control issues for the beverton holt equation in ecology by locally monitoring the environment carrying capacity non adaptive and adaptive cases this paper proposes a control algorithm to govern the solution of the beverton holt equation bhe under the potentially presence of additive disturbances the bhe to be controlled is defined by certain intrinsic growth rate and environment carrying capacity sequences the last one being susceptible of local modifications around nominal values in fact the control action provides the carrying capacity which makes that the solution of the current bhe tracks a reference sequence given by another bhe defined by appropriate intrinsic growth rate and environment carrying capacity sequences in this context the fact that the inverse of the bhe is a discrete time varying linear system is taken into account where the inverse of the carrying capacity sequence plays the role of control sequence the current and the reference bhes have to be close enough to each other in order that local modifications of the carrying capacity be able to meet the tracking objective a feedback control law is designed to achieve such an objective with a zero tracking error in the ideal case of known intrinsic growth rate sequence and no presence of disturbances an adaptive control law with the associated parameter estimation algorithm is considered when the intrinsic growth rate is fully or partially unknown and disturbances are present such a control strategy guarantees a bounded tracking error with the error converging asymptotically to zero in case that additive disturbances also converge to zero some results obtained from a simulation example illustrate the effectiveness of this control strategy

adaptive systems and time varying plants abstract the behaviour of four adaptive algorithms lms equation error output error identification and the goodwin ramadge caines adaptive control algorithm are examined in the face of plant parameter variations the key point to note is that persistency of excitation conditions in the time invariant parameter case guarantees exponential convergence then standard and newly developed lyapunov stability results allow us to guarantee tracking error and parameter error boundedness when the plant parameters are actually time varying

a further algebraic version of cochran s theorem and matrix partial orderings abstract a new version of cochran s theorem for rectangular matrices is established being oriented toward partial isometries the new version parallels corresponding results concerned with arbitrary tripotent matrices and covers results concerned with hermitian tripotent matrices a discussion of a related new matrix partial ordering is also given

partial orderings preorderings and the polar decomposition of matrices abstract when a unique decomposition of a complex rectangular matrix into two components is given then a partial ordering on the domain of one of the components induces a preordering on the whole set of matrices and partial orderings on the domains of both components induce a partial ordering on the whole set in this not we consider the three main partial orderings lo wner star and rank subtractivity on the respective domains of the two components of matrices subjected to polar decomposition a ben israel t n e greville generalized inverses theory and applications wiley new york 1974 p 255 and investigate the resulting pre and partial orderings

an indirect robust continuous time adaptive controller with minimal modifications abstract the goal of this paper is to examine the robustness of an indirect continuous time adaptive controller parameter projection which is the only modification on the basis of earlier conventional adaptive control algorithms is employed to constrain the estimates inside a prior known region following the somewhat standard analysis of indirect adaptive control systems it is shown that without any restriction on signals in the closed loop system such as persistence of excitation global stability of the system is guaranteed in the presence of unmodelled dynamics and bounded external disturbances furthermore the adaptive controller can still retain the properties of earlier unmodified conventional adaptive controllers when the controlled plant satisfies so called ideal assumptions for implementation no a priori knowledge on the unmodelled dynamics is needed

robustness of discrete time direct adaptive controllers the problem of preserving stability of discrete time adaptive controllers in spite of reduced order modeling and output disturbances is addressed in this paper conditions for global stability convergence of the tracking error with bounded signals are derived for a discrete time pole zero placement adaptive controller where the parameter estimator is modified in terms of normalized signals following an input output perpective the overall system is decomposed into two subsystems reflecting the parameter estimation and modeling errors respectively and its stability is studied using the sector stability and passivity theorems first the analysis is carried for the class of disturbances and reference inputs that are either decaying or can be exactly hulled by a linear controller of the chosen structure in this l 2 framework it is shown that the only substantive assumption to assure stability is the existence of a linear controller such that the closed loop transfer function verifies certain conicity conditions the convergence speed and alertness properties of various parameter adaptation algorithms regarding this condition are discussed the results are further extended to a broader class of l infty disturbances and reference inputs

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 sets of elements in rickart rings induced by partial orders abstract let a be a rickart ring and let a 1 be the set of all regular elements in a the set of all a a such that a b are characterized where b a 1 is given and is the minus partial order in case when a is a rickart ring such sets are characterized for the diamond the left star the right star the left sharp and the right sharp partial orders some recent results of mosic et al on partial orders in b h the algebra of all bounded linear operators on a hilbert space h are thus generalized

robust direct adaptive controllers with a new normalization technique this note presents a robust direct adaptive control scheme with a new normalization technique and its stability analysis in the presence of unmodeled dynamics and or bounded disturbances following input output stability theory l sub 2 and l sub spl infin stability of the system is studied using the sector stability and passivity theorems and conditions for global stability are derived it is also shown that robustness of the adaptive control system can be improved when relative dead zone and the novel normalization technique are incorporated into the scheme

integration theory on the zero sets of polyfold fredholm sections we construct an integration theory for sc differential forms on oriented branched ep subgroupoid for which stokes theorem holds true the construction is compatible with equivalences between ep groupoids and so gives rise to an integration theory for branched suborbifolds of polyfolds examples are the solutions sets of proper oriented fredholm sections of strong polyfold bundles for which we obtain invariants this way

