit design of the stabilizing controllers

integrator backstepping for rounded controls and control rates we present a backstepping procedure for the design of globally stabilizing state feedback control laws such that the magnitudes of the control signals and their derivatives are bounded by constants which do not depend on the initial conditions we accomplish this by propagating such boundedness properties through each step of the recursive design

lyapunov design of stabilizing controllers for cascaded systems the design of a state feedback law for an affine nonlinear system to render a as small as possible compact neighborhood of the equilibrium of interest globally attractive is discussed following z artstein s theorem 1983 the problem can be solved by designing a so called control lyapunov function for systems which are in a cascade form a lyapunov function meeting artstein s conditions is designed assuming the knowledge of a control law stabilizing the equilibrium of the head nonlinear subsystem in particular for planar systems this gives sufficient and necessary conditions for a compact neighborhood of the equilibrium to be stabilized

homogeneous approximation recursive observer design and output feedback we introduce two new tools that can be useful in nonlinear observer and output feedback design the first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity homogeneity in the bi limit exploiting this extension we give several results concerning stability and robustness for a homogeneous in the bi limit vector field the second tool is a new recursive observer design procedure for a chain of integrator combining these two tools we propose a new global asymptotic stabilization result by output feedback for feedback and feedforward systems

interval homogeneity based control for a class of nonlinear systems with unknown power drifts this technical note considers the global stabilization problem for a class of nonlinear systems with unknown power exponent drifts based on the concept of interval homogeneity with monotone degrees the allowable bounds of the unknown power drifts can be explicitly determined to guarantee the solvability of the problem the technique of adding a power integrator is revamped based on a new lyapunov function with interval parameters and is recursively employed to construct a global stabilizer for the nonlinear systems

versions of sontag s input to state stability condition and the global stabilizability problem this paper deals with the global feedback stabilizability problem for interconnected nonlinear systems that are affine in the control the corresponding feedback stabilizers are supposed to be almost smooth real mappings the results of this paper extend those developed in recent works of the author siam j control optim 29 1991 pp 457 473 systems control lett 15 1990 pp 441 448 siam j control optim 30 1992 pp 879 893 concerning the local stabilizability problem the main sufficient conditions presented are of lyapunov type and the main idea of the paper is based on the input to state stability condition introduced by sontag ieee trans automat control 35 1990 pp 473 477

an explicit formula of bounded feedback stabilizers for feedforward systems abstract this work constitutes continuation of a recent result of the same authors which provides an explicit formula for bounded feedback stabilizers for a wide class of triangular nonlinear systems in the present paper the previous result is extended for nonlinear systems having feedforward structure and whose linearization at the equilibrium is in general uncontrollable

inverse optimality in robust stabilization the concept of a robust control lyapunov function bf rclf is introduced and it is shown that the existence of an bf rclf for a control affine system is equivalent to robust stabilizability via continuous state feedback this extends artstein s theorem on nonlinear stabilizability to systems with disturbances it is then shown that every bf rclf satisfies the steady state hamilton jacobi isaacs hji equation associated with a meaningful game and that every member of a class of pointwise min norm control laws is optimal for such a game these control laws have desirable properties of optimality and can be computed directly from the bf rclf without solving the hji equation for the upper value function

a new class of wavelet networks for nonlinear system identification a new class of wavelet networks wns is proposed for nonlinear system identification in the new networks the model structure for a high dimensional system is chosen to be a superimposition of a number of functions with fewer variables by expanding each function using truncated wavelet decompositions the multivariate nonlinear networks can be converted into linear in the parameter regressions which can be solved using least squares type methods an efficient model term selection approach based upon a forward orthogonal least squares ols algorithm and the error reduction ratio err is applied to solve the linear in the parameters problem in the present study the main advantage of the new wn is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks by adopting the analysis of variance anova expansion wns can now handle nonlinear identification problems in high dimensions

a simple lemma on greedy approximation in hilbert space and convergence rates for projection pursuit regression and neural network training a general convergence criterion for certain iterative sequences in hilbert space is presented for an important subclass of these sequences estimates of the rate of convergence are given under very mild assumptions these results establish an 0 1 f4n nonsampling convergence rate for projection pursuit regression and neural network training where n represents the number of ridge functions neurons or coefficients in a greedy basis expansion

