output feedback nn control for two classes of discrete time systems with unknown control directions in a unified approach in this paper output feedback adaptive neural network nn controls are investigated for two classes of nonlinear discrete time systems with unknown control directions 1 nonlinear pure feedback systems and 2 nonlinear autoregressive moving average with exogenous inputs narmax systems to overcome the noncausal problem which has been known to be a major obstacle in the discrete time control design both systems are transformed to a predictor for output feedback control design implicit function theorem is used to overcome the difficulty of the nonaffine appearance of the control input the problem of lacking a priori knowledge on the control directions is solved by using discrete nussbaum gain the high order neural network honn is employed to approximate the unknown control the closed loop system achieves semiglobal uniformly ultimately bounded sguub stability and the output tracking error is made within a neighborhood around zero simulation results are presented to demonstrate the effectiveness of the proposed control

approximate solution of np optimization problems abstract this paper presents the main results obtained in the field of approximation algorithms in a unified framework most of these results have been revisited in order to emphasize two basic tools useful for characterizing approximation classes that is combinatorial properties of problems and approximation preserving reducibilities in particular after reviewing the most important combinatorial characterizations of the classes ptas and fptas we concentrate on the class apx and as a concluding result we show that this class coincides with the class of optimization problems which are reducible to the maximum satisfiability problem with respect to a polynomial time approximation preserving reducibility

polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers it is shown that the binary expansions of algebraic numbers do not form secure pseudorandom sequences given sufficiently many initial bits of an algebraic number its minimal polynomial can be reconstructed and therefore the further bits of the algebraic number can be computed this also enables the authors to devise a simple algorithm to factorise polynomials with rational coefficients all algorithms work in polynomial time

adaptive fuzzy control of nonlinear systems in pure feedback form based on input to state stability using mean value theorem and backstepping technique a robust adaptive fuzzy control scheme is proposed for a class of pure feedback nonlinear systems with unknown dead zone and disturbances via input to state stability takagi sugeno t s type fuzzy logic systems are used to approximate the uncertain nonlinear functions and fewer learning parameters need to be adjusted online based on small gain theorem the closed loop control system is proven to be semiglobally uniformly ultimately bounded and the tracking error converges to a neighborhood of zero by choosing appropriate parameters simulation results demonstrate the effectiveness of the control scheme

blind carrier phase tracking with guaranteed global convergence conventional blind carrier recovery algorithms have been observed to show unstable behaviors for large constellation modulation schemes such as 64 qam or 256 qam we propose a new carrier tracking approach that has guaranteed global convergence first we show that the carrier tracking problem is equivalent to a blind source separation problem which involves the separation of a linear unitary mixture of two independent components that are the real and imaginary parts of the emitted signal then by using a blind source separation procedure we derive a new and robust carrier tracking algorithm with guaranteed global convergence some numerical simulations are provided to illustrate the effectiveness of the proposed method

a novel robust adaptive fuzzy tracking control for a class of nonlinearmulti input multi output systems robust adaptive fuzzy tracking control of a class of uncertain multi input multi output nonlinear systems with coupled interconnections is considered in this paper takagi sugeno t s fuzzy systems are used to approximate the unknown system functions a novel adaptive control scheme is developed on the basis of the so called dynamic surface control and minimal learning parameters techniques the proposed scheme has following two key features first the number of parameters updated online for each subsystem is reduced to one and both problems of curse of dimension for high dimensional systems and explosion of complexity inherent in the conventional backstepping methods are circumvented second the potential controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques is overcome it is shown via lyapunov theory that all the signals in the closed loop system are semiglobally uniformly ultimately bounded finally simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme

observer based adaptive neural network controller for uncertain nonlinear systems with unknown control directions subject to input time delay and saturation abstract this paper addresses the design of an observer based adaptive neural controller for a class of strict feedback nonlinear uncertain systems subject to input delay saturation and unknown direction the input delay has been handled using an integral compensator term in the controller design a neural network observer has been developed to estimate the unmeasured states in the observer design the lipschitz condition has been relaxed to solve the problem of unknown control directions the nussbaum gain function has been applied in the backstepping controller design the explosion of complexity occurred in the traditional backstepping technique has been avoided utilizing the dynamic surface control dsc technique and the designed controller is singularity free it has been shown that all closed loop signals are semi globally uniformly ultimately bounded sguub and the output tracking error converges to a small neighborhood of the origin by choosing the design parameters appropriately the numerical examples illustrate the effectiveness of the proposed control scheme

adaptive neural tracking control for a class of nonstrict feedback stochastic nonlinear systems with unknown backlash like hysteresis this paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict feedback form with unknown backlash like hysteresis nonlinearities to overcome the design difficulty of nonstrict feedback structure variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic by combining radial basis function neural networks universal approximation capability with an adaptive backstepping technique an adaptive neural control algorithm is proposed it is shown that the proposed controller guarantees that all the signals in the closed loop system are four moment semiglobally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value simulation results further show the effectiveness of the presented control scheme

