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

trajectory piecewise quadratic reduced order model for subsurface flow with application to pde constrained optimization abstract a new reduced order model based on trajectory piecewise quadratic tpwq approximations and proper orthogonal decomposition pod is introduced and applied for subsurface oil water flow simulation the method extends existing techniques based on trajectory piecewise linear tpwl approximations by incorporating second derivative terms into the reduced order treatment both the linear and quadratic reduced order methods referred to as pod tpwl and pod tpwq entail the representation of new solutions as expansions around previously simulated high fidelity full order training solutions along with pod based projection into a low dimensional space pod tpwq entails significantly more offline preprocessing than pod tpwl as it requires generating and projecting several third order hessian type terms the pod tpwq method is implemented for two dimensional systems extensive numerical results demonstrate that it provides consistently better accuracy than pod tpwl with speedups of about two orders of magnitude relative to high fidelity simulations for the problems considered we demonstrate that pod tpwq can be used as an error estimator for pod tpwl which motivates the development of a trust region based optimization framework this procedure uses pod tpwl for fast function evaluations and a pod tpwq error estimator to determine when retraining which entails a high fidelity simulation is required optimization results for an oil water problem demonstrate the substantial speedups that can be achieved relative to optimizations based on high fidelity simulation

accelerating optimization of parametric linear systems by model order reduction design optimization problems are often formulated as an optimization problem whose objective is a function of the output of a large scale parametric linear system obtained from the discretization of a pde to reduce the high computational cost of the objective and its gradient model order reduction techniques can be used this paper uses interpolatory reduced models as surrogate models in an optimization procedure we replace the standard first order condition by the relaxed first order condition which is more suitable when algebraic reduced models are used as surrogate models the relaxed first order condition imposes that the approximation quality of the surrogate model at the interpolation point can be measured and refined and that the surrogate model is equipped with an error bound on the entire parameter space we propose two optimization algorithms one uses the error bound to define a trust region and the other penalizes the objective with the error bound we prove convergence of both methods un

discrete time adaptive iterative learning control for high order nonlinear systems with unknown control directions an adaptive iterative learning control method is proposed for a class of nonlinear strict feedback discrete time systems with random initial conditions and iteration varying desired trajectories an n step ahead predictor approach is employed to estimate the future states in the control design discrete nussbaum gain method is utilised to deal with the lack of a priori knowledge of control directions the proposed control algorithm guarantees the boundedness of all the signals in the controlled system the tracking error converges to zero asymptotically along the iterative learning axis except for beginning states affected by random initial conditions the effectiveness of the proposed control scheme is verified through numerical simulation

adaptive fuzzy asymptotic control of mimo systems with unknown input coefficients via a robust nussbaum gain based approach this paper proposes an adaptive fuzzy asymptotic control method for multiple input multiple output mimo nonlinear systems with unknown input coefficients with a focus on handling unknown input nonlinearities and control directions for all the existing nussbaum gain based approaches it is difficult to investigate unknown input coefficients problem since multiple time varying coefficients and disturbances coexist and should be simultaneously tackled in the stability analysis to overcome the above difficulty we propose a robust nussbaum gain based approach for the adaptive fuzzy asymptotic control of mimo nonlinear systems benefiting from the proposed nussbaum gain based approach bounded disturbances including unmodeled system dynamics and universal approximation errors are handled furthermore the proposed approach helps extend the bounded fuzzy control result to the asymptotic convergence hence both the control robustness and control accuracy are prompted within the frame of the developed nussbaum gain approach finally a simulation example is carried out to illustrate the effectiveness of the proposed control method

discrete time switching periodic adaptive control for time varying parameters with unknown periodicity abstractin this paper we address the problem of unknown periodicity for a class of discrete time nonlinear parametric systems without assuming any growth conditions on the nonlinearities the unknown periodicity hides in the parametric uncertainties which is difficult to estimate with existing techniques by incorporating a logic based switching mechanism we identify the period and bound of unknown parameter simultaneously lyapunov based analysis is given to demonstrate that a finite number of switchings can guarantee the asymptotic tracking for the nonlinear parametric systems the simulation result also shows the efficacy of the proposed switching periodic adaptive control approach