homogeneous lyapunov function for homogeneous continuous vector field the goal of this article is to provide a construction of a homogeneous lyapunov function p associated with a system of differential equations j f x x r n 1 under the hypotheses 1 f c r n vanishes at x 0 and is homogeneous 2 the zero solution of this system is locally asymptotically stable moreover the lyapunov function v x tends to infinity with 1 x i and belongs to c r 0 r n cp with p e as large as wanted as application to the theory of homogeneous systems we present two well known results of robustness in a slightly extended form and with simpler proofs

tracking time varying causality and directionality of information flow using an error reduction ratio test with applications to electroencephalography data this paper introduces an error reduction ratio causality err causality test that can be used to detect and track causal relationships between two signals in comparison to the traditional granger method one significant advantage of the new err causality test is that it can effectively detect the time varying direction of linear or nonlinear causality between two signals without fitting a complete model another important advantage is that the err causality test can detect both the direction of interactions and estimate the relative time shift between the two signals numerical examples are provided to illustrate the effectiveness of the new method together with the determination of the causality between electroencephalograph signals from different cortical sites for patients during an epileptic seizure

identification of nonlinear spatiotemporal dynamical systems with nonuniform observations using reproducing kernel based integral least square regulation the identification of nonlinear spatiotemporal dynamical systems given by partial differential equations has attracted a lot of attention in the past decades several methods such as searching principle based algorithms partially linear kernel methods and coupled lattice methods have been developed to address the identification problems however most existing methods have some restrictions on sampling processes in that the sampling intervals should usually be very small and uniformly distributed in spatiotemporal domains these are actually not applicable for some practical applications in this paper to tackle this issue a novel kernel based learning algorithm named integral least square regularization regression ilsrr is proposed which can be used to effectively achieve accurate derivative estimation for nonlinear functions in the time domain with this technique a discretization method named inverse meshless collocation is then developed to realize the dimensional reduction of the system to be identified thereafter with this novel inverse meshless collocation model the ilsrr and a multiple kernel based learning algorithm a multistep identification method is systematically proposed to address the identification problem of spatiotemporal systems with pointwise nonuniform observations numerical studies for benchmark systems with necessary discussions are presented to illustrate the effectiveness and the advantages of the proposed method

stabilization of feedforward systems approximated by a non linear chain of integrators we prove that for any odd integer p and any strictly positive integer n feedforward systems which are approximated at the origin by a chain of integrators of degree p and length n can be globally asymptotically stabilized by bounded smooth time invariant state feedbacks our proof is based on the construction of a lyapunov function and the feedback laws we obtain are given by explicit formulas

asymptotically stabilizing feedback controls and the nonlinear regulator problem continuous asymptotically stabilizing feedback controls are constructed for two dimensional and certain three dimensional small time locally controllable affine systems the lie products which de

brief practical l2 disturbance attenuation for nonlinear systems in this work a notion of generalized l 2 gain for nonlinear systems where the gain is considered as a function of the state instead of a global constant is presented this new notion seems to be adequate to characterize the gain properties of several nonlinear systems which do not possess a uniform l 2 gain property i e the l 2 gain depends on the operating point moreover a notion of practical l 2 gain attenuation which extends the standard definition and parallels mutatae mutandis the concepts of practical stability is also proposed

lattice dynamical wavelet neural networks implemented using particle swarm optimization for spatio temporal system identification in this brief by combining an efficient wavelet representation with a coupled map lattice model a new family of adaptive wavelet neural networks called lattice dynamical wavelet neural networks ldwnns is introduced for spatio temporal system identification a new orthogonal projection pursuit opp method coupled with a particle swarm optimization pso algorithm is proposed for augmenting the proposed network a novel two stage hybrid training scheme is developed for constructing a parsimonious network model in the first stage by applying the opp algorithm significant wavelet neurons are adaptively and successively recruited into the network where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer the resultant network model obtained in the first stage however may be redundant in the second stage an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network an example for a real spatio temporal system identification problem is presented to demonstrate the performance of the proposed new modeling framework

inverse polynomial optimization we consider the inverse optimization problem associated with the polynomial program f min f bx colon bx in k and a given current feasible solution y in k we provide a systematic numerical scheme to compute an inverse optimal solution that is we compute a polynomial tilde f which may be of the same degree as f if desired with the following properties a y is a global minimizer of tilde f on k with a putinar s certificate with an a priori degree bound d fixed and b tilde f minimizes vert f tilde f vert which can be the l1 l2 or l norm of the coefficients over all polynomials with such properties computing tilde f d reduces to solving a semidefinite program whose optimal value also provides a bound on how far fy is from the unknown optimal value f the size of the semidefinite program can be adapted to the available computational capabilities moreover if one uses the l1 norm then tilde f takes a simple and explicit canonical form some variations are also discussed