bayesian nonparametric adaptive control using gaussian processes most current model reference adaptive control mrac methods rely on parametric adaptive elements in which the number of parameters of the adaptive element are fixed a priori often through expert judgment an example of such an adaptive element is radial basis function networks rbfns with rbf centers preallocated based on the expected operating domain if the system operates outside of the expected operating domain this adaptive element can become noneffective in capturing and canceling the uncertainty thus rendering the adaptive controller only semiglobal in nature this paper investigates a gaussian process based bayesian mrac architecture gp mrac which leverages the power and flexibility of gp bayesian nonparametric models of uncertainty the gp mrac does not require the centers to be preallocated can inherently handle measurement noise and enables mrac to handle a broader set of uncertainties including those that are defined as distributions over functions we use stochastic stability arguments to show that gp mrac guarantees good closed loop performance with no prior domain knowledge of the uncertainty online implementable gp inference methods are compared in numerical simulations against rbfn mrac with preallocated centers and are shown to provide better tracking and improved long term learning

robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance in this technical note we consider adaptive control of single input uncertain nonlinear systems in the presence of input saturation and unknown external disturbance by using backstepping approaches two new robust adaptive control algorithms are developed by introducing a well defined smooth function and using a nussbaum function the nussbaum function is introduced to compensate for the nonlinear term arising from the input saturation unlike some existing control schemes for systems with input saturation the developed controllers do not require assumptions on the uncertain parameters within a known compact set and a priori knowledge on the bound of the external disturbance besides showing global stability transient performance is also established and can be adjusted by tuning certain design parameters

adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances a novel function approximator is constructed by combining a fuzzy logic system with a fourier series expansion in order to model unknown periodically disturbed system functions then an adaptive backstepping tracking control scheme is developed where the dynamic surface control approach is used to solve the problem of explosion of complexity in the backstepping design procedure and the time varying parameter dependent integral lyapunov function is used to analyze the stability of the closed loop system the semiglobal uniform ultimate boundedness of all closed loop signals is guaranteed and the tracking error is proved to converge to a small residual set around the origin two simulation examples are provided to illustrate the effectiveness of the control scheme designed in this paper

on the hardness of approximating minimization problems we prove results indicating that it is hard to compute efficiently good approximate solutions to the graph coloring set covering and other related minimization problems specifically there is an e 0 such that graph coloring cannot be approximated with ratio n e unless p np set covering cannot be approximated with ratio c log n for any c 1 4 unless np is contained in dtime n poly log n similar results follow for related problems such as clique cover fractional chromatic number dominating set and others

observer based adaptive neural network control for nonlinear systems in nonstrict feedback form this paper focuses on the problem of adaptive neural network nn control for a class of nonlinear nonstrict feedback systems via output feedback a novel adaptive nn backstepping output feedback control approach is first proposed for nonlinear nonstrict feedback systems the monotonicity of system bounding functions and the structure character of radial basis function rbf nns are used to overcome the difficulties that arise from nonstrict feedback structure a state observer is constructed to estimate the immeasurable state variables by combining adaptive backstepping technique with approximation capability of radial basis function nns an output feedback adaptive nn controller is designed through backstepping approach it is shown that the proposed controller guarantees semiglobal boundedness of all the signals in the closed loop systems two examples are used to illustrate the effectiveness of the proposed approach

robust adaptive sliding mode control for fuzzy systems with mismatched uncertainties this paper is devoted to design adaptive sliding mode controllers for the takagi sugeno t s fuzzy system with mismatched uncertainties and exogenous disturbances the uncertainties in state matrices are mismatched and norm bounded while the exogenous disturbances are assumed to be bounded with an unknown bound which is estimated by a simple and effective adaptive approach both state and static output feedback sliding mode control problems are considered in terms of linear matrix inequalities lmis both sliding surfaces and sliding mode controllers can be easily obtained via a convex optimization technique finally two simulation examples and a real experiment are utilized to illustrate the applicability and effectiveness of the design procedures proposed in this paper

on the hardness of approximating shortest integer relations among rational numbers given x rn an integer relation for x is a non trivial vector m zn with inner product m x 0 in this paper we prove the following unless every np language is recognizable in deterministic quasi polynomial time i e in time o npoly log n the l shortest integer relation for a given vector x qn cannot be approximated in polynomial time within a factor of 2log0 5 n where is an arbitrarily small positive constant this result is quasi complementary to positive results derived from lattice basis reduction a variant of the well known l3 algorithm approximates for a vector x qn the l2 shortest integer relation within a factor of 2n2 in polynomial time our proof relies on recent advances in the theory of probabilistically checkable proofs in particular on a reduction from 2 prover 1 round interactive proof systems the same inapproximability result is valid for finding the l shortest integer solution for a homogeneous linear system of equations over q

