twisting and kappa poincare we demonstrate that the coproduct of and quantum poincare algebras in a classical algebra basis cannot be obtained by a cochain twist depending only on poincare algebra generators we also argue that the nonexistence of such a twist does not imply the nonexistence of a universal r matrix

robust observer design under measurement noise with gain adaptation and saturated estimates abstract we use incremental homogeneity gain adaptation and incremental observability for proving new results on robust observer design for systems with noisy measurement and bounded trajectories a state observer is designed by dominating the incrementally homogeneous nonlinearities of the observation error system with its linear approximation while gain adaptation and incremental observability guarantee an asymptotic upper bound for the estimation error depending on the limsup of the norm of the measurement noise a characteristic and innovative feature of this observer is the mixed low high gain structure in combination with saturated state estimates and dynamically tuned gains and saturation levels the gain adaptation is implemented as the output of a stable filter using the squared norm of the measured output estimation error and the mismatch between each estimate and its saturated value

on the stability proof of adaptive schemes with static normalizing signals and parameter projection it has been shown previously that robust stability in model reference adaptive control mrac is guaranteed by simply using a static instead of a dynamic normalizing signal together with a parameter projection in the adaptive law it is shown here that the stability proof associated with such modification follows directly from the proof of schemes with dynamic normalization consequently the proofs and stability arguments can be simplified considerably

further facts about input to state stabilization previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls provided that a more general type of feedback is allowed applications to certain stabilization problems and coprime factorizations as well as comparisons to other results on input to state stability are briefly discussed

distributed robust consensus control of multi agent systems with heterogeneous matching uncertainties this paper considers the distributed consensus problem of linear multi agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown control input due to the existence of nonidentical uncertainties the multi agent systems discussed in this paper are essentially heterogeneous for the case where the communication graph is undirected and connected based on the local state information of neighboring agents a fully distributed continuous adaptive consensus protocol is designed under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable bounded set for the case where there exists a leader whose control input is unknown and bounded a distributed adaptive consensus protocol is proposed to ensure the boundedness of the consensus error a sufficient condition for the existence of the proposed protocols is that each agent is stabilizable

convergence of asynchronous variational integrators in linear elastodynamics within the setting of linear elastodynamics of simple bodies we prove that the discrete action functional obtained by following the scheme of asynchronous variational integrators converges in time the convergence in space is assured by standard arguments when the finite element mesh is progressively refined our strategy exploits directly the action functional in particular we show that if the asynchronicity of time steps and nodal initial data satisfy a boundedness condition any sequence of stationary points of the discrete action functional is pre compact in the weak w1 topology and all its cluster points are stationary points for the continuous in time action in this sense our proof is new with respect to existing ones copyright 2007 john wiley sons ltd

disturbance generated bifurcation in a prototype adaptive system with e sub 1 modification law the e sub 1 modification law has been proposed by k s narendra and a m annaswamy ibid vol 32 no 2 pp 134 5 1987 for robust model reference adaptive control in the presence of bounded disturbances using this law it is shown by the present authors that in the case of regulation a prototype adaptive control system with a single unknown pole and an unknown constant disturbance at its input possesses multiple equilibria and undergoes various bifurcations simulations and local analysis give a complete characterization of the possible dynamics exhibited by the disturbance adaptive system as the constant disturbance is varied saddle node bifurcation subcritical hopf bifurcation and saddle connection bifurcation occur in that order consequently in this case the e sub 1 modification law is qualitatively equivalent to the sigma modification law

brief variable structure control design for uncertain dynamic systems with disturbances in input and output channels in this paper a design scheme of variable structure model reference control using only input and output measurements is presented for linear time invariant systems with uncertain additive and multiplicative dynamics and disturbances existing in the input and output channels by introducing auxiliary signals and normalized signals with memory and an appropriate choice of control parameters the controller guarantees the global stability of the closed loop system and the tracking error reach zero in finite time

nonassociative tori and applications to t duality in this paper we initiate the study of c algebras open image in new window endowed with a twisted action of a locally compact abelian lie group open image in new window and we construct a twisted crossed product open image in new window which is in general a nonassociative noncommutative algebra the duality properties of this twisted crossed product algebra are studied in detail and are applied to t duality in type ii string theory to obtain the t dual of a general principal torus bundle with general h flux which we will argue to be a bundle of noncommutative nonassociative tori nonassociativity is interpreted in the context of monoidal categories of modules we also show that this construction of the t dual includes the other special cases already analysed in a series of papers