fuzzy wavelet polynomial neural networks analysis and design in this study we propose a concept of fuzzy wavelet polynomial neural networks fwpnns based on concepts and constructs of polynomial neural networks and fuzzy wavelet neurons fwns these networks exhibit a rule based architecture while each rule in the fwn consists of the premise part and consequence part the premise part is realized by using c means clustering method while the consequence part is realized by means of wavelet functions whose parameters are estimated with the aid of the least square method in some sense the fwpnn can be regarded as a generalized fuzzy wavelet neural network fwnn unlike gaussian membership functions that are commonly utilized to implement the premise part of the rules in typical fwnns c means method is employed here to overcome a possible curse of dimensionality polynomial neural networks pnns are used to express the nonlinearity of a complex system furthermore the particle swarm optimization is used to optimize the design parameters of the proposed network based on the pnns and fwnns the proposed fwpnns take advantages of these two neural networks it exhibits the abilities to describe high order nonlinear relations between input and output variables and it is beneficial to describe models impacted by uncertainty the proposed fwpnns are applied for time series prediction and regression problems e g control of dynamic plants several well known modeling benchmarks including regression and time series are considered to evaluate the performance of the proposed fwpnns a comparative analysis shows that the proposed fwpnns result in better performance when comparing with some previous models reported in the literature

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

classifiability based discriminatory projection pursuit fisher s linear discriminant fld is one of the most widely used linear feature extraction method especially in many visual computation tasks based on the analysis on several limitations of the traditional fld this paper attempts to propose a new computational paradigm for discriminative linear feature extraction named classifiability based discriminatory projection pursuit cdpp which is different from the traditional fld and its variants there are two steps in the proposed cdpp one is the construction of a candidate projection set cps and the other is the pursuit of discriminatory projections specifically in the former step candidate projections are generated by using the nearest between class boundary samples while the latter is efficiently achieved by classifiability based adaboost learning from the cps we show that the new projection pursuit paradigm not only does not suffer from the limitations of the traditional fld but also inherits good generalizability from the boundary attribute of candidate projections extensive experiments on both synthetic and real datasets validate the effectiveness of cdpp for discriminative linear feature extraction

universal approximation using incremental constructive feedforward networks with random hidden nodes according to conventional neural network theories single hidden layer feedforward networks slfns with additive or radial basis function rbf hidden nodes are universal approximators when all the parameters of the networks are allowed adjustable however as observed in most neural network implementations tuning all the parameters of the networks may cause learning complicated and inefficient and it may be difficult to train networks with nondifferential activation functions such as threshold networks unlike conventional neural network theories this paper proves in an incremental constructive method that in order to let slfns work as universal approximators one may simply randomly choose hidden nodes and then only need to adjust the output weights linking the hidden layer and the output layer in such slfns implementations the activation functions for additive nodes can be any bounded nonconstant piecewise continuous functions g r r and the activation functions for rbf nodes can be any integrable piecewise continuous functions g r r and rg x dx 0 the proposed incremental method is efficient not only for sflns with continuous including nondifferentiable activation functions but also for slfns with piecewise continuous such as threshold activation functions compared to other popular methods such a new network is fully automatic and users need not intervene the learning process by manually tuning control parameters

polytopic control lyapunov functions for robust stabilization of a class of nonlinear systems abstract we develop a method for computing a region in state space over which a nonlinear system is guaranteed by a given polytopic control lyapunov function to be stable in closed loop under some appropriate control law for systems which are nonlinear in only a few state variables the procedure is computationally tractable the computation time required to evaluate stability over each cone comprising a level set of the lyapunov function is exponential in the number of nonlinear states but otherwise polynomial in the dimension of the full state space control constraints and robustness to bounded disturbances are easily incorporated

propagating asymptotic controllability through integrators for a class of systems with triangular structure we derive sufficient conditions for global asymptotic controllability which according to clarke ledyaev sontag subbotin theorem guarantees asymptotic stabilization by discontinuous static feedback

