adaptive backstepping control design for linear multivariable plants a nonlinear backstepping scheme is developed for adaptive control of linear plants with multiple inputs and multiple outputs solutions to plant parametrization state observer and adaptive control law for the multivariable backstepping design are proposed the developed adaptive controller has the desired properties for ensuring closed loop signal boundedness and asymptotical tracking

a model reference adaptive control scheme for pure feedback nonlinear systems a model reference adaptive control mrac scheme is presented for nonlinear systems in a pure feedback canonical form with unknown parameters the present of parameter uncertainty in the system causes imperfect linearization i e it introduces nonlinear additive terms in the transformed coordinates under some mild technical assumptions global convergence of the output error is established for all initial estimates of the parameter vector lying in an open neighborhood of the true parameters in the parameter space

adaptive asymptotic control of multivariable systems based on a one parameter estimation approach multivariable adaptive control is an important and challenging research area where it usually requires designing adaptive laws to estimate a number of unknown parameters hence this process may excessively consume limitedly available computational resources and large amount of computational time which may degrade system performances particularly for the case of online updating of parameter estimates thus reducing the number of parameters to be estimated is a promising way to solve the problem the state of the art result in the area is to update just one adaptive parameter however the tracking errors are only ensured bounded and thus the resulting closed loop system is not asymptotically stable hence a question that arises is whether such a result of non zero tracking errors is the price paid for reducing the number of updating parameters up to now there is still no answer to this question in this paper we address such an issue and realize asymptotic stability with online estimation of just one parameter to achieve such a goal a novel dynamic loop gain function based approach is proposed to incorporate with the backstepping control design procedure which enables us to solve the algebraic loop problem caused by all the existing traditional nussbaum function based approaches and thus establish system stability a bound for the tracking error is explicitly established in terms of l2 norm which helps improve the transient performance by selecting the control parameters moreover guaranteed by the barbalats lemma the tracking error is further ensured to approach zero asymptotically finally simulation examples are conducted to testify the effectiveness of the proposed approach

prinjective modules reflection functors quadratic forms and auslander reiten sequences let a b be artinian rings and let a m b be an a b bimodule which is a finitely generated left a module and a finitely generated right b module a right a m b prinjective module is a finitely genrated module x r x a x b x a a m b x b over the triangular matrix ring r a o a m b b such that x a is a projective a module x b is an injective b module and is a b homomorphism we study the category prin r b a of right a m b prinjective modules it is an additive krull schmidt subcategory of mod r closed under extensions

variable structure model reference adaptive control using only input and output measurements abstract a variable structure model reference adaptive controller vs mrac using only the input and output measurements of the plant is proposed stability and transient properties are analysed and discussed remarkable transient behaviour is revealed in particular model following can be perfectly achieved in a finite time the effect of plant input disturbance is investigated and the performance of the vs controller is also shown to be qualitatively superior to that obtained with conventional integral adaptation algorithms a link between the vs mrac and the conventional mrac is suggested simulations are presented to highlight the theoretical results

global adaptive output feedback tracking for a class of multivariable nonlinear systems in this paper global adaptive output feedback tracking problem is considered for a class of multivariable nonlinear systems with unknown parameters and nonlinear terms linear in unmeasured states based on a modified high gain observer and symmetric positive diagonal unity upper triangular factorisation of high frequency gain matrix an adaptive backstepping design is proposed which is able to guarantee global stability of the closed loop system and circumvent the over parameterisation problem raised by using conventional backstepping method moreover with the introduction of an error modification and an initialisation technique it is proved that the tracking performance can be achieved

surface consistent deconvolution in the log fourier domain in the surface consistent hypothesis a seismic trace is the convolution of a source operator a receiver operator a reflectivity operator representing the subsurface structure and an offset related operator in the log fourier domain convolutions become sums and the log of signal amplitude at a given frequency is the sum of source receiver structural and offset related terms recovering the amplitude of the reflectivity for a given frequency is then a linear problem very similar to a surface consistent static correction problem however this linear system is underconstrained thus among the infinite number of possible solutions a particular one must be selected studies with real data support the choice of a spatially band limited solution the surface consistent operators can then be calculated very efficiently using an inverse hessian method applications to real seismic data show improvement compared with previous techniques surface consistent deconvolution is robust and fast in the log f