robust continuous time adaptive control by parameter projection the problem of adaptive control of a continuous time plant of arbitrary relative degree in the presence of bounded disturbances as well as unmodeled dynamics is addressed the adaptation considered is the usual gradient update law with parameter projection the latter being the only robustness enhancement modification employed it is shown that if the unmodeled dynamics which consists of multiplicative as well as additive system uncertainty is small enough then all the signals in the closed loop system are bounded this shows that extra modifications are not necessary for robustness with respect to bounded disturbances and small unmodeled dynamics in the nominal case where unmodeled dynamics and disturbances are absent the asymptotic error in tracking a given reference signal is zero moreover the performance of the adaptive controller is also robust

maps preserving the diamond partial order the present paper is devoted to the study of the diamond partial order in c algebras we characterize linear maps preserving this partial order

polyfolds cobordisms and the strong weinstein conjecture abstract we prove the strong weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres

robust adaptive control of discrete nominally stabilizable plants this paper presents an indirect pole placement based adaptive control scheme for discrete linear time invariant non necessarily inversely stable and stabilizable systems the scheme is a pole placement type without requiring the plant inverse stability assumption the control objective is that the plant output should asymptotically track in the absence of unmodeled dynamics and bounded disturbances a reference signal given by an arbitrary stable filter under a bounded tracking error while ensuring robust closed loop stability the adaptive stabilizability and the robustness of this system under the presence of unmodeled dynamics and possibly bounded disturbances are proved without assuming the controllability of the modeled plant a normalized least squares algorithm with a relative adaptation dead zone and a posteriori modification of the parameter estimates is used to ensure the controllability of the modified estimation plant model at all sampling instants and at the limit such a property is crucial to solve the stable pole placement problem on the other hand the relative adaptation dead zone is included for robustness purposes under unmodeled dynamics and possibly bounded disturbances

on rank additivity and the polynomial equation p a 0 for an arbitrary polynomial p two characterizations of a square matrix a satisfying the polynomial equation p a 0 are obtained some results on rank additivity closely related to the matrix theoretic version of cochran s statistical theorem are given

adaptive control of linear singular time invariant single input single output systems with external point delay this paper is devoted to the robust adaptive control of solvable single input single output impulse free linear time invariant singular dynamic systems of known orders and unknown parameterizations subject to single external point delays the control law is of pole placement type and based on input output measurements and parametrical estimation only the parametrical estimation algorithm incorporates adaptation dead zones to prevent against potential instability caused by disturbances and unmodeled dynamics the weierstrass canonical form is investigated in detail concerning the properties of controllability and observability via testable conditions of the given arbitrary state space realization of the same order robust closed loop stability is proved under similar conditions to those used for nonsingular standard systems

a new adaptive law for robust adaptation without persistent excitation a new adaptive law motivated by the work of loannou and kokotovic 1983 is proposed for the robust adaptive control of plants with unknown parameters in this adaptive law the output error plays a dual role in the adjustment of the control parameter vector the advantages of using the adaptive law over others proposed in the literature are discussed in the ideal case the adaptive system has bounded solutions in addition the origin of the error equations is exponentially stable when the reference input is persistently exciting and has a sufficiently large amplitude the adaptive system is also shown to be robust under bounded external disturbances finally it is shown that by suitably modifying the adaptive law the overall system can be made robust in the presence of a class of unmodeled dynamics of the plant simulation results are presented throughout the paper to complement the theoretical developments

linear preservers for matrix inequalities and partial orderings we characterize the linear preservers of minus partial order on matrix algebras the developed approach allows us to classify linear transformations that live fixed several matrix relations arising as extremal cases in some classical matrix inequalities including rank additivity relation and related properties applications to the determinant preservers are considered

on some characterizations of the star partial ordering for matrices and rank subtractivity abstract the main result is that drazin s star partial ordering a b holds if and only if a b and b a b a where a b is defined by a a a b and aa ba and where a b denotes rank subtractivity here a and b are m n complex matrices and the superscript denotes the moore penrose inverse several other characterizations of a b are given with particular emphasis on what extra condition must be added in order that rank subtractivity becomes the stronger star order a key tool is a new canonical form for rank subtractivity connections with simultaneous singular value decompositions schur complements and idempotent matrices are also mentioned

some orders for operators on hilbert spaces in this paper we present some interesting properties of the diamond left right star and sharp orders for operators on hilbert spaces

stability of discrete model reference adaptive control revisited abstract we demonstrate that the model reference adaptive controller is robust with respect to small model plant mismatch the sign and a lower bound on the high frequency gain are known and the control parameters are constrained to belong to a compact set which contains the parameters of a stabilizing controller data normalization and deadzones do not play a role in the analysis a constructive proof is used to develop bounds for the allowable gain of the model mismatch when the algorithm state is far from equilibrium the signals are measured by a decaying exponential the rate of convergence is estimated an expression which can be used to calculate the size of an overbounding set is developed its size scales uniformly with respect to the external disturbances the inverse of the adaptive gain and the reference the ideal case is obtained as these tend to zero this result holds true even when there is a model mismatch

