the largest singular value of e sup x a sub 0 e sup x is convex on convex sets of commuting matrices a short and direct proof of the convexity property is given it is shown that the theorem applies to any convex commuting set of matrices in r sup nxn where a sub 0 in r sup nxn is fixed it is also shown that the result does not hold if x is permitted to be a general square matrix a counterexample is supplied for noncommuting matrices

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

designs for generalized linear models with several variables and model uncertainty standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model for example for describing a binary response in terms of several variables a method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function the linear predictor or the model parameters together with a design search designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models exact designs are investigated for two applications and their advantages over factorial and central composite designs are demonstrated

output feedback control of nonlinear systems using direct adaptive fuzzy neural controller in this paper a direct adaptive fuzzy neural output feedback controller dafoc for a class of uncertain nonlinear systems is developed under the constraint that only the system output is available for measurement an output feedback control law and an update law are derived for on line tuning the weighting factors of the dafoc by using strictly positive real lyapunov theory the stability of the closed loop system compensated by the dafoc can be verified moreover the proposed overall control scheme guarantees that all signals involved are bounded and the output of the closed loop system asymptotically tracks the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

adaptive control of linear time varying plants abstract in this paper the model reference adaptive control mrac problem of a class of linear time varying ltv plants is considered the plant parameters are assumed to be smooth bounded functions of time which satisfy the usual assumptions of mrac for time invariant plants at each frozen time instant it is first shown that if the plant parameters are sufficiently slowly varying with time a control parameter vector with smooth elements exists such that the closed loop plant behaves almost like a linear time invariant reference model the robust adaptive law proposed in ioannou and tsakalis 1986 ieee trans aut control ac 31 1033 is then used to adjust the controller parameters and establish boundedness of all signals in the adaptive loop for any bounded initial conditions it is shown that the bound for the residual tracking error depends on the speed of the plant parameter variations in such a way that as these parameters become constant the bound reduces to zero

robustness of adaptive control for stochastic systems robustness of the stochastic adaptive systems with unmodelled dynamics and external disturbances is discussed in this paper an adaptive controller is designed using the els algorithm except for the finite switches it is shown that the closed loop system is globally stable both the estimation error and the tracking error approach their minima when the unmodelled dynamics diminish that is the asymptotically adaptive system operating with the els algorithm has a good robustness with respect to unmodelled dynamics and external disturbances

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

model reference adaptive control for plants with unknown relative degree a parameterization scheme for model reference control which guarantees stable model plant transfer function matching is presented this scheme has a linear dynamic feedforward block whose numerator and denominator should be stable polynomials for closed loop stability an adaptive law is designed to update the controller parameters in the feedback loop and the coefficients of the numerator of the feedforward block as well as some additional parameters since for stability the inverse of the polynomial differential operator defined by some of the estimated parameters has to be stable the adaptive law is modified using a projection technique the stability analysis of the model reference adaptive control mrac scheme is given the robustness of the mrac scheme with respect to unmodeled dynamics is established

a robust indirect adaptive control approach this paper considers the robust design of an indirect adaptive control approach which is applicable when the unknown parameters of a linear time invariant plant lie in a known convex set throughout which no unstable pole zero cancellation occurs in order to achieve the robustness the use of a relative dead zone in the adaptive law is proposed it is shown that with a suitably designed relative dead zone the adaptive control system is globally stable even in the presence of small unmodeled plant uncertainties

adaptive system stability robustness via burst recovery abstract adaptive systems which are based on a posteriori parameter update algorithms are shown to possess a specific type of self stabilization property termed burst recovery this results in bounded disturbance bounded error stability provided that unbounded parameter drift does not occur persistent excitation prevents unbounded parameter drift but only when both upper and lower bounds on excitation exist for many adaptive systems an upper bound on excitation cannot be assured using standard perturbation analyses which require the disturbance to be suitably small compared to the lower bound on excitation this paper proves that burst recovery in conjunction with only a lower bound on excitation provides bounded disturbance bounded error stability the disturbance need not be small and additional algorithm modifications such as parameter projection are not necessary