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

global output feedback stabilization of nonlinear systems with nonlinearity of unmeasured states this technical note deals with global stabilization of class of nonlinear dynamic systems using output feedback the systems considered have nonlinear functions of unmeasured state variables in addition to nonlinear functions of the system outputs a nonlinear reduced order observer is proposed to estimate the unknown system states estimated state variables are used for control design together with the system output certain conditions are identified for the proposed observer and control design under these conditions the proposed control design ensures the global asymptotic stability of the closed loop control system

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

on morse s new adaptive controller parameter convergence and transient performance some transient and asymptotic performance properties are established for the model reference adaptive controller proposed by a s morse proc us italy joint seminar syst models feedback 1992 it is proved that the l sub 2 norm of the tracking error is uniformly bounded by the initial parameter estimation error further if the initial conditions are sufficiently small it is shown that the l sub infinity norm of the tracking error is uniformly bounded by the l sub m2 norm of the reference signal these transient bounds are independent of the signals richness and the adaptation gain making them arguably the strongest transient results available in the literature second excitation conditions for exponential stability a property which is well known to insure some local performance measures are given to this end it is shown that modulo a signal dependent time scale change morse s estimator is equivalent to a normalized gradient plus filtering identifier

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

adaptive neural output feedback controller design with reduced order observer for a class of uncertain nonlinear siso systems an adaptive output feedback control is studied for uncertain nonlinear single input single output systems with partial unmeasured states in the scheme a reduced order observer roo is designed to estimate those unmeasured states by employing radial basis function neural networks and incorporating the roo into a new backstepping design an adaptive output feedback controller is constructively developed a prominent advantage is its ability to balance the control action between the state feedback and the output feedback in addition the scheme can be still implemented when all the states are not available the stability of the closed loop system is guaranteed in the sense that all the signals are semiglobal uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set a simulation example is given to validate the effectiveness of the proposed scheme

design of adaptive block backstepping controllers for uncertain nonlinear dynamic systems with n blocks based on the lyapunov stability theorem a design methodology of adaptive block backstepping control is proposed in this article for a class of multi input systems with matched and mismatched perturbations to solve regulation problems the systems to be controlled contain n blocks dynamic equations hence n 1 virtual input controllers are firstly designed so that the state variables of first n 1 blocks are asymptotically stable if each virtual control input is equal to the state variable of next block then the control input is designed in the last nth block to ensure asymptotic stability for the whole state variables even if the perturbations exist in addition adaptive mechanisms are embedded in each virtual input function and control input so that the upper bound of perturbations is not required to be known beforehand finally a numerical example is given for demonstrating the feasibility of the proposed control scheme

a reduction functor tameness and tits form for a class of orders abstract let d be a complete discrete valuation domain which is an algebra over an algebraically closed field k we study in the paper a class of suborders of tiled d orders by means of a rational quadratic form q associated to and a finite poset i having exactly two maximal elements and criteria for finite lattice type and for tame lattice type of are given in terms of the form q and of the category i spr of socle projective k linear representations of the poset i the shape of auslander reiten quiver latt is described in corollary 3 2 a reduction functor h latt i spr preserving representation types is constructed it is shown in corollary 2 10 that for any poset i having exactly two maximal elements there exists a d order in our class an additive functor latt i spr preserving representation types and a poset isomorphism i i

interactor and multivariable adaptive model matching the necessary minimal prior knowledge of a system in order to implement adaptive model matching and prove global stability is discussed some results concerning the degrees of interactor matrix entries are given it is shown that the bounds on the degrees of the interactor off diagonal terms given by m das j dynam sust measurement contr vol 108 p 151 153 1986 are the best possible ones