constrained infinite horizon model predictive control for fuzzy discrete time systems the problem of constrained infinite horizon model predictive control for fuzzy discrete systems is considered in this paper new sufficient conditions are proposed in terms of linear matrix inequalities based on the optimal solutions of these sufficient conditions at each sampling instant we design both parallel distributed compensation and nonparallel distributed compensation state feedback controllers which can guarantee that the resulting closed loop fuzzy discrete system is asymptotically stable in addition the fuzzy feedback controllers meet the specifications for the fuzzy discrete systems with both input and output constraints numerical examples are presented to demonstrate the effectiveness of the proposed techniques

observer based direct adaptive fuzzy neural control for nonaffine nonlinear systems in this paper an observer based direct adaptive fuzzy neural control scheme is presented for nonaffine nonlinear systems in the presence of unknown structure of nonlinearities a direct adaptive fuzzy neural controller and a class of generalized nonlinear systems which are called nonaffine nonlinear systems are instead of the indirect one and affine nonlinear systems given by leu et al by using implicit function theorem and taylor series expansion the observer based control law and the weight update law of the fuzzy neural controller are derived for the nonaffine nonlinear systems based on strictly positive real spr lyapunov theory the stability of the closed loop system can be verified moreover the overall adaptive scheme guarantees that all signals involved are bounded and the output of the closed loop system will asymptotically track the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead zone inputs this paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi input and multi output mimo strict feedback nonlinear systems with both unknown nonsymmetric dead zone inputs and immeasurable states in this research fuzzy logic systems are utilized to evaluate the unknown nonlinear functions and a fuzzy adaptive state observer is established to estimate the unmeasured states based on the information of the bounds of the dead zone slopes as well as treating the time varying inputs coefficients as a system uncertainty a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique it is shown that the proposed control approach can assure that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded it is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters simulation examples are also provided to illustrate the effectiveness of the proposed approach

on the limits of computations with the floor function abstract up to now few models of computation with the power of evaluating discontinuous functions have been analyzed and few of their lower bounds or results on the decidability of languages are known in this paper we present a model of an analytic computation tree act these trees operate on real numbers and are able to compare real numbers to evaluate functions on real numbers and to evaluate certain discontinuous functions like the floor function this model generalizes the model of algebraic computation trees introduced by ben or we show by topological arguments that by acts one cannot decide certain classes of languages examples of which are q n and the set of tuples x1 xn r n that have components which are z linearly or algebraically dependent

adaptive fuzzy control for synchronization of nonlinear teleoperators with stochastic time varying communication delays in this paper adaptive fuzzy control is investigated for nonlinear teleoperators with time delays which ensures synchronization of positions and velocities of the master and slave manipulators and does not rely on the use of the scattering transformation compared with the previous passivity framework the communication delays are assumed to be stochastic time varying by feedback linearization the nonlinear dynamics of the teleoperation system is transformed into two subsystems local master slave position control with unmodeled dynamics and delayed motion synchronization then based on linear matrix inequalities lmi and markov jump linear systems adaptive fuzzy control strategies are developed for the nonlinear teleoperators with modeling uncertainties and external disturbances by using the approximation property of the fuzzy logic systems it is proven that the master slave teleoperation system is stochastically stable in mean square under specific lmi conditions and all the signals of the resulting closed loop system are uniformly bounded finally the extensive simulations are performed to show the effectiveness of the proposed method

adaptive fuzzy output feedback tracking backstepping control of strict feedback nonlinear systems with unknown dead zones in this paper an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict feedback systems with unknown functions unknown dead zones and immeasurable states fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy filters state observer is designed to estimate the immeasurable states by using the adaptive backstepping recursive design technique and constructing the dead zone inverse a new adaptive fuzzy backstepping output feedback control approach is developed it is mathematically proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters the proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement two simulation examples are provided to show the effectiveness of the proposed approach

observer based adaptive neural network control for nonlinear stochastic systems with time delay this paper considers the problem of observer based adaptive neural network nn control for a class of single input single output strict feedback nonlinear stochastic systems with unknown time delays dynamic surface control is used to avoid the so called explosion of complexity in the backstepping design process radial basis function nns are directly utilized to approximate the unknown and desired control input signals instead of the unknown nonlinear functions the proposed adaptive nn output feedback controller can guarantee all the signals in the closed loop system to be mean square semi globally uniformly ultimately bounded simulation results are provided to demonstrate the effectiveness of the proposed methods