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

non linear dynamics in adaptive control chaotic and periodic stabilization abstract in this paper the non linear features of adaptive control algorithms are highlighted using a simple linear discrete time example based on classical design it is demonstrated that in the presence of undermodelling errors non linear phenomena in the feedback gain such as limit cycles and even chaos arise despite these complicated dynamics robust stabilization of the plant can still occur for the class of undermodelling errors considered the set of plants stabilizable by this adaptive controller is completely characterized

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods

paper an input output view of robustness in adaptive control the stability and robustness properties of adaptive control systems are examined using input output stability theory i e passivity and small gain theory a generic adaptive error system is developed based on the concept of a tuned system an ideal converged nonadaptive closed loop system using this error system with passivity theory gives conditions for global stability where only boundedness in norm is required on the external inputs e g disturbance reference and initial conditions small gain theory is used to develop local stability results where the magnitudes of the external inputs are restricted in the global case a particular system operator not the plant is required to be strictly passive a condition which is unlikely to hold in actual use due to unmodeled dynamics the local results however are not so restricted and allow for unmodeled dynamics in this latter case an estimate of the stability margin is given under a persistent excitation condition

extrapolation methods and rubio de francia s extrapolation theorem we develop a general framework to study extrapolation of inequalities 2005 elsevier inc all rights reserved msc primary 47b38 46m35 secondary 42b25 42b20

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

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

brief robust adaptive identification of slowly time varying parameters with bounded disturbances in this paper the robustness limitations of current recursive identification algorithms are highlighted then it is shown how a particular non recursive identification algorithm may improve the robustness to bounded disturbances and slowly time varying parameters at the expense of performing an on line eigenvalue decomposition on a symmetric semidefinite positive matrix furthermore contrary to robustified recursive identification algorithms this algorithm does not require any a priori knowledge of a bound on the disturbances and of a bound on the unknown parameter values

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

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

a globally stable apcs in the presence of bounded noises and disturbances this paper presents a globally stable adaptive predictive control system apcs for discrete linear processes with pure time delays in the presence of bounded measurement and process noise plus unmeasured disturbances the main contribution is the proof of stability in the context of discrete adaptive control schemes this proof is based on the minimization of the a posteriori estimation error and the convergence of the estimated parameters

direct adaptive tuning of robust controllers with guaranteed stability properties we address the following problem given a fixed regulator that insures closed loop stability for a partially known plant design a mechanism to adaptively tune the controller parameters in order to improve performance our main concern is to insure that global l stability of the overall system is preserved the proposed parameter update law includes a signal normalization 1 and a modification 2 the condition for global l stability relates the margin of stability of the closed loop linear system the speed of adaptation and the size of the residual set for the tracking error

integral manifolds of slow adaptation conditions are given under which an integral manifold slow manifold exists for a nonlinear system representing a broad class of adaptive algorithms the parameter update equation restricted to the manifold is an exact description of the slow adaptation process which can be approximately analyzed by averaging stability properties of the slow motion in the manifold are extended off the manifold by a set of conditions under which the manifold is shown to be attractive this two time scale analysis provides a geometrical visualization of instability phenomena observed in adaptive systems and generalizes earlier local stability results

intermediate spaces between 2 τ lτ and l abstract in this paper we introduce an intermediate space l t between 2 l t and l t where l t are the l subspaces of a nonatomic finite measure space t and study its properties in particular this space is banach and rearrangement invariant with respect to the measure our main result states that under some conditions l t coincides with a special marcinkiewicz space in addition we obtain zygmund type weak and integral estimates for functions from l t and apply them to estimate the norms of the conjugate fourier and littlewood paley operators from l t to l t where t is the unit circle in c relationships between l t and bmo t are discussed as well

distributionally concave symmetric spaces and uniqueness of symmetric structure abstract we present new results concerning the uniqueness of symmetric structure of symmetric function spaces our methods are partly based on a detailed study of distributionally concave spaces and the tensor product operator

maximal functions on classical lorentz spaces and hardy s inequality with weights for nonincreasing functions a characterization is given of a class of classical lorentz spaces on which the hardy littlewood maximal operator is bounded this is done by determining the weights for which hardy s inequality holds for nonincreasing functions an alternate characterization valid for nondecreasing weights is also derived