a gain matrix decomposition and some of its applications abstract any real square matrix m can be written as m u i l s where u is a matrix of 0 s 1 s and 1 s having exactly one nonzero element in each row and column l is a strictly lower triangular matrix and s is a symmetric positive semidefinite matrix the aim of this paper is to demonstrate the utility of this easily derived fact this is done in two ways first the decomposition is used to develop an identifier based solution to a simplified multivariable adaptive stabilization problem solved previously using nonidentifier based methods second it is briefly explained how to use the decomposition together with hysteresis switching and a certain lifted discrete time system representation to obtain an excitation free identifier based adaptive stabilizer for the entire class of n dimensional siso controllable observable discrete time linear process models this is accomplished by exploiting a new method of discrete time parameter adjustment called pseudo continuous tuning

adaptive neural network dynamic surface control for a class of time delay nonlinear systems with hysteresis inputs and dynamic uncertainties in this paper an adaptive neural network nn dynamic surface control is proposed for a class of time delay nonlinear systems with dynamic uncertainties and unknown hysteresis the main advantages of the developed scheme are 1 nns are utilized to approximately describe nonlinearities and unknown dynamics of the nonlinear time delay systems making it possible to deal with unknown nonlinear uncertain systems and pursue the mathcal l infty performance of the tracking error 2 using the finite covering lemma together with the nns approximators the krasovskii function is abandoned which paves the way for obtaining the mathcal l infty performance of the tracking error 3 by introducing an initializing technique the mathcal l infty performance of the tracking error can be achieved 4 using a generalized prandtl ishlinskii pi model the limitation of the traditional pi hysteresis model is overcome and 5 by applying the young s inequalities to deal with the weight vector of the nns the updated laws are needed only at the last controller design step with only two parameters being estimated which reduces the computational burden it is proved that the proposed scheme can guarantee semiglobal stability of the closed loop system and achieves the mathcal l infty performance of the tracking error simulation results for general second order time delay nonlinear systems and the tuning metal cutting system are presented to demonstrate the efficiency of the proposed method

prior information in the design of multivariable adaptive controllers this note discusses the design of a dynamic precompensator w c s for an m times m mimo plant w p s such that for almost all cases w p s w c s has a diagonal hermite form

almost split sequences in subcategories let r be a commutative artin ring and let i be an r algebra which is a finitely generated r module in 5 auslander and reiten introduced the notion of an almost split sequence in mod a the category of finitely generated modules over a and the existence and uniqueness of such short exact sequences were established there the theory of almost split sequences developed further and similar results for certain subcategories of mod i were proved by bautista and martinez 8 and roggenkamp 9 the main purpose of this paper is to develop a more general theory for subcategories of mod i having almost split sequences which has the previous examples as special cases notions closely related to that of almost split sequences are those of minimal left and right almost split morphisms these notions were introduced in 61 for mod i and further developed in 7 for subcategories of mod ii this paper is based upon 7 and we therefore use the same notations and conventions as used there we now give some definitions and then proceed to describe the content of the paper section by section let c be a subcategory of mod ii then a morphism g b c in c is said to be a right almost split morphism in c if i g is not a splittable epimorphism and ii whenever there is a nonsplittable epimorphism h c c in c there exists an h c b such that gh h dually a morphismfi a f b in c is said to be left almost split if i f is not a splittable monomorphism and ii whenever there is a nonsplittable monomorphism h a a there exists an h b a such that h f h we say that c has right almost split morphisms if for all indecomposable objects

asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented we consider two possible input nonlinearities that is backlash like hysteresis and symmetric dead zone which can be simultaneously dealt with by using the proposed compensation controllers the knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required only the boundedness of the reference signal is assumed the nussbaum gain approach is employed to remove the assumption on the control gain sign the first scheme is based on the backstepping technique the final step of the recursive design is crucial for the closed loop stability in the second scheme a direct adaptive control law is designed the controller has a simple structure and only one adaptation parameter is updated in both controllers it is shown that asymptotic tracking is ensured two numerical examples are provided to show the effectiveness of the theor