adaptive nn controller design for a class of nonlinear mimo discrete time systems an adaptive neural network tracking control is studied for a class of multiple input multiple output mimo nonlinear systems the studied systems are in discrete time form and the discretized dead zone inputs are considered in addition the studied mimo systems are composed of n subsystems and each subsystem contains unknown functions and external disturbance due to the complicated framework of the discrete time systems the existence of the dead zone and the noncausal problem in discrete time it brings about difficulties for controlling such a class of systems to overcome the noncausal problem by defining the coordinate transformations the studied systems are transformed into a special form which is suitable for the backstepping design the radial basis functions nns are utilized to approximate the unknown functions of the systems the adaptation laws and the controllers are designed based on the transformed systems by using the lyapunov method it is proved that the closed loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set the simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm

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

barrier lyapunov functions based adaptive control for a class of nonlinear pure feedback systems with full state constraints in this study an adaptive control technique is developed for a class of uncertain nonlinear parametric systems the considered systems can be viewed as a class of nonlinear pure feedback systems and the full state constraints are strictly required in the systems one remarkable advantage is that only less adjustable parameters are used in the design this advantage is first to take into account the pure feedback systems with the full state constraints the characteristics of the considered systems will lead to a difficult task for designing a stable controller to this end the mean value theorem is employed to transform the pure feedback systems to a strict feedback structure but non affine terms still exist for the transformed systems a novel recursive design procedure is constructed to remove the difficulties for avoiding non affine terms and guarantee that the full state constraints are not violated by introducing barrier lyapunov function blf with the error variables moreover it is proved that all the signals in the closed loop system are global uniformly bounded and the tracking error is remained in a bounded compact set two simulation studies are worked out to show the effectiveness of the proposed approach

brief paper output feedback adaptive control of a class of nonlinear discrete time systems with unknown control directions in this paper output feedback adaptive control is investigated for a class of nonlinear systems in output feedback form with unknown control gains to construct output feedback control the system is transformed into the form of the narma nonlinear auto regressive moving average model based on which future output prediction is carried out with employment of the predicted future output a constructive output feedback adaptive control is given with the discrete nussbaum gain exploited to overcome the difficulty due to unknown control directions under the global lipschitz condition of the system functions the boundedness of all the closed loop signals and asymptotical output tracking are achieved by the proposed control simulation results are presented to show the effectiveness of the proposed approach

adaptive discrete time sliding mode control of nonlinear systems described by wiener models abstractin this paper we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters the considered class of nonlinear systems is described by the block oriented models specifically the wiener models these models consist of dynamic linear blocks in series with static nonlinear blocks the proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete time sliding mode controller the parameters adaptation are performed using a new recursive parametric estimation algorithm this algorithm is developed using the adjustable model method and the least squares technique a recursive least squares rls algorithm is used to estimate the inverse nonlinear function a time varying gain is proposed in the discrete time sliding mode controller to reduce the chattering problem the stability of the closed loop nonlinear system with the proposed adaptive control scheme has been proved an application to a ph neutralisation

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

nonlinear adaptive control using neural networks and multiple models in this paper adaptive control of a class of nonlinear discrete time dynamical systems with boundedness of all signals is established by using a linear robust adaptive controller and a neural network based nonlinear adaptive controller and switching between them by a suitably defined switching law the linear controller when used alone assures boundedness of all the signals but not satisfactory performance the nonlinear controller may result in improved response but may also result in instability by using a switching scheme it is demonstrated that improved performance and stability can be simultaneously achieved

