direct adaptive nn control of a class of nonlinear systems in this paper direct adaptive neural network nn control is presented for a class of affine nonlinear systems in the strict feedback form with unknown nonlinearities by utilizing a special property of the affine term the developed scheme avoids the controller singularity problem completely all the signals in the closed loop are guaranteed to be semiglobally uniformly ultimately bounded and the output of the system is proven to converge to a small neighborhood of the desired trajectory the control performance of the closed loop system is guaranteed by suitably choosing the design parameters simulation results are presented to show the effectiveness of the approach

direct adaptive controller for nonaffine nonlinear systems using self structuring neural networks a direct adaptive state feedback controller is proposed for highly nonlinear systems we consider uncertain or ill defined nonaffine nonlinear systems and employ a neural network nn with flexible structure i e an online variation of the number of neurons the nn approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for the weights in the hidden layer and output layer of the nn are established so that the whole closed loop system is stable in the sense of lyapunov moreover the tracking error is guaranteed to be uniformly asymptotically stable uas rather than uniformly ultimately bounded uub with the aid of an additional robustifying control term the proposed control algorithm is relatively simple and requires no restrictive conditions on the design constants for the stability the efficiency of the proposed scheme is shown through the simulation of a simple nonaffine nonlinear system

semi free hamiltonian circle actions on 6 dimensional symplectic manifolds assume m is a connected compact 6 dimensional symplectic manifold equipped with a semi free hamiltonian circle action such that the fixed point set consists of isolated points or compact orientable surfaces we restrict attention to the case dim h 2 m 3 we give a complete list of the possible manifolds and determine their equivariant cohomology rings and equivariant chern classes some of these manifolds are classified up to diffeomorphism we also show the existence for a few cases

stable adaptive tracking of uncertain systems using nonlinearly parametrized on line approximators the design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities is considered the lyapunov synthesis approach is used to develop state feedback adaptive control schemes based on a general class of nonlinearly parametrized on line approximation models the key assumptions are that the system uncertainty satisfies a strict feedback condition and that the network reconstruction error and higher order terms of the on line approximator with respect to the network weights satisfy certain bounding conditions an adaptive bounding design is used to show that the overall neural control system guarantees semi global uniform ultimate boundedness within a neighbourhood of zero tracking error the theoretical results are illustrated through a simulation example

adaptive nn control for a class of strict feedback discrete time nonlinear systems in this paper both full state and output feedback adaptive neural network nn controllers are presented for a class of strict feedback discrete time nonlinear systems firstly lyapunov based full state adaptive nn control is presented via backstepping which avoids the possible controller singularity problem in adaptive nonlinear control and solves the noncausal problem in the discrete time backstepping design procedure after the strict feedback form is transformed into a cascade form another relatively simple lyapunov based direct output feedback control is developed the closed loop systems for both control schemes are proven to be semi globally uniformly ultimately bounded

robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors this paper describes the design of the robust adaptive fuzzy controller for uncertain single input single output nonlinear dynamical systems with unknown nonlinearities these unknown nonlinearities are approximated by the fuzzy system with a set of fuzzy if then rules whose parameters are adjusted on line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track a given trajectory the lyapunov synthesis approach is used to develop a state feedback adaptive control algorithm based on the adaptive fuzzy model the key assumption is that the reconstruction errors satisfy certain bounding conditions the control law consists of two terms one is the certainty equivalent control and the other is the bounding control a bounding parameter adaptive law is used to obtain this bounding control the overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded it is also shown that in the special case the tracking error exponentially converges to zero even though the approximation errors exist

output feedback control of a class of discrete mimo nonlinear systems with triangular form inputs in this paper adaptive neural network nn control is investigated for a class of discrete time multi input multi output mimo nonlinear systems with triangular form inputs each subsystem of the mimo system is in strict feedback form first through two phases of coordinate transformation the mimo system is transformed into input output representation with the triangular form input structure unchanged by using high order neural networks honns as the emulators of the desired controls effective output feedback adaptive control is developed using backstepping the closed loop system is proved to be semiglobally uniformly ultimate bounded sguub by using lyapunov method the output tracking errors are guaranteed to converge into a compact set whose size is adjustable and all the other signals in the closed loop system are proved to be bounded simulation results show the effectiveness of the proposed control scheme