a reduced tits quadratic form and tameness of three partite subamalgams of tiled orders let d be a complete discrete valuation domain with the unique maximal ideal p we suppose that d is an algebra over an algebraically closed field k and d p k subamalgam d suborders of a tiled d order are studied in the paper by means of the integral tits quadratic form q zn1 2n3 2 z a criterion for a subamalgam d order to be of tame lattice type is given in terms of the tits quadratic form q and a forbidden list 1 17 of minor d suborders of presented in the tables

output feedback control for mimo nonlinear systems using factorization abstract a new output feedback adaptive control scheme for multi input and multi output mimo nonlinear systems is presented based on the high frequency gain matrix factorization and the backstepping approach with vector form the only required prior knowledge about the high frequency gain matrix of the linear part of the system is the signs of its leading principal minors the proposed controller is a dynamic one that only needs the measurement of the system output and the observer and the filters are introduced in order to construct a virtual estimate of the unmeasured system states the global stability of the closed loop systems is guaranteed through this control scheme and the tracking error converges to zero finally the numerical simulation results illustrate the effectiveness of the proposed scheme

dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation in this paper a dynamic surface control dsc scheme is proposed for a class of uncertain strict feedback nonlinear systems in the presence of input saturation and unknown external disturbance the radial basis function neural network rbfnn is employed to approximate the unknown system function to efficiently tackle the unknown external disturbance a nonlinear disturbance observer ndo is developed the developed ndo can relax the known boundary requirement of the unknown disturbance and can guarantee the disturbance estimation error converge to a bounded compact set using ndo and rbfnn the dsc scheme is developed for uncertain nonlinear systems based on a backstepping method using a dsc technique the problem of explosion of complexity inherent in the conventional backstepping method is avoided which is specially important for designs using neural network approximations under the proposed dsc scheme the ultimately bounded convergence of all closed loop signals is guaranteed via lyapunov analysis simulation results are given to show the effectiveness of the proposed dsc design using ndo and rbfnn

dynamic surface control for a class of nonlinear systems a method is proposed for designing controllers with arbitrarily small tracking error for uncertain mismatched nonlinear systems in the strict feedback form this method is another synthetic input technique similar to backstepping and multiple surface control methods but with an important addition spl tau 1 low pass filters are included in the design where spl tau is the relative degree of the output to be controlled it is shown that these low pass filters allow a design where the model is not differentiated thus ending the complexity arising due to the explosion of terms that has made other methods difficult to implement in practice the backstepping approach while suffering from the problem of explosion of terms guarantees boundedness of tracking errors globally however the proposed approach while being simpler to implement can only guarantee boundedness of tracking error semiglobally when the nonlinearities in the system are non lipschitz

robust adaptive control of strict feedback nonlinear systems with unmodelled dynamics and time varying delays abstractthis paper presents a novel robust adaptive neural control scheme which can be taken as a robustification of the adaptive backstepping design the considered class of uncertainties contains unknown non symmetric dead zone inputs time varying delay uncertainties unknown dynamic disturbances and unmodelled dynamics the radial basis function neural networks rbfnns are employed to approximate the unknown nonlinear functions obtained by young s inequality by constructing exponential lyapunov krasovskii functionals the upper bound functions of the time varying delay uncertainties are compensated for using young s inequality and rbfnns the assumptions with respect to unmodelled dynamics are relaxed it is demonstrated that the proposed controller guarantees that all the signals in the closed loop system are semi globally uniformly ultimately bounded and the tracking error eventually converges to a neighbourhood of zero