the computational complexity of simultaneous diophantine approximation problems simultaneous diophantine approximation in d dimensions deals with the approximation of a vector bf alpha alpha 1 cdots alpha d of d real numbers by vectors of rational numbers all having the same denominator this paper considers the computational complexity of algorithms to find good simultaneous approximations to a given vector bf alpha of d rational numbers we measure the goodness of an approximation using the sup norm we show that a result of h w lenstra jr produces polynomial time algorithms to find sup norm best approximations to a given vector bf alpha when the dimension d is fixed we show that a recent algorithm of a k lenstra h w lenstra jr and l lovasz to find short vectors in an integral lattice can be used to find a good approximation to a given vector bf alpha in d dimensions with a denominator q satisfying 1 leqq q leqq 2 d 2 n which is within a factor sqrt 5d 2 d 1 2 of the best approximation with denominato

polynomial time algorithms for finding integer relations among real numbers in this article we state and prove a corrected version of theorem 3 5 in siam j comput 18 1989 pp 859 881

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

adaptive output feedback fuzzy tracking control for a class of nonlinear systems this paper is concerned with the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems the dynamic feedback strategy begins with an input driven filter by utilizing fuzzy logic systems to approximate unknown and desired control input signals directly instead of the unknown nonlinear functions an output feedback fuzzy tracking controller is designed via a backstepping approach it is shown that the proposed fuzzy adaptive output controller can guarantee that all the signals remain bounded and that the tracking error converges to a small neighborhood of the origin simulations results are presented to demonstrate the effectiveness of the proposed methods

the complexity and approximability of finding maximum feasible subsystems of linear relations we study the combinatorial problem which consists given a system of linear relations of finding a maximum feasible subsystem that is a solution satisfying as many relations as possible the computational complexity of this general problem named max fls is investigated for the four types of relations and various constrained versions of max fls where a subset of relations must be satisfied or where the variables take bounded discrete values are also considered we establish the complexity of solving these problems optimally and whenever they are intractable we determine their degree of approximability max fls with or relations is np hard even when restricted to homogeneous systems with bipolar coefficients whereas it can be solved in polynomial time for relations with real coefficients the various np hard versions of max fls belong to different approximability classes depending on the type of relations and the additional constraints we show that the range of approximability stretches from apx complete problems which can be approximated within a constant but not within every constant unless p np to npo pb complete ones that are as hard to approximate as all np optimization problems with polynomially bounded objective functions while max fls with equations and integer coefficients cannot be approximated within pe for some e 0 where p is the number of relations the same problem over gf q for a prime q can be approximated within q but not within qe for some e 0 max fls with strict or nonstrict inequalities can be approximated within 2 but not within every constant factor our results also provide strong bounds on the approximability of two variants of max fls with and relations that arise when training perceptrons which are the building blocks of artificial neural networks and when designing linear classifiers

robust control for a class of uncertain nonlinear systems adaptive fuzzy approach based on backstepping a robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances the controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique for each auxiliary system an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well it is shown that the resulting closed loop systems guarantee a satisfactory transient and asymptotic performance a simulation example is also presented to illustrate the design procedure and controller performance

adaptive neural output feedback tracking control for a class of uncertain discrete time nonlinear systems this brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi input multi output mimo systems in the discrete time form the considered mimo systems are composed of n subsystems with the couplings of inputs and states among subsystems in order to solve the noncausal problem and decouple the couplings it needs to transform the systems into a predictor form the higher order neural networks are utilized to approximate the desired controllers by using lyapunov analysis it is proven that all the signals in the closed loop system is the semi globally uniformly ultimately bounded and the output errors converge to a compact set in contrast to the existing results the advantage of the scheme is that the number of the adjustable parameters is highly reduced the effectiveness of the scheme is verified by a simulation example

a class of hierarchical fuzzy systems with constraints on the fuzzy rules this paper presents a class of hierarchical fuzzy systems where previous layer outputs are used not in if parts but only in then parts of the fuzzy rules of the current layer the proposed scheme is shown to be a universal approximator to any real continuous function on a compact set if complete fuzzy sets are used in the if parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier from the example of ball and beam control system simulation it is demonstrated that the proposed scheme approximates with high accuracy a model nonlinear controller with fewer fuzzy rules than a centralized fuzzy system and its control performance is comparable to that of a nonlinear controller

a simplified adaptive neural network prescribed performance controller for uncertain mimo feedback linearizable systems in this paper the problem of deriving a continuous state feedback controller for a class of multiinput multioutput feedback linearizable systems is considered with special emphasis on controller simplification and reduction of the overall design complexity with respect to the current state of the art the proposed scheme achieves prescribed bounds on the transient and steady state performance of the output tracking errors despite the uncertainty in system nonlinearities contrary to the current state of the art however only a single neural network is utilized to approximate a scalar function that partly incorporates the system nonlinearities furthermore the loss of model controllability problem typically introduced owing to approximation model singularities is avoided without attaching additional complexity to the control or adaptive law simulations are performed to verify and clarify the theoretical findings