finite time input to state stability and applications to finite time control design this paper extends the well known concept sontag s input to state stability iss to finite time control problems in other words a new concept finite time input to state stability ftiss is proposed and then is applied to both the analysis of finite time stability and the design of finite time stabilizing feedback laws of control systems with finite time stability nonsmoothness has to be considered and serious technical challenges arise in the design of finite time controllers and the stability analysis of the closed loop system it is found that ftiss plays an important role as the conventional iss in the context of asymptotic stability analysis and smooth feedback stabilization moreover a robust adaptive controller is proposed to handle nonlinear systems with parametric and dynamic uncertainties by virtue of ftiss and related arguments

optimal control using an algebraic method for control affine non linear systems a deterministic optimal control problem is solved for a control affine non linear system with a non quadratic cost function we algebraically solve the hamilton jacobi equation for the gradient of the value function this eliminates the need to explicitly solve the solution of a hamilton jacobi partial differential equation we interpret the value function in terms of the control lyapunov function then we provide the stabilizing controller and the stability margins furthermore we derive an optimal controller for a control affine non linear system using the state dependent riccati equation sdre method this method gives a similar optimal controller as the controller from the algebraic method we also find the optimal controller when the cost function is the exponential of integral case which is known as risk sensitive rs control finally we show that sdre and rs methods give equivalent optimal controllers for non linear deterministic systems examples demonstrate the proposed methods

adding an integrator for the stabilization problem abstract we study the relationship between the following two properties p1 the system x f x y y v is locally asymptotically stabilizable and p2 the system x f x u is locally asymptotically stabilizable where x r n y r dayawansa martin and knowles have proved that these properties are equivalent if the dimension n 1 here using the so called control lyapunov function approach a we propose another more constructive and somewhat simpler proof of dayawansa martin and knowles s result b we show that in general p1 does not imply p2 for dimensions n larger than 1 c we prove that p2 implies p1 if some extra assumptions are added like homogeneity of the system by using the latter result recursively we obtain a sufficient condition for the local asymptotic stabilizability of systems in a triangular form

global stabilization of the generalized mimo triangular systems with singular input output links this work is devoted to the problem of global stabilization for a class of the general multi input and multi output mimo triangular systems which are not feedback linearizable to solve the problem we develop a specific backstepping procedure and generalize some existing results since we deal with the global stabilization for the singular and mimo case the technique of the proof differs from the standard backstepping algorithms

practical output tracking of nonlinear systems with uncontrollable unstable linearization the paper focuses on the problem of having the output of nonlinear systems track a prescribed c sup 1 reference signal it is proved that under mild assumptions global practical output tracking is achievable by smooth state feedback although asymptotic output tracking is usually not possible even locally because the linearized system has uncontrollable modes whose eigenvalues are on the right half plane smooth feedback controllers which solve the problem of global practical output tracking are explicitly constructed based on a modified adding a power integrator approach this feedback design method also leads to solutions to challenging benchmark control problems including practical output tracking of an underactuated unstable two degrees of freedom mechanical system

recursive observer design homogeneous approximation and nonsmooth output feedback stabilization of nonlinear systems we present a nonsmooth output feedback framework for local and or global stabilization of a class of nonlinear systems that are not smoothly stabilizable nor uniformly observable a systematic design method is presented for the construction of stabilizing dynamic output compensators that are nonsmooth but houmllder continuous a new ingredient of the proposed output feedback control scheme is the introduction of a recursive observer design algorithm making it possible to construct a reduced order observer step by step in a naturally augmented manner such a nonsmooth design leads to a number of new results on output feedback stabilization of nonlinear systems one of them is the global stabilizability of a chain of odd power integrators by holder continuous output feedback the other one is the local stabilization using nonsmooth output feedback for a wide class of nonlinear systems in the hessenberg form studied in a previous paper where global stabilizability by nonsmooth state feedback was already proved to be possible

global stabilization of cascade systems by c sup 0 partial state feedback this paper shows how the nonsmooth but continuous feedback design approach developed recently for global stabilization of nonlinear systems with uncontrollable unstable linearization and the notion and properties of the input to state stability lyapunov function can be effectively coupled resulting in globally stabilizing c sup 0 partial state feedback controllers for a class of cascade systems which may not be smoothly stabilizable even locally

identification of mimo non linear systems using a forward regression orthogonal estimator abstract an orthogonal least squares estimator which was originally derived for single input single output systems is extended to multi input multi output non linear systems the estimator can provide information about the structure or which terms to include in the model and final parameter estimates in a very simple and efficient manner multivariable non linear model validity tests are also discussed and the results of applying the orthogonal estimator to both simulated and real data are included

explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization for a class of nonlinear systems having triangular structure we provide explicit formulas for feedback controllers that exhibit global stabilization the global part of our analysis is mainly based on a version of sontag s input to state stability property and constitutes a generalization of previous works of the second author