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

adaptive neural control for output feedback nonlinear systems using a barrier lyapunov function in this brief adaptive neural control is presented for a class of output feedback nonlinear systems in the presence of unknown functions the unknown functions are handled via on line neural network nn control using only output measurements a barrier lyapunov function blf is introduced to address two open and challenging problems in the neuro control area 1 for any initial compact set how to determine a priori the compact superset on which nn approximation is valid and 2 how to ensure that the arguments of the unknown functions remain within the specified compact superset by ensuring boundedness of the blf we actively constrain the argument of the unknown functions to remain within a compact superset such that the nn approximation conditions hold the semiglobal boundedness of all closed loop signals is ensured and the tracking error converges to a neighborhood of zero simulation results demonstrate the effectiveness of the proposed approach

fully automated near surface analysis by surface consistent refraction method abstractindustry practices for near surface analysis indicate difficulties in coping with the increased number of channels in seismic acquisition systems and new approaches are needed to fully exploit the resolution embedded in modern seismic data sets to achieve this goal we have developed a novel surface consistent refraction analysis method for low relief geology to automatically derive near surface corrections for seismic data processing the method uses concepts from surface consistent analysis applied to refracted arrivals the key aspects of the method consist of the use of common midpoint cmp offset azimuth binning evaluation of mean traveltime and standard deviation for each bin rejection of anomalous first break fb picks derivation of cmp based traveltime offset functions conversion to velocity depth functions evaluation of long wavelength statics and calculation of surface consistent residual statics through waveform crosscorrelation residual time lags are evaluated in multiple cm

output feedback control for mimo non linear systems with unknown sign of the high frequency gain matrix the paper presents a new output feedback adaptive control scheme for multi input and multi output mimo non linear systems whose non linear terms depend only on the output variable based on the backstepping approach with vector form the assumption on the prior knowledge of the high frequency gain matrix in existing results is reduced and the new required condition for the high frequency gain matrix can be easily checked for certain plants so that the proposed method is widely applicable this control scheme guarantees the global stability of the closed loop systems and makes the tracking error be arbitrary small a simulation example is included to demonstrate the proposed algorithm

dynamic surface control via singular perturbation analysis this note contributes to the technical nature of dynamic surface control dsc based on a class of strict feedback nonlinear systems the dsc technique prevents the complexity problem in integrator backstepping control ibc yet the stability results obtained by existing dscs are conservative and consequently cannot fully reveal the technical nature of dsc by the exploitation of the singular perturbation theory several novel features of dsc are revealed as follows 1 semiglobal practical exponential stability can be guaranteed only by a suitably small filter parameter 2 steady state tracking accuracy does not rely on high control gains 3 the performance of ibc can be recovered via the decrease of the filter parameter these features are not only significant for understanding the technical nature of dsc but also useful for establishing an efficient strategy of parameter selection and system debugging simulation results have verified correctness of the theoretical result

brief lyapunov based adaptive control of mimo systems the design of model reference adaptive control for mimo linear systems has not yet achieved in spite of significant efforts the completeness and simplicity of its siso counterpart one of the main obstacles has been the generalization of the siso assumption that the sign of the high frequency gain hfg is known here we overcome this obstacle and present a more complete mimo analog to the well known lyapunov based siso design which is significantly less restrictive than the existing analogs our algorithm makes use of a new control parametrization derived from a factorization of the hfg matrix k p sdu where s is symmetric positive definite d is diagonal and u is unity upper triangular only the signs of the entries of d or equivalently the signs of the leading principal minors of k p are assumed to be known

the existence of hall polynomials for posets of finite prinjective type abstract we prove the existence of hall polynomials for prinjective representations of finite partially ordered sets of finite prinjective type in section 4 we shortly discuss consequences of the existence of hall polynomials in particular we are able to define a generic ringel hall algebra for prinjective representations of posets of finite prinjective type

adaptive dynamic surface control for mimo nonlinear time varying systems with prescribed tracking performance in this paper an adaptive dynamic surface control scheme is proposed for a class of multi input multi output mimo nonlinear time varying systems by fusing a bound estimation approach a smooth function and a time varying matrix factorisation the obstacle caused by unknown time varying parameters is circumvented the proposed scheme is free of the problem of explosion of complexity and needs only one updated parameter at each design step moreover all tracking errors can converge to predefined arbitrarily small residual sets with a prescribed convergence rate and maximum overshoot such features result in a simple adaptive controller which can be easily implemented in applications with less computational burden and satisfactory tracking performance simulation results are presented to illustrate the effectiveness of the proposed scheme

