a stability instability boundary for disturbance free slow adaptation with unmodeled dynamics the instability of adaptive schemes for small values of parameter adjustment gain has the form of a slow drift of adjustable parameters with an averaging analysis we derive not only a sufficient condition for stability of this drift but also a sufficient condition for it to be unstable a sharp boundary between stability and instability is signal dependent and much less demanding than the usual strict positive realness property the new positivity condition has a simple signal energy interpretation

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

optimal robustness via constrained controller in siso discrete time feedback systems a new sufficient condition for robust stabilization of siso discrete time feedback systems with both non linear or linear time varying uncertainties and constrained actuators is derived in this paper neither the plant nor the controller has to be restricted to the stable or minimum phase case the necessary and sufficient condition for solvability of a stabilizer satisfying such a robust constraint is also introduced the optimal h norm theory is employed to achieve the maximum robustness to tolerate the uncertainties via constrained control finally a design algorithm is proposed to specify adequate parameters in the compensator to satisfy the criterion of optimal robustness and an example with computer simulation is given to illustrate the results

convergence of numerical solutions to stochastic age structured population system with diffusion in this paper stochastic age structured population system with diffusion are studied in general most of stochastic age structured population system with diffusion do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties the main purpose of this paper is to develop a numerical scheme and show the convergence of the numerical approximation solution to the true solution

on reduced order adaptive output error identification and adaptive iir filtering the reduced order application of landau s adaptive output error identifier results in a perturbed error system where the perturbation signal is a moving average of the unmodeled portion of the unknown plant output or desired signal in adaptive filter parlance it is proven in this paper that if this perturbation signal is sufficiently small and a reduced order dimension model is sufficiently excited then the output and parameter estimates of this adaptive identifier filter remain bounded the influence of various operating conditions on this quantitatively defined bound are noted this robustness property is crucial in all real applications which due to nonlinearities and distributed effects are subject to reduced order modeling

existence and uniqueness attraction for stochastic age structured population systems with diffusion and poisson jump in this paper the problems about the existence and uniqueness attraction for strong solution of stochastic age structured population systems with diffusion and poisson jump are considered under the non lipschitz condition with the lipschitz condition being considered as a special case the existence and uniqueness for such systems is firstly proved by using the burkholder davis gundy inequality b d g inequality and ito s formula and then by using a novel inequality technique some sufficient conditions ensuring the existence for the domain of attraction are established as another by product the exponential stability in mean square moment of strong solution for such systems can be also discussed

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

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

fuzzy lattice operations on first order terms over signatures with similar constructors a constraint based approach abstract unification and generalization are operations on two terms computing respectively their greatest lower bound and least upper bound when the terms are quasi ordered by subsumption up to variable renaming i e t 1 t 2 iff t 1 t 2 for some variable substitution when term signatures are such that distinct functor symbols may be related with a fuzzy equivalence called a similarity these operations can be formally extended to tolerate mismatches on functor names and or arity or argument order we reformulate and extend previous work with a declarative approach defining unification and generalization as sets of axioms and rules forming a complete constraint normalization proof system these include the reynolds plotkin term generalization procedures maria sessa s weak unification with partially fuzzy signatures and its corresponding generalization as well as novel extensions of such operations to signatures with weaker functor similarities i e with possibly different arities one advantage of this approach is that it requires no modification of the conventional data structures for terms and substitutions this and the fact that these declarative specifications are efficiently executable conditional horn clauses offers great practical potential for fuzzy information handling applications

the equational theory of parameterized specifications abstract equational theorems that are valid in a given parameterized data type can be derived in the inductive theory of the corresponding specification certain syntactical requirements to the specification guarantee that its equational theory agrees with the set of those equations which are satisfied by all consistent models of the specification

optimal control for elliptic volterra lotka type equations abstract an optimal control problem for elliptic volterra lotka type equations is considered the control problem simulates optimal harvesting of growing species under certain assumptions an optimality system is derived characterizing optimal control constructive analytic procedure is designed providing a complete solution of the optimal control problem in some cases

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

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

optimal control strategies for a new ecosystem governed by reaction diffusion equations abstract an optimal control problem for a new ecosystem described by reaction diffusion equations is studied in this contribution different from the classical prey predator law the phenomenon that the growth of predator population gradually reduces due to the after effects of prey population is ubiquitous in the real world such as allelopathy phenomenon in planktonic ecosystems to model this relationship between predator and prey populations together with diffusion behaviors a novel model with general holling type functional response is presented after that the existence and uniqueness of the global positive strong solution to the ecosystem is obtained by the method of semigroups of operators on this basis an optimal control problem of the ecosystem is considered the existence of optimal control strategy is proved by using minimal sequence then the first order necessary optimality condition is obtained and the corresponding optimal control is found to be of on off form furthermore the second order necessary condition for optimal control and sufficient condition for local optimal control are all established finally a numerical example is offered to demonstrate the applications of the results obtained in this work

a robust approach to adaptive control algorithms in this note a robust approach is proposed for various modified adaptive control algorithms to counteract the presence of bounded disturbances a key feature of the approach is that when using it neither the knowledge of the upper bound on the disturbance nor the knowledge of the upper bound on the norm of the matching controller parameters is required for time implementation of those adaptive control algorithms modified with dead zone constrained estimation and spl sigma modification the stability and convergence results of the resulting algorithms are provided