integrated design of a linear neuro adaptive controller in the presence of norm bounded uncertainties adaptive neural controllers are often criticised for the lack of clear and easy design methodologies that relate adaptive neural network nn design parameters to performance requirements this study proposes a methodology for the design of an integrated linear adaptive model reference controller that guarantees component wise boundedness of the tracking error within an a priori specified compact domain the approach is based on the design of a robust invariant ellipsoidal set where both the nn reconstruction error and the neuro adaptive control are considered as bounded persistent uncertainties we show that all the performance and control requirements for the closed loop system can be expressed as linear matrix inequality constraints this brings the advantage that feasibility and optimal design parameters can be effectively computed while solving a linear optimisation problem an advantage of the method is that it allows a systematic and quantitative evaluation of the interplay between the design param

some properties of the class of positive dunford pettis operators abstract we characterize banach lattices for which each positive dunford pettis operator is m weakly compact resp l weakly compact and we give some consequences

about positive dunford pettis operators on banach lattices abstract we give several characterizations of banach lattices on which each positive dunford pettis operator is compact as consequences we obtain new sufficient and necessary conditions under which a norm of a banach lattice is order continuous a positive weakly compact operator is compact and the dual operator of a positive dunford pettis operator is dunford pettis

optimal control of nonlinear continuous time systems in strict feedback form this paper proposes a novel optimal tracking control scheme for nonlinear continuous time systems in strict feedback form with uncertain dynamics the optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique subsequently a neural network based optimal control scheme is introduced to estimate the cost or value function over an infinite horizon for the resulting nonlinear continuous time systems in affine form when the internal dynamics are unknown the estimated cost function is then used to obtain the optimal feedback control input therefore the overall optimal control input for the nonlinear continuous time system in strict feedback form includes the feedforward plus the optimal feedback terms it is shown that the estimated cost function minimizes the hamilton jacobi bellman estimation error in a forward in time manner without using any value or policy iterations finally optimal output feedback control is introduced through the design of a suitable observer lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller simulation examples are provided to validate the theoretical results

on the variation in the cohomology of the symplectic form of the reduced phase space is called the momentum mapping of the hamiltonian t action given 1 1 the condition 1 2 just means that t acts along the fibers of j for the basic definitions and properties of non commutative hamiltonian group actions see am the results of this paper can easily be extended to hamiltonian actions of arbitrary compact connected lie groups by applying our results to the action of its maximal toms and using the equivariance of the momentum mapping for some more details see the remarks at the end of sect 2 we will assume throughout this paper that the momentum map is proper that is j i u is compact for each compact subset u of t now let r be a regular value of j that is t j tmm t is surjective for all meye j 1 4 then ye is a smooth submanifold of m compact because

robust output tracking for non linear systems the problem of output tracking for a single input single output non linear system in the presence of uncertainties is studied the notions relative degree and minimum phase for non linear systems are reviewed given a bounded desired tracking signal with bounded derivatives a control law is designed for minimum phase non linear systems which results in tracking of this signal by the output this control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors two types of uncertainties are considered those satisfying a generalized matching condition but otherwise unstructured and linear parametric uncertainties it is shown that for systems with the first type of uncertainty high gain control laws can result in small tracking errors of o where e is a small design parameter an alternative scheme based on variable structure control strategy is shown to yield zero tracking errors adaptive control te

further results on adaptive control for a class of nonlinear systems using neural networks zhang et al presented an excellent neural network nn controller for a class of nonlinear control designs the singularity issue is completely avoided based on a modified lyapunov function their lemma illustrates the existence of an ideal control which is important in establishing the nn approximator in this paper we provide a lyapunov function to realize an alternative ideal control which is more direct and simpler the major contributions of this paper are divided into two parts first it proposes a control scheme which results in a smaller dimensionality of nn than that of zhang et al in this way the proposed nn controller is easier to implement and more reliable for practical purposes second by removing certain restrictions from the design reported by zhang et al we further develop a new nn controller which can be applied to a wider class of systems