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

a stable adaptive implementation of the internal model principle an adaptive implementation of the internal model principle for linear time invariant systems that allows for rejection of unknown deterministically modeled disturbances is provided the minimal representation of the system model is used for parameter estimation and the global convergence and stability of the algorithm are investigated with unmodeled dynamics with proper modification of the parameter estimation algorithm global convergence and stability for the algorithm are obtained without the requirement of persistent excitation some simulation results are given to support the analysis

robustness of discrete time adaptive controllers an input output approach a general input output approach that can be used for the design and analysis of robust discrete time adaptive control schemes is presented in particular a model reference adaptive controller is considered the design approach involves the use of the certainty equivalence principle to combine a robust control structure with a robust adaptive law using exponentially weighted i sub 2 norms and exploiting the properties of the adaptive law and the control structure robust stability is established for the closed loop adaptive control scheme

robust parameter adjustment with nonparametric weighted ball in h sup infinity uncertainty using a parameter adjustment law robust monotonic parameter error reduction is proved for a linear parameter estimation problem in which the signal is corrupted by the presence of nonparametric dynamical uncertainty the nonparameterized dynamics are characterized by a known frequency domain magnitude bound a nonconservative bound on the finite time energy of the nonparametric dynamics output is constructed in real time when the error single energy is small enough to be due to nonparametric dynamics alone the parameter adjustment is shut off to avoid misadjustment the approach is an extension of existing adaptive control error dead zone ideas to the case of frequency domain bounded uncertainty

robust adaptive control conditions for global stability an input output approach is presented for analyzing the global stability and robustness properties of adaptive controllers to unmodeled dynamics the concept of a tuned system is introduced i e the control system that could be obtained if the plant were known comparing the adaptive system to the tuned system results in the development of a generic adaptive error system passivity theory is used to derive conditions which guarantee global stability of the error system associated with the adaptive controller and ensure boundedness of the adaptive gains specific bounds are presented for certain significant signals in the control systems limitations of these global results are discussed particularly the requirement that a certain operator be strictly positive real spr a condition that is unlikely to hold due to unmodeled dynamics

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

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

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

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

stability and robustness properties of a simple adaptive controller a low order adaptive tracking controller is proposed for linear time invariant plants with a relative degree not exceeding two the order of the plant is not required to be known a priori the algorithm is robustly stable with respect to small linear time invariant plant perturbations and bounded disturbances the robustness is achieved by using a projection of the parameter estimates in the control law an additional a priori information needed to design the controller is bounds on the plant parameters in the absence of plant perturbations and disturbances perfect tracking is obtained

robust adaptive pole placement for linear time varying systems this paper studies the robustness properties of a basic adaptive control algorithm with respect to plant parameter variation as well as modeling errors and bounded disturbances the algorithm consists of a projected gradient estimator and a pole assignment controller a unified method of proof is presented for robust stability of both discrete and continuous time adaptively controlled time varying systems the robust performance of an adaptive pole assignment controller is also discussed

disturbance instabilities in an adaptive system two types of disturbance instability of simple adaptive schemes are analyzed a drift equation shows how stable equilibria are forced to infinity by infrequent but persistent switches of a constant disturbance the modification proposed by p ioannou counteracts these instabilities

globally convergent multistep receding horizon adaptive controller abstract a complete proof is given of global convergence to zero of the prediction error and asymptotic optimality for a direct adaptive controller is established based on multistep quadratic cost minimization with a receding horizon philosophy the only substantial assumptions are that the controller designed when the parameters are known stabilizes the plant and the exact knowledge of the first n y n y optimization horizon impulse response coefficients of the plant the technical hurdles for the development of a comprehensive convergence theory of this type of controller are also highlighted