barrier lyapunov functions for nussbaum gain adaptive control of full state constrained nonlinear systems abstract in this paper an adaptive controller design is studied for single input single output siso nonlinear systems with parameter uncertainties and the systems are enforced to subject to the full state constraints a remarkable feature of the constrained systems is that the so called control direction is unknown or in other words the signs of control gains are unknown in the existing results we discover that all the state constraint control results are required to determine a priori knowledge of control direction it will be inevitable to bring about a different design procedure and a difficult task when no a priori knowledge of control direction is known to stabilize this class of systems two parameter adaptive controllers with nussbaum gain technique are constructively framed to overcome the unknown control direction problem and the novel symmetric and asymmetric barrier lyapunov functions blfs are adopted to guarantee that the states are not to violate their constraints then the proposed blf strategy can be to conquer the conservatism of the traditional blf based controls for the full state constraints finally two theorems are provided to show that all the signals in the closed loop system are bounded the outputs are driven to follow the reference signals and all the states are ensured to remain in the predefined compact sets the effectiveness of the proposed scheme is performed via a simulation example

continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction in this paper a robust control scheme is proposed for a class of nonlinear systems that have not only additive nonlinear uncertainties but also unknown multiplicative signs these signs are called control directions since they represent effectively the direction of motion under any given control except for the unknown control directions the class of systems satisfy the generalized matching conditions nonlinear robust control is designed to identify on line unknown control directions and to guarantee global stability of uniform ultimate boundedness without the knowledge of nonlinear dynamics except their size bounding functions it is also shown that the proposed robust control can be made continuous through utilizing the so called shifting laws that change smoothly and accordingly the signs of robust controls and that no matter what time constants and gains of the shifting laws are global stability is always ensured the analysis and design is done using lyapunov s direct method

automorphisms of free groups have finitely generated fixed point sets an automorphism of a finitely generated free group f extends to a homeomorphism of the end completion e of f the set of fixed points of this homeomorphism is finitely generated in a certain sense in particular this implies that the subgroup of elements fixed by the automorphism is finitely generated in the usual sense the emphasis on e instead of f in this paper is analogous to thurston s study of surface groups where measured laminations are studied instead of simple closed curves the techniques in this paper arose from a study of the behaviour of an automorphism under iteration that is the dynamics of the automorphism see 11 i thank bill thurston for explaining some of his ideas to me for analysing automorphisms of free groups in particular the result on bounded cancellation below is due to thurston and matt grayson peter scott asked whether the fixed subgroup is always finitely generated in 3 and gersten first answered this question in 2 using quite different methods

enhanced linearized reduced order models for subsurface flow simulation trajectory piecewise linearization tpwl represents a promising approach for constructing reduced order models using tpwl new solutions are represented in terms of expansions around previously simulated and saved solutions high degrees of efficiency are achieved when the representation is projected into a low dimensional space using a basis constructed by proper orthogonal decomposition of snapshots generated in a training run in recent work a tpwl procedure applicable for two phase subsurface flow problems was presented the method was shown to perform well for many cases such as those with no density differences between phases though accuracy and robustness were found to degrade in other cases in this work these limitations are shown to be related to model accuracy at key locations and model stability enhancements addressing both of these issues are introduced a new tpwl procedure referred to as local resolution tpwl enables key grid blocks such as those containing injection or production wells to be represented at full resolution i e these blocks are not projected into the low dimensional space this leads to high accuracy at selected locations and will be shown to improve the accuracy of important simulation quantities such as injection and production rates next two techniques for enhancing the stability of the tpwl model are presented the first approach involves a basis optimization procedure in which the number of columns in the basis matrix is determined to minimize the spectral radius of an appropriately defined amplification matrix the second procedure incorporates a basis matrix constructed using snapshots from a simulation with equal phase densities both approaches are compatible with the local resolution procedure results for a series of test cases demonstrate the accuracy and stability provided by the new treatments finally the tpwl model is used as a surrogate in a direct search optimization algorithm and comparison with results using the full order model demonstrates the efficacy of the enhanced tpwl procedures for this application