nonlinear age dependent population growth under harvesting we consider the nonlinear age dependent population growth model introduced by gurtin maccamy arch rat mech anal 54 281 300 1974 to which is added a harvest of members at a rate which is constant in time but may depend on the age of members being harvested this partial differential equation may be transformed by the method of characteristics into a pair of functional equations for the total population size and the birth rate we discuss the behaviour of solutions when the birth and death moduli are functions of a single variable either the age or the total population size

paper asymptotic stability of nonlinear singularly perturbed systems using higher order corrections this paper examines a methodology for investigating the asymptotic stability properties of nonlinear singularly perturbed systems this is achieved by constructing the so called zeroth order model uncorrected model based on this model a weighted scalar sum of the lyapunov functions for two lower order subsystems is obtained the estimates of the region of attraction and the upper bound on the perturbed parameter are established it is shown that by extending this methodology to higher order corrected models less conservative results are obtained these considerable improvements are facilitated by introducing a new fast variable in both uncorrected and corrected models

optimal damping control and nonlinear elliptic systems optimal control for an elliptic equation when the control is the zero order coefficient of the differential operator is considered and an optimality system is derived under certain assumptions the problem is solved completely by giving the uniqueness and the constructive existence proof for the nonlinear optimality system an extension to the case when the state equation is a particular elliptic system is considered as well

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

decentralized adaptive robust control for a class of large scale systems with uncertainties in the interconnections the problem of decentralized control is considered for a class of time varying large scale systems with uncertainties and external disturbances in the interconnections in this paper the upper bounds of the uncertainties and external disturbances are assumed to be unknown the adaptation laws are proposed to estimate such unknown bounds and by making use of the updated values of these unknown bounds a class of decentralized linear and non linear state feedback controllers are constructed it is shown that by employing the proposed decentralized non linear state feedback controllers the solutions of the resulting adaptive closed loop large scale system can be guaranteed to be uniformly bounded and the states are uniformly asymptotically stable by using the decentralized linear state feedback controllers one can guarantee the uniform ultimate boundedness of the resulting adaptive closed loop large scale system finally a numerical example is given to demonstrate the validity of the results

optimal harvesting for a nonlinear age dependent population dynamics here we investigate an optimal harvesting problem for a nonlinear age dependent population dynamics existence and uniqueness of a positive solution for the model are demonstrated the structure of the solution is also investigated we establish the existence of the optimal control and the convergence of a certain fractional step scheme for some approximating problems we obtain the optimal controllers in feedback form via the dynamic programming method

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

characterizing specification languages which admit initial semantics abstract the paper proposes an axiomatic approach to specification languages and introduces notions of reducibility and equivalence as tools for their study and comparison algebraic specification languages are characterized up to equivalence they are shown to be limited in expressive power by implicational languages

robustness of absolute stability the stability of a class of single input single output singularly perturbed systems formed by a linear time invariant feedforward block with a sector bounded time varying feedback is considered it is shown that if the reduced order slow subsystem is absolutely stable and the parasitics are asymptotically stable and sufficiently fast then the full system is absolutely stable bounds on the singular perturbation parameter for uniform asymptotic stability and absolute stability are obtained

exponential stability of numerical solutions to a stochastic age structured population system with diffusion the main aim of this paper is to investigate the exponential stability of the euler method for a stochastic age structured population system with diffusion the definition of exponential mean square stability of numerical method is introduced it is proved that the euler scheme is exponentially stable in mean square sense an example is given for illustration

optimal harvesting for periodic age dependent population dynamics here we investigate the optimal harvesting problem for some periodic age dependent population dynamics namely we consider the linear lotka mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations existence and uniqueness of a positive periodic solution are demonstrated and the existence and uniqueness of the optimal control are established we also state necessary optimality conditions a numerical algorithm is developed to approximate the optimal control and the optimal harvest some numerical results are presented

on the existence of free models in abstract algebraic institutions abstract to provide a formal framework for discussing specifications of abstract data types we restrict the notion of institution due to goguen and burstall 1984 which formalises the concept of a logical system for writing specifications and deal with abstract algebraic institutions these are institutions equipped with a notion of submodel which satisfy a number of technical conditions our main results concern the problem of the existence of free constructions in abstract algebraic institutions we generalise a characterization of algebraic specification languages that guarantee the existence of reachable initial models for any consistent set of axioms given by mahr and makowsky 1984 then the more general problem of the existence of free functors left adjoints to forgetful functors for any theory morphism is analysed we give a construction of a free model of a theory over a model of a subtheory with respect to an arbitrary theory morphism which requires only the existence of initial models this yields a characterization of strongly liberal abstract algebraic institutions we also show how to specialise there characterisation results for the partial algebras

a new model reference robust adaptive controller in the presence of unmodeled dynamics and bounded disturbances abstract this paper presents a new model reference robust adaptive controller which does not require a priori knowledge of the norm desired controller parameter vector the algorithm is designed according to a reduced order plant which is assumed to be of minimum phase and of an arbitrary relative degree in the adaptive law the output error plays a dual role in the adjustment of the control parameter vector in the absence of unmodeled dynamics and disturbances the tracking error is shown to be zero when reference input is persistently exciting

optimal control of a competitive system with age structure we investigate optimal control of a first order partial differential equation pde system representing a competitive population model with age structure the controls are the proportions of the populations to be harvested and the objective functional represents the profit from harvesting the existence and unique characterization of the optimal control pair are established