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

comments on adaptive control of linearizable systems by s s sastry and a isidori in the above titled paper by s s sastry and a isidori ibid vol 34 p 1123 31 nov 1989 the use of feedback linearizing controls for adaptive control of nonlinear systems which have an unknown linear parameterization is discussed the requirement that a nonlinear system of relative degree greater than one be globally lipschitz continuous is quite strong the commenters argue that the theorems of sastry and isidori fail when that hypothesis is relaxed by providing simple examples of systems which cannot be globally stabilized with their proposed adaptive feedback linearizing control law

robustness analysis of identification and adaptive control for stochastic systems abstract this paper gives a preliminary robustness analysis for stochastic systems with unmodelled dynamics the extended least squares algorithm and stochastic adaptive control for tracking are defined on the basis of the modelled part of the system and it is shown that the parameter estimate is closed to the true one and the tracking error is small if the unmodelled dynamics is small

robust redesign of adaptive control effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed in the regulation problem global stability properties are no longer guaranteed but a region of attraction exists for exact adaptive regulation the dependence of the region of attraction on unmodeled parasitics is examined first then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties a modified adaptive law is proposed guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking the size of this set depends on design parameters the frequency range of parasitics and the reference input signal characteristics

multisymplectic geometry variational integrators and nonlinear pdes this paper presents a geometric variational approach to continuous and discrete mechanics and field theories using multisymplectic geometry we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle in particular we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function and use this structure to prove covariant generalizations of conservation of symplecticity and noether s theorem natural discretization schemes for pdes which have these important preservation properties then follow by choosing a discrete action functional in the case of mechanics we recover the variational symplectic integrators of veselov type while for pdes we obtain covariant spacetime integrators which conserve the corresponding discrete multisymplectic form as well as the discrete momentum mappings corresponding to symmetries we show that the usual notion of symplecticity along an infinite dimensional space of fields can be naturally obtained by making a spacetime split all of the aspects of our method are demonstrated with a nonlinear sine gordon equation including computational results and a comparison with other discretization schemes

on the robustness of output feedback control methods to modeling errors singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time invariant systems the effect of designing the control strategy using a model that neglects unknown parasitic elements is considered it is shown that such a strategy may in general be destabilizing even when the neglected modes are asymptotically stable special structures that will not permit this situation and will guarantee asymptotic stability are illustrated

quasialgebra structure of the octonions abstract we show that the octonions are a twisting of the group algebra of z 2 z 2 z 2 in the quasitensor category of representations of a quasi hopf algebra associated to a group 3 cocycle in particular we show that they are quasialgebras associative up to a 3 cocycle isomorphism we show that one may make general constructions for quasialgebras exactly along the lines of the associative theory including quasilinear algebra representation theory and an automorphism quasi hopf algebra we study the algebraic properties of quasialgebras of the type which includes the octonions further examples include the higher 2n onion cayley algebras and examples associated to hadamard matrices

brief robust high order tuner of simplified structure recently morse has proposed a new adaptation scheme so called high order tuner which generates as outputs not only tuned parameters but also their time derivatives up to a certain order in this paper a robustified variant of the high order tuner is introduced to adaptively stabilize a siso linear plant subjected to external disturbances in comparison with morse s tuner the proposed one has essentially simplified structure namely the total order of time varying auxiliary filters is reduced 2n times where n is the order of the plant to be controlled