control of nonlinear systems with partial state constraints using a barrier lyapunov function this article addresses the problem of control design for strict feedback systems with constraints on the states to prevent the states from violating the constraints we employ a barrier lyapunov function blf which grows to infinity whenever its arguments approaches some finite limits based on blf based backstepping we show that asymptotic output tracking is achieved without violation of any constraint provided that the initial states and control parameters are feasible we also establish sufficient conditions to ensure feasibility which can be checked offline without precise knowledge of the initial states the feasibility conditions are relaxed when handling the partial state constraint problem as compared to the full state constraint problem in the presence of parametric uncertainties blf based adaptive backstepping is useful in preventing the states from transgressing the constrained region during the transient stages of online parameter adaptation to relax the feasibility conditions asymme

adaptive control of a class of slowly time varying systems with modeling uncertainties in a recent work a new linear adaptive controller based on certainty equivalence and backstepping design which promises a level of transient and asymptotic performance comparable to that of the tuning functions adaptive backstepping controller without using high order nonlinearities was proposed for linear time invariant systems the proposal was supplemented with robustness and performance analysis in the presence of modeling uncertainties in this note the same idea is used to develop a new linear adaptive controller for slowly time varying systems with modeling uncertainties the new adaptive control scheme guarantees robustness with respect to modeling errors via normalizing damping parameter projection and static normalization use of normalizing damping is essential in protecting the linearity of the system which plays a key role in reaching the stability and robustness results

brief paper adaptive dynamic surface control for linear multivariable systems in this paper an output feedback adaptive control is presented for linear time invariant multivariable plants by using the dynamic surface control technique it is shown that the explosion of complexity problem in multivariable backstepping design can be eliminated the proposed scheme has the following features 1 the l performance of the system s tracking error can be guaranteed 2 it has least number of updated parameters in comparison with other multivariable adaptive schemes and 3 the adaptive law is necessary only at the first design step which significantly reduces the design procedure simulation results are presented to demonstrate the effectiveness of the proposed scheme

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

hysteresis switching adaptive control of linear multivariable systems this paper presents a model reference adaptive control scheme for deterministic continuous time multivariable systems represented by square strictly proper minimum phase transfer function matrices a typical requirement of existing algorithms is to assume that the zero structure at infinity and the high frequency gain matrix are fully or at least partially known it is well known that these requirements may be very restrictive since in general both the zero structure at infinity and the high frequency gain matrix depend on plant parameters in this paper we show that these restrictive assumptions may be considerably weakened using morse et al s hysteresis switching control strategy 1992 the strategy entails running a finite number of parameter estimators in parallel and using a switching algorithm to select between candidate estimators based on their associated prediction errors hysteresis in the switching algorithm precludes switching arbitrarily rapidly between estimators and all switching ceases within a finite time the results represent a significant step forward in understanding the minimal amount of prior knowledge necessary to design a stabilizing controller for a linear multivariable system

multivariable adaptive control using high frequency gain matrix factorization in this note we extend the application of a less restrictive condition about the high frequency gain matrix to design stable direct model reference adaptive control for a class of multivariable plants with relative degree greater than one the new approach is based on a control parametrization derived from a factorization of the high frequency gain matrix k sub p in the form of a product of three matrices one of them being diagonal three possible factorizations are presented only the signs of the diagonal factor or equivalently the signs of the leading principal minors of k sub p are assumed known