adaptive neural control of nonlinear mimo systems with time varying output constraints in this paper adaptive neural control is investigated for a class of unknown multiple input multiple output nonlinear systems with time varying asymmetric output constraints to ensure constraint satisfaction we employ a system transformation technique to transform the original constrained in the sense of the output restrictions system into an equivalent unconstrained one whose stability is sufficient to solve the output constraint problem it is shown that output tracking is achieved without violation of the output constraint more specifically we can shape the system performance arbitrarily on transient and steady state stages with the output evolving in predefined time varying boundaries all the time a single neural network whose weights are tuned online is used in our design to approximate the unknown functions in the system dynamics while the singularity problem of the control coefficient matrix is avoided without assumption on the prior knowledge of control input s bound all the signals in the closed loop system are proved to be semiglobally uniformly ultimately bounded via lyapunov synthesis finally the merits of the proposed controller are verified in the simulation environment

on the construction of certain 6 dimensional symplectic manifolds with hamiltonian circle actions let m w be a connected compact 6 dimensional symplectic manifold equipped with a semi free hamiltonian s 1 action such that the fixed point set consists of isolated points or surfaces assume dim h 2 m 3 in an earlier paper we defined a certain invariant of such spaces which consists of fixed point data and twist type and we divided the possible values of these invariants into six types in this paper we construct such manifolds with these types as a consequence we have a precise list of the values of these invariants

the structure of rational and ruled symplectic 4 manifolds this paper investigates the structure of compact symplectic 4 manifolds v w which contain a symplectically embedded copy c of s2 with nonnegative self intersection number such a pair v c w is called minimal if in addition the open manifold v c contains no exceptional curves i e symplectically embedded 2 spheres with self intersection 1 we show that every such pair v c w covers a minimal pair v c c which may be obtained from v by blowing down a finite number of disjoint exceptional curves in v c further the family of manifold pairs v c w under consideration is closed under blowing up and down we next give a complete list of the possible minimal pairs we show that v is symplectomorphic either to p2 with its standard form or to an s2 bundle over a compact surface with a symplectic structure which is uniquely determined by its cohomology class moreover this symplectomorphism may be chosen so that it takes c either to 2 a complex line or quadric in cp2 or in the case when v is a bundle to a fiber or section of the bundle department of mathematics state university of new york at stony brook stony brook new york 11794 3651 e mail address dusa math sunysb edu this content downloaded from 207 46 13 145 on wed 27 apr 2016 05 10 07 utc all use subject to http about jstor org terms

addendum to on the variation in the cohomology of the symplectic form of the reduced phase space here we have used the notation rlx for the inner product of the vector field x with the form a and ix m x j m for the x component of a in an earlier paper 4 it was shown that the push forward j dm of the liouville measure dm on m under the momentum mapping j is a piecewise polynomial measure on moreover in case x has isolated isolated zeros on m an explicit formula for the integral

peaking free output feedback adaptive neural control under a nonseparation principle high gain observers have been extensively applied to construct output feedback adaptive neural control anc for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle yet due to static gain and linear properties high gain observers are usually subject to peaking responses and noise sensitivity existing adaptive neural network nn observers cannot effectively relax the limitations of high gain observers this paper presents an output feedback indirect anc strategy under a nonseparation principle where a hybrid estimation scheme that integrates an adaptive nn observer with state variable filters is proposed to estimate plant states by applying a single lyapunov function candidate to the entire system it is proved that the closed loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability simulation results have shown effectiveness and superiority of this approach

adaptive neural control for strict feedback nonlinear systems without backstepping in this brief a new adaptive neurocontrol algorithm for a single input single output siso strict feedback nonlinear system is proposed most of the previous adaptive neural control algorithms for strict feedback nonlinear systems were based on the backstepping scheme which makes the control law and stability analysis very complicated the main contribution of the proposed method is that it demonstrates that the state feedback control of the strict feedback system can be viewed as the output feedback control problem of the system in the normal form as a result the proposed control algorithm is considerably simpler than the previous ones based on backstepping depending heavily on the universal approximation property of the neural network nn only one nn is employed to approximate the lumped uncertain system nonlinearity the lyapunov stability of the nn weights and filtered tracking error is guaranteed in the semiglobal sense