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

design of a unified adaptive fuzzy observer for uncertain nonlinear systems this paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems more precisely we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high gain or a sliding mode observer by selecting its gain appropriately additionally we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances we also show that the observation error is ultimately bounded using a lyapunov approach without having recourse to the usual strictly positive real spr condition or a suitable observation error filtering the effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature

slow drift instability in model reference adaptive systems an averaging analysis the paper presents instability theorems for one and two time scale time varying non linear systems using averaging theory these theorems are then applied to the model reference adaptive control system with unmodelled dynamics and output disturbance to analyse the mechanism of slow drift instability

unmodeled dynamics in adaptive control systems revisited an alternative approach to analyze the robustness of adaptive systems with respect to unmodeled dynamics and external disturbances is presented this approach shows that certain restrictive assumptions needed earlier can in fact be discarded it also shows that an adaptation algorithm based on a time varying factor equivalent to a constant factor together with projection can provide a globally asymptotically stable system with respect to a compact residual set under mild requirements

bifurcation in model reference adaptive control systems abstract we study the effect of unmodeled dynamics on the performance of a simple model reference adaptive control mechanism exact stability boundaries are computed and different routes to chaotic behavior and global instability are described typically we observed a region of period doubling and hopf bifurcations similar to those observed in the ziegler nichols approach to pid control design the analysis applies to higher order and certain nonlinear systems as well

quantization by cochain twists and nonassociative differentials we show that several standard associative quantizations in mathematical physics can be expressed as cochain module algebra twists in the spirit of moyal products at least to o 3 but to achieve this we twist not by a 2 cocycle but by a 2 cochain this implies a hidden nonassociativity not visible in the algebra itself but present in its deeper noncommutative differential geometry a phenomenon first seen in our previous work on semiclassicalization of differential structures the quantizations are induced by a classical group covariance and include enveloping algebras u g as quantizations of g a fedosov type quantization of the sphere s2 under a lorentz group covariance the mackey quantization of homogeneous spaces and the standard quantum groups cq g we also consider the differential quantization of rn for a given symplectic connection as part of our semiclassical analysis and we outline a proposal for the dirac operator

multiple model adaptive mixing control the discrete time case most of the work in multiple model adaptive control with various forms of switching focused on continuous time systems the purpose of this technical note is to extend the results of one approach the adaptive mixing control amc to discrete time systems further the technical note solves the tracking problem which has not been addressed in most schemes of this class stability and robustness properties of the amc scheme for discrete time systems are analyzed it is shown that in the ideal case when no disturbances or unmodeled dynamics are present the tracking error converges to zero in the non ideal case the mean square tracking error is of the order of magnitude of the modeling error provided the unmodeled dynamics satisfy a norm bound condition while these robustness results are conceptually similar to those of traditional robust adaptive control the proposed scheme does not suffer from the drawback of stabilizability of the estimated plant and in addition performs much better in simulation studies furthermore it allows well developed results from robust control to be incorporated in the design

noncommutative geometry of angular momentum space u su 2 we study the standard angular momentum algebra xi xj i eijkxk as a noncommutative manifold r 3 we show that there is a natural 4d differential calculus and obtain its cohomology and hodge operator we solve the spin 0 wave equation and some aspects of the maxwell or electromagnetic theory including solutions for a uniform electric current density and we find a natural dirac operator we embed r 3 inside a 4d noncommutative space time which is the limit q 1 of q minkowski space and show that r 3 has a natural quantum isometry group given by the quantum double c su 2 u su 2 which is a singular limit of the q lorentz group we view r 3 as a collection of all fuzzy spheres taken together we also analyze the semiclassical limit via minimum uncertainty states j approximating classical positions in polar coordinates

on adaptive state regulation an indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed in a rigorous analysis lyapunov stability of the resulting closed loop system without the need for external excitation possible global instabilities as well as global convergence subject to sufficient excitation are shown moreover the behavior of the closed loop system is analyzed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order contains slight nonlinearities and time variation effects and is subject to plant and measurement disturbances

unbiased and stable leakage based adaptive filters the paper develops a leakage based adaptive algorithm referred to as circular leaky which in addition to solving the drift problem of the classical least mean squares lms adaptive algorithm it also avoids the bias problem that is created by the standard leaky lms solution these two desirable properties of unbiased and bounded estimates are guaranteed by circular leaky at essentially the same computational cost as lms the derivation in the paper relies on results from averaging theory and from lyapunov stability theory and the analysis shows that the above properties hold not only in infinite precision but also in finite precision arithmetic the paper further extends the results to a so called switching spl sigma algorithm which is a leakage based solution used in adaptive control