adaptive nonlinear output feedback dynamic surface control with unknown high frequency gain sign in this paper an adaptive dynamic surface control dsc for a class of nonlinear systems with unknown high frequency gain hfg sign is proposed the novelty of our scheme is that we separate the first virtual control signal from the hfg which enables us to estimate the hfg directly as a result the traditional nussbaum function nf approach is abandoned by using the proposed dsc the adaptive laws are needed only at the first design step and the explosion of terms in backstepping control can be eliminated which greatly reduces the computational burden in particular based on an initialisation technique we prove that the performance of the system tracking error can be guaranteed even when the hfg sign is unknown it is shown that all signals of the closed loop system are semi globally uniformly bounded simulation results illustrate that the proposed scheme is more applicable than that of the nf based backstepping control

multivariable adaptive dynamic surface control based on norm estimation of unknown parameter matrices in this article a novel output feedback adaptive dynamic surface control scheme is proposed for linear time invariant multivariable plants based on the norm estimation of unknown parameter matrices besides avoiding the explosion of complexity problem in traditional multivariable backstepping design the proposed scheme has the following features 1 only one parameter needs to be updated on line regardless of the plant order and input output dimension 2 only the hurwitz condition is required for the high frequency gain matrix and 3 the performance of the tracking error can be guaranteed it is shown that all signals of the closed loop system are semi globally uniformly bounded simulation results are given to illustrate the effectiveness of the proposed scheme

multivariable adaptive backstepping control a norm estimation approach in this note a novel output feedback adaptive backstepping control is proposed for linear time invariant multivariable plants under a mild assumption that the hurwitz condition for high frequency gain matrix is satisfied by estimating the norm of those unknown parameter matrices instead of their elements it is shown that only one parameter needs to be updated online and therefore the computational burden can be greatly reduced compared with any current multivariable adaptive control scheme

observer based dynamic surface control for a class of nonlinear systems an lmi approach this note presents a new analysis method to design an observer based dynamic surface controller odsc for a class of nonlinear systems while the separation principle from linear system theory does not generally hold for nonlinear systems a separation principle for the odsc systems will be shown for a class of nonlinear systems thus enabling the independent design of the observer and dsc furthermore a convex optimization problem to test quadratic stability of odsc will be formulated later

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

bipartite posets of finite prinjective type one of the main results of this paper is theorem 1 2 which contains a characterization of finite bipartite posetsi i i for which the category prin ki of prinjective modules over the incidencek algebrakiofiis of finite representation type wherekis a field in particular it is shown that for any such poseti the auslander reiten quiver of the category prin ki has no oriented cycle and there is a bijection between the isomorphism classes of indecomposable objects in prin ki and the positive roots of the quadratic formqiassociated withi an existence of a preprojective component in prin ki is proved for faithful posetsiwhich area free

brief paper control of nonlinear systems with time varying output constraints this paper presents control design for strict feedback nonlinear systems with time varying output constraints an asymmetric time varying barrier lyapunov function blf is employed to ensure constraint satisfaction by allowing the barriers to vary with the desired trajectory in time the initial condition requirements are relaxed through a change of tracking error coordinates we eliminate the explicit dependence of the blf on time thereby simplifying the analysis of constraint satisfaction we show that asymptotic output tracking is achieved without violation of the output constraint and also quantify the transient performance bound as a function of time that converges to zero to handle parametric model uncertainty we present an adaptive controller that ensures constraint satisfaction during the transient phase of online parameter adaptation the performance of the proposed control is illustrated through a simulation example

adaptive output feedback control for a class of nonlinear systems with full state constraints this paper studies an adaptive output feedback control for a class of nonlinear single input and single output siso systems with the full state constraints a state observer is designed to estimate those unmeasured states at present all the results in the output feedback area ignore the effects of the full state constraints the presence of these constraints results in a complicated procedure and the major difficulties in the design the barrier lyapunov function blf and a novel design procedure are given to overcome these difficulties the adaptation law and the controllers are obtained based on the backstepping design procedure in addition only one adjustable parameter needs to be updated and thus the online computation burden is alleviated the stability of the closed loop system is proven by using the lyapunov theorem a simulation example is given to verify the effectiveness of the approach