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

the gain scheduling and the robust state feedback stabilization problems we consider dynamical uncertain systems of the form x spl dot a x w b x w u where w t spl isin w is an unknown but bounded time varying parameter we consider the robust state feedback stabilization problem in which we consider a control of the form u spl phi x and the gain scheduling stabilization problem in which a control of the form u spl phi x w full information control is admitted we show that for convex processes those systems in which for fixed x the set of all a x w b x w is convex the two problems are equivalent i e if there exists a locally lipschitz gain scheduling stabilizing control then there exists a robustly stabilizing control continuous everywhere except possibly at the origin thus for convex process stabilization knowledge of w t is not an advantage for the compensator then we consider the special class of polytopic lpv systems and show that there is no loss of regularity as in the general case if we pass from a gain scheduling controller to a state feedback controller in particular no discontinuity at the origin may occur we show that the existence of a dynamic controller always implies the existence of a static one finally we show that we can always find a linear gain scheduling controller for a stabilizable system this means that a possible advantage of the online measurement of the parameter w t is that this always allows for linear compensators whose implementation can be easier than that of nonlinear ones

c 1 fuzzy manifolds abstract this paper introduces the notion of a c 1 fuzzy manifold as a natural development of the notions of a fuzzy topological vector space and of a fuzzy derivative of a fuzzy continuous mapping between fuzzy topological vector spaces first a fuzzy atlas of class c 1 on a set is constructed and shown to yield a fuzzy topology that is compatible with the fuzzy atlas the structure of a c 1 fuzzy manifold on the set then follows next it is shown that the product of two fuzzy manifolds is a fuzzy manifold and that the composition of two fuzzy differentiable mappings between fuzzy manifolds is fuzzy differentiable finally the notions of a tangent vector and of a tangent space at a point in a fuzzy manifold are formulated and the tangent space is shown to be a vector space

nonsmooth output feedback stabilization of a class of genuinely nonlinear systems in the plane in this note we address the problem of output feedback stabilization for a class of planar systems that are inherently nonlinear in the sense that the linearized system at the origin is neither controllable nor observable moreover the uncontrollable modes contain eigenvalues on the right half plane by the well known necessary condition such planar systems cannot be stabilized even locally by any smooth output feedback and hence must be dealt with by nonsmooth output feedback the main contribution of this work is the development of a non lipschitz continuous output feedback design method that leads to a solution to the problem the proposed output feedback control scheme is not based on the separation principle but rather relies on the design of a reduced order nonlinear observer from an earlier paper with an appropriate twist and the tool of adding a power integrator a non lipschitz continuous output feedback controller is explicitly constructed achieving global stabilization of the planar systems without imposing the high order growth conditions required in a previous paper

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

a continuous feedback approach to global strong stabilization of nonlinear systems we present a continuous feedback approach to the problem of global strong stabilization for genuinely nonlinear systems that may not be stabilized even locally by any smooth feedback we describe conditions under which it is possible to prove while no smooth controllers exist the existence of continuous state feedback control laws that achieve global strong stability gss in the sense of kurzweil 1956 the proof is constructive and carried out by developing a machinery which combines the theory of homogeneous systems with the idea of adding a power integrator for the explicit construction of globally stabilizing continuous controllers we then illustrate by means of examples how this machinery can be used to overcome the topological obstruction caused by smooth feedback and hence resulting in new solutions to a variety of open control problems including global stabilization of an underactuated unstable two degree of freedom mechanical system

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

constrained control of input output linearizable systems using control sharing barrier functions abstract control barrier functions cbfs have been used as an effective tool for designing a family of controls that ensures the forward invariance of a set when multiple cbfs are present it is important that the set of controls satisfying all the barrier conditions is non empty in this paper we investigate such a control sharing property for multiple cbfs and provide sufficient and necessary conditions for the property to hold based on that we study the tracking control design problem of an input output linearizable system with multiple time varying output constraints where the output constraints are encoded as cbfs and the barrier conditions are expressed as hard constraints in a quadratic program qp whose feasibility is guaranteed by the control sharing property of the cbfs with the controller generated from the qp the output constraints are always satisfied and the tracking objective is achieved when it is not conflicting with the constraints the effectiveness of our control design method is illustrated by two examples