error estimation for reduced order models of dynamical systems the use of reduced order models to describe a dynamical system is pervasive in science and engineering often these models are used without an estimate of their error or range of validity in this paper we consider dynamical systems and reduced models built using proper orthogonal decomposition we show how to compute estimates and bounds for these errors by a combination of small sample statistical condition estimation and error estimation using the adjoint method most important the proposed approach allows the assessment of regions of validity for reduced models i e ranges of perturbations in the original system over which the reduced model is still appropriate numerical examples validate our approach the error norm estimates approximate well the forward error while the derived bounds are within an order of magnitude

active identification for discrete time nonlinear control ii strict feedback systems the problem of controlling nonlinear systems with unknown parameters has received a great deal of attention in the continuous time case in contrast its discrete time counterpart remains largely unexplored primarily due to the difficulties associated with utilizing lyapunov design techniques in a discrete time framework existing results impose restrictive growth conditions on the nonlinearities to yield global stability in this paper we propose a novel approach which removes this obstacle and yields global stability and tracking for systems that can be transformed into an output feedback canonical form in which the nonlinearities depend only on the measured output but are otherwise arbitrary the main novelties of our design are i the temporal and algorithmic separation of the parameter estimation task from the control task and ii the development of an active identification procedure which uses the control input to actively drive the system state to points in the state space that allow the orthogonalized projection estimator to acquire all the necessary information about the unknown parameters we prove that our algorithm guarantees complete for control purposes identification in a finite time interval whose maximum length we compute thus the traditional structure of concurrent online estimation and control is replaced by a two phase control strategy first use active identification and then utilize the acquired parameter information to implement any control strategy as if the parameters were known

galerkin proper orthogonal decomposition methods for parabolic problems in this work error estimates for galerkin proper orthogonal decomposition pod methods for linear and certain non linear parabolic systems are proved the resulting error bounds depend on the number of pod basis functions and on the time discretization numerical examples are included

stable discrete adaptive control with unknown high frequency gain this note presents a globally stable adaptive control algorithm applicable to discrete time single input single output linear time invariant systems a priori knowledge of neither the sign of the system s high frequency gain nor an upper bound on its magnitude is needed to prove global stability

neural network control based adaptive learning design for nonlinear systems with full state constraints in order to stabilize a class of uncertain nonlinear strict feedback systems with full state constraints an adaptive neural network control method is investigated in this paper the state constraints are frequently emerged in the real life plants and how to avoid the violation of state constraints is an important task by introducing a barrier lyapunov function blf to every step in a backstepping procedure a novel adaptive backstepping design is well developed to ensure that the full state constraints are not violated at the same time one remarkable feature is that the minimal learning parameters are employed in blf backstepping design by making use of lyapunov analysis we can prove that all the signals in the closed loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output finally a simulation is given to verify the effectiveness of the method

a unified approach to adaptive neural control for nonlinear discrete time systems with nonlinear dead zone input in this paper an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete time systems which contain unknown functions unknown dead zone input and unknown control direction different from linear dead zone the dead zone in this paper is a kind of nonlinear dead zone to overcome the noncausal problem which leads to the control scheme infeasible the systems can be transformed into a m step ahead predictor due to nonlinear dead zone appearance the transformed predictor still contains the nonaffine function in addition it is assumed that the gain function of dead zone input and the control direction are unknown these conditions bring about the difficulties and the complicacy in the controller design thus the implicit function theorem is applied to deal with nonaffine dead zone appearance the problem caused by the unknown control direction can be resolved through applying the discrete nussbaum gain and the neural networks are used to approximate the unknown function based on the lyapunov theory all the signals of the resulting closed loop system are proved to be semiglobal uniformly ultimately bounded moreover the tracking error is proved to be regulated to a small neighborhood around zero the feasibility of the proposed approach is demonstrated by a simulation example

immersion and invariance adaptive control for discrete time systems in strict feedback form abstract this paper presents a new design procedure for the adaptive regulation tracking via state feedback for discrete time nonlinear systems in a parametric strict feedback form the algorithm utilizes discrete time adaptive backstepping together with a new parameter estimator design this approach provides an adaptive control law which guarantees boundedness of the closed loop trajectories global convergence to the origin tracking of the state of the closed loop system and local stability the performance of the proposed method is illustrated by simulations