multivariable model reference adaptive control without constraints on the high frequency gain matrix abstract a multivariable model reference adaptive control algorithm is presented for the case when the high frequency gain matrix is unknown only an upper bound on the norm of the matrix needs to be known a priori a transformation of the parameters with a sort of hysteresis is used to guarantee that a controller matrix which is normally the inverse of the estimate of the high frequency gain matrix remains nonsingular it is shown that all the signals in the adaptive system are bounded and that the tracking error and the regressor error converge to zero for all bounded reference inputs furthermore exponential convergence is achieved when the regressor vector is persistently exciting

adaptive control of a class of discrete time mimo nonlinear systems with uncertain couplings in this article adaptive control is investigated for a class of discrete time multi input multi output nonlinear systems in block triangular form with uncertain couplings of delayed states among subsystems future states prediction is carried out to facilitate adaptive control design and auxiliary outputs are introduced to develop a novel compensation mechanism for the uncertain nonlinear couplings by using lyapunov method and ordering signals growth rate it is rigorously proved that all the signals in the whole closed loop systems are globally bounded and the output tracking errors asymptotically converge to zeros the effectiveness of the proposed control is demonstrated in the simulation study

on weakly non negative unit forms and tame algebras in this paper we consider integral quadratic forms q ip z of the form q x 2i x i jqijx xj and call them unit forms such a unit form q is said to be weakly non negative if q x q whenever jt2 0 that is whenever x o for i 1 n our main purpose is to formulate a criterion for weak non negativity of unit forms this question arises in various areas of representation theory in connection with the characterization of tame representation type in the representation theory of quivers 17 6 partially ordered sets 18 19 certain classes of bimodules 8 23 1 3 and certain classes of algebras 20 14 24 16 for each of these structures q there is a unit form qn naturally attached to q such that the weak non negativity of qn is an equivalent or at least a necessary condition for q to be of tame representation type a class of algebras for which tame representation type is equivalent to the weak non negativity of the associated unit form is described in the last section of this paper a general criterion for weak non negativity using determinants was given by zeldich 28 see also 21 another criterion was obtained by de la pena 21 our approach is similar to that in 11 where we gave a characterization of weakly positive unit forms based on the classification of the critical forms let us recall some notions given a unit form q ip tl and a non empty subset ix im of 1 n we denote by qt the quadratic form qd where d z it maps the cth natural basis vector ek onto eik such a unit form q is called the restriction of q to we call a unit form q on ip a hypercritical form if q is weakly non negative for every proper subset 1 n though q itself is not in these terms a unit form q is weakly non negative if and only if q admits no hypercritical restriction so we have to classify the hypercritical forms in 1 we show that they can be obtained by certain elementary transformations from the unit forms naturally attached to the hyperbolic graphs of fig 1 on p 50 in particular there are only finitely many hypercritical forms however their number is large by a simple process we reduce the problem to the classification of the stretched hypercritical forms in 2 we show that except for a few of them these are of the shape q x q x xn xn ixn where q q n d is critical in a similar way the unit forms attached to the hyperbolic graphs am dm em correspond to those

barrier lyapunov functions for the control of output constrained nonlinear systems in this paper we present control designs for single input single output siso nonlinear systems in strict feedback form with an output constraint to prevent constraint violation we employ a barrier lyapunov function which grows to infinity when its arguments approach some limits by ensuring boundedness of the barrier lyapunov function in the closed loop we ensure that those limits are not transgressed besides the nominal case where full knowledge of the plant is available we also tackle scenarios wherein parametric uncertainties are present asymptotic tracking is achieved without violation of the constraint and all closed loop signals remain bounded under a mild condition on the initial output furthermore we explore the use of an asymmetric barrier lyapunov function as a generalized approach that relaxes the requirements on the initial conditions we also compare our control with one that is based on a quadratic lyapunov function and we show that our control requires less restrictive initial conditions a numerical example is provided to illustrate the performance of the proposed control