fully distributed adaptive sliding mode controller design for containment control of multiple lagrangian systems abstract in this paper we study the containment control problem for multiple lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties and external disturbances with fully distributed controllers under an undirected graph we first propose a fully distributed adaptive sliding mode control algorithm combined with distributed sliding mode estimators without requiring the upper bounds of the derivatives of the leaders states and any other global information to be known by each follower to reduce the effect on the varying gain during the adaption mainly caused by the initial error fully distributed adaptive time varying sliding mode control is presented for controller design to tackle the chattering effect caused by the discontinuous controller we further propose a fully distributed continuous adaptive controller under which both the containment errors and the adaptive gains are ultimately bounded simulation results are given to illustrate the theoretical results

hopf bifurcation in an adaptive d c servo system occurrence of hopf bifurcation is demonstrated in a practical adaptive servo system by computer simulations and experimental results the bifurcation is caused by a decaying term added to the adaptive law for improving the robustness of the system the bifurcation analysis is successfully applied to the design of stable adaptive controller

gauge theory on nonassociative spaces we show how to do gauge theory on the octonions and other nonassociative algebras such as quasi r4 models proposed in string theory we use the theory of quasialgebras obtained by cochain twist introduced previously the gauge theory in this case is twisting equivalent to the usual gauge theory on the underlying classical space we give a general u 1 yang mills example for any quasialgebra and a full description of the moduli space of flat connections in this theory for the cube z23 and hence for the octonions we also obtain further results about the octonions themselves an explicit moyal product description of them as a nonassociative quantization of functions on the cube and a characterization of their cochain twist as invariant under fourier transform

asymptotic tracking of uncertain systems with continuous control using adaptive bounding this paper presents a robust adaptive control design method for a class of multiple input multiple output uncertain nonlinear systems in the presence of parametric and nonparametric uncertainties and bounded disturbances using the approximation properties of the unknown continuous nonlinearities and the adaptive bounding technique the developed controller achieves asymptotic convergence of the tracking error to zero while ensuring boundedness of parameter estimation errors the algorithm does not assume the knowledge of any bound on the unknown quantities in designing the controller it is based on an integral technique involving the filtered tracking error and produces a continuous control theoretical developments are illustrated via simulation results

twisting of quantum differentials and the planck scale hopf algebra we show that the crossed modules and bicovariant differential calculi on two hopf algebras related by a cocycle twist are in 1 1 correspondence in particular for quantum groups which are cocycle deformation quantisations of classical groups the calculi are obtained as deformation quantisations of the classical ones as an application we classify all bicovariant differential calculi on the planck scale hopf algebra this is a quantum group which has an limit as the functions on a classical but non abelian group and a limit as flat space quantum mechanics we further study the noncommutative differential geometry and fourier theory for this hopf algebra as a toy model for planck scale physics the fourier theory implements a t duality like self duality the noncommutative geometry turns out to be singular when and is therefore not visible in flat space quantum mechanics alone

an asymptotic error analysis of identifiers and adaptive observers in the presence of parasitics the behavior of identifiers and adaptive observers in the presence of parasitics is analyzed bounds for the state parameter error are established the adaptive schemes considered are shown to be robust provided the input signal is rich for the dominant modes but does not contain high frequencies in the parasitic range the bounds indicate possibilities for reducing the error by a proper choice of the input signal

brief paper stability analysis of adaptively controlled systems subject to bounded disturbances an approach for studying stability of adaptively controlled systems subject to bounded disturbances with unknown statistics is given a shorter proof of some results established for minimum phase systems is also given new results are established for nonminimum phase systems in each case the uniform boundedness of all signals is proven under a condition that is discussed examples of adaptive schemes that can be treated with this approach are given

deformation quasi hopf algebras of non semisimple type from cochain twists given a symmetric decomposition mathfrak g mathfrak h oplus mathfrak p of a semisimple lie algebra mathfrak g we define the notion of a mathfrak p contractible quantized universal enveloping algebra quea for these queas the contraction mathfrak g rightarrow mathfrak g 0 making mathfrak p abelian is nonsingular and yields a quea of mathfrak g 0 for a certain class of symmetric decompositions we prove by refining cohomological arguments due to drinfel d that every quea of mathfrak g 0 so obtained is isomorphic to a cochain twist of the undeformed envelope mathcal u mathfrak g 0 to do so we introduce the mathfrak p contractible chevalley eilenberg complex and prove for this class of symmetric decompositions a version of whitehead s lemma for this complex by virtue of the existence of the cochain twist there exist triangular quasi hopf algebras based on these contracted queas and in the approach due to beggs and majid the dual quantized coordinate algebras admit quasi associative differential calculi of classical dimensions as examples we consider poincare in 3 and 4 spacetime dimensions

adaptive control of passifiable linear systems with quantized measurements and bounded disturbances we consider a linear uncertain system with an unknown bounded disturbance under a passification based adaptive controller with quantized measurements first we derive conditions ensuring ultimate boundedness of the system then we develop a switching procedure for an adaptive controller with a dynamic quantizer that ensures convergence to a smaller set the size of the limit set is defined by the disturbance bound finally we demonstrate applicability of the proposed controller to polytopic type uncertain systems and its efficiency by the example of a yaw angle control of a flying vehicle

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

braided cyclic cocycles and nonassociative geometry we use monoidal category methods to study the noncommutative geometry of nonassociative algebras obtained by a drinfeld type cochain twist these are the so called quasialgebras and include the octonions as braided commutative but nonassociative coordinate rings as well as quasialgebra versions cq g of the standard q deformation quantum groups we introduce the notion of ribbon algebras in the category which are algebras equipped with a suitable generalized automorphism and obtain the required generalization of cyclic cohomology we show that this braided cyclic cohomology is invariant under a cochain twist we also extend to our generalization the relation between cyclic cohomology and differential calculus on the ribbon quasialgebra the paper includes differential calculus and cyclic cocycles on the octonions as a finite nonassociative geometry as well as the algebraic noncommutative torus as an associative example

stable model reference adaptive control in the presence of bounded disturbances the adaptive control of a linear time invariant plant in the presence of bounded disturbances is considered in addition to the usual assumptions made regarding the plant transfer function it is also assumed that the high frequency gain k p of the plant and an upper bound on the magnitude of the controller parameters are known under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system

limitations on the stabilizability of globally minimum phase systems the author gives examples showing that in general it is possible for a globally minimum phase system in normal form to have states that cannot be driven asymptotically to the origin by means of any open loop control in particular this provides counterexamples to a number of recently published stabilization theorems it is established by means of examples that a minimum phase system in normal form need not be semiglobally stabilizable or small input semiglobally bibo stabilizable even if the zero dynamics is exponentially stable and the completeness condition holds

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

robust adaptive controller with zero residual tracking errors the adaptive control of a plant whose dominant part has transfer function with relative degree n ast 1 has been considered in the presence of parasitics and disturbances a new adaptive law is proposed which guarantees the existence of a large region of attraction from which all signals are bounded and the tracking error converges to a small residual set in contrast to the adaptive law used in 1 2 the new adaptive law guarantees a smaller residual set for the tracking error which reduces to zero when the parasitics and disturbances disappear

variational time integrators the purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest in particular the conservation properties of both synchronous and asynchronous variational integrators avis are discussed in detail we present selected numerical examples which demonstrate the excellent accuracy conservation and convergence characteristics of avis in these tests avis are found to result in substantial speed ups at equal accuracy relative to explicit newmark a mathematical proof of convergence of the avis is also presented in this paper finally we develop the subject of horizontal variations and configurational forces in discrete dynamics this theory leads to exact path independent characterizations of the configurational forces acting on discrete systems notable examples are the configurational forces acting on material nodes in a finite element discretisation and the j integral at the tip of a crack in a finite element mesh

new approach to robust model reference adaptive control for a class of plants motivated by recent advances in designing robust adaptive controllers and in dealing with uncertain dynamical systems a new model reference adaptive control which is robust to a class of unmodelled dynamics and bounded output disturbances in the case of relative degree one is presented the implementation of the controllers includes a switching mechanism which plays a crucially important role in functions of stabilizing as well as tracking it is shown that global stability of the overall system is achieved under no assumption of persistency of excitation and tracking errors will converge to a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances explicitly in the ideal case the residual set degenerates to a single null point and convergence can be achieved in finite time without any requirement of persistency of excitation

disturbance generated bifurcations in a simple adaptive system simulation evidence abstract we present complete characterization based on computer simulation of the possible dynamics exhibited by an adaptive control system where the first order plant with a single unknown pole has constant disturbance at the input the adaptive system is taken from the current adaptive control systems literature here we show that the system in fact undergoes bifurcations and exhibits rich dynamics as the constant disturbance is varied the system undergoes saddle node bifurcation subcritical hopf bifurcation and a saddle connection bifurcation the last bifurcation means that the system acquires a homoclinic orbit for a specific disturbance while the first two bifurcations are local the presence of the homoclinic orbit has the potential when periodically disturbed to generate nonlocal complicated behavior this latter behavior is often referred to as horseshoe chaos

global boundedness of discrete time adaptive control just using estimator projection in this paper we study a discrete time indirect adaptive control algorithm which contains a constrained gradient parameter estimator and a pole assignment control law synthesis module this adaptive control algorithm does not involve modifications like data normalization use of deadzones or injection of persistently excited signals also it requires no a priori knowledge of system modelling errors it is shown that global robustness properties still hold when this simple algorithm is applied to systems with bounded disturbances and arbitrarily small fast parasitic dynamics the problem of indirect decentralized adaptive control of interconnected systems is also considered we use the above adaptive algorithm to design completely decentralized local adaptive controllers for each isolated subsystem by ignoring interactions between subsystems we show that the local controllers designed in this way are robust in the sense that all signals in the closed loop adaptive system are bounded for bounded initial conditions reference inputs disturbances and an arbitrarily small amount of interaction between subsystems and unmodelled dynamics of each subsystem

asynchronous variational integrators we describe a class of asynchronous variational integrators avi for nonlinear elastodynamics the avis are characterized by the following distinguishing attributes i the algorithms permit the selection of independent time steps in each element and the local time steps need not bear an integral relation to each other ii the algorithms derive from a spacetime form of a discrete version of hamilton s principle as a consequence of this variational structure the algorithms conserve local energy and momenta exactly subject to solvability of the local time steps numerical tests reveal that even when local energy balance is not enforced exactly the global and local energy behavior of the avis is quite remarkable a property which can probably be traced to the symplectic nature of the algorithm

analysis of a new algorithm for continuous time robust adaptive control analysis of a robust indirect adaptive control scheme is presented it is shown that a new dead zone technique can be used so that the knowledge of the parameters of the upper bounding function on the unmodeled dynamics and the disturbance is not necessarily required furthermore the allowable unmodeled dynamics could be enlarged if the knowledge of the upper bound of the unmodeled dynamics is given

a new robust mrac using variable structure design for relative degree two plants abstract variable structure design concept has been shown not only useful in dealing with uncertain systems but also useful in establishing controllers in the adaptive context continuing the work this research proposed a new robust model reference adaptive control for single input single output linear plants with relative degree two a class which encompasses a large number of linearized mechanical systems when compared with the conventional mrac schemes the current approach drastically improves the transient behavior and the tracking performance of the closed loop system from several numerical simulations furthermore if the reference input satisfies the persistently exciting condition or if the prior knowledge about the interval in which the true parameter vector lies is available the magnitude of the input force can be considerably reduced into a more realistic level in the presence of mild unmodelled dynamics and bounded output disturbances the proposed scheme possesses similar well behaved properties it can be shown that the tracking error will in fact fall into a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances

finite dimensional adaptive control for infinite dimensional systems this paper deals with the design of a finite dimensional model reference adaptive controller for a distributed parameter system the space of inputs and the space of outputs are both one dimensional first an input output representation is introduced using filtered values generated from the inputs and outputs next it is shown that we can design a finite dimensional adaptive control system by a new adaptive law the new adaptive law guarantees the existence of a large region of attraction from which all signals are bounded and the tracking error converges to a small residual set

robust adaptive control of proper systems to date all the adaptive control algorithms have been proposed only for strictly proper systems in this paper a scheme is proposed to design an adaptive controller for proper systems to study the robustness of the adaptive controller both additive and multiplicative types of unmodeled dynamics are considered and can also be allowed to be proper or even improper global bounded input bounded output stability is established the achievement of a small in the mean tracking error and perfect tracking rejection of deterministic trajectories disturbances in the absence of system unmodeled dynamics are discussed the results are also verified by simulation studies