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

partial orderings of matrices referring to singular values or eigenvalues abstract a new partial ordering in the set of complex matrices is defined which is weaker than the star ordering introduced by drazin in 1978 and stronger than the minus ordering introduced by hartwig in 1980 this ordering refers to singular values of matrices and the interest in it was generated by canonical interpretations of the minus and star orderings given by hartwig and styan in 1986 for hermitian matrices a similar ordering referring to eigenvalues is also considered and its connection with a problem concerning distributions of quadratic forms in normal variables is pointed out

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

on the wedderburn guttman theorem abstract let a be a u by v matrix of rank a and let m and n be u by g and v by g matrices respectively such that m an is nonsingular then rank a n m an 1m a a g where g rank an m an 1m a rank m an this is called wedderburn guttman theorem what happens if m an is rectangular and or singular in this paper we investigate conditions under which the regular inverse m an 1 can be replaced by a g inverse m an of some kind thereby extending the wedderburn guttman theorem the resultant conditions look similar to those arising in seemingly unrelated contexts namely cochran s and related theorems on distributions of quadratic forms involving a normal random vector

involutions obstructions and mirror symmetry abstract consider a maslov zero lagrangian submanifold diffeomorphic to a lie group on which an anti symplectic involution acts by the inverse map of the group we show that the fukaya a endomorphism algebra of such a lagrangian is quasi isomorphic to its de rham cohomology tensored with the novikov field in particular it is unobstructed formal and its floer and de rham cohomologies coincide our result implies that the smooth fibers of a large class of singular lagrangian fibrations are unobstructed and their floer and de rham cohomologies coincide this is a step in the syz and family floer cohomology approaches to mirror symmetry more generally our result continues to hold if the lagrangian has cohomology the free graded algebra on a graded vector space v concentrated in odd degree and the anti symplectic involution acts on the cohomology of the lagrangian by the induced map of negative the identity on v it suffices for the maslov class to vanish modulo 4

adaptive pole placement without excitation probing signals this paper presents an indirect adaptive control scheme for linear systems which may possibly be a nonminimum phase the control scheme achieves asymptotical pole placement without either introducing persistent excitation probing signals into the systems or assuming any a priori knowledge on the plant parameters the system order is the only a priori knowledge required on the plant the adaptive control law is free from singularities in the sense that the estimated plant model is always controllable the singularities are overcome by a suitable parameter estimates modification which is based upon standard least squares covariance matrix properties the analysis of the stability and the global convergence of a closed loop system is given in detail for both discrete time and continuous time systems

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

a relationship between the star and minus orderings abstract the result of hartwig and styan 1986 stating that matrices a and b are star ordered if and only if they are minus ordered and b a b a 1 3 or b a b a 1 4 is extended by considering generalized inverses of a linear combination b a with any 0

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

on a matrix version of cochran s statistical theorem abstract cochran s theorem on the distribution of quadratic forms in normal random variables can be equivalently formulated as a rank additivity result for symmetric idempotent matrices a generalization of this theorem to matrices satisfying a general matrix polynomial equation p a 0 is given

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

contact homology and virtual fundamental cycles we give a construction of contact homology in the sense of eliashberg givental hofer specifically we construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of pseudo holomorphic curves the aim of this work is to provide a rigorous construction of contact homology an invariant of contact manifolds and exact symplectic cobordisms due to eliashberg givental hofer eli98 egh00 the contact homology of y is defined in terms of pseudo holomorphic curve counts in the sense of gromov gro85 in the symplectization r y unfortunately the moduli spaces of such curves often suffer from a severe lack of transversality and for this reason it has until now remained an important open problem to define the relevant curve counts in full generality we will use the framework developed in par15 to construct coherent virtual fundamental cycles on the moduli spaces in question thus giving rise to the desired curve counts our methods are quite general and should apply equally well to many other moduli spaces of interest previously a number of important special cases of contact homology and closely related invariants have been constructed rigorously using generic and or automatic transversality techniques cylindrical contact homology of some three manifolds was constructed by bao

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

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

some properties of matrix partial orderings abstract the matrix partial orderings considered are 1 the star ordering and 2 the minus ordering or rank subtractivity both in the set of m n complex matrices and 3 the lowner ordering in the set of m m matrices the problems discussed are 1 inheriting certain properties under a given ordering 2 preserving an ordering under some matrix multiplications 3 relationships between an ordering among direct or kronecker and hadamard products and the corresponding orderings between the factors involved 4 orderings between generalized inverses of a given matrix and 5 preserving or reversing a given ordering under generalized inversions several generalizations of results known in the literature and a number of new results are derived

robust stable pole placement adaptive control of linear systems with multiestimation this paper is concerned with a robust pole placement based adaptive control of continuous linear systems in the presence of bounded noise and a common class of unmodeled dynamics with the use of multiple estimation schemes working in parallel the multiestimation scheme consists of the above set of various single estimation schemes while being a tool used to minimize the plant identification error by building an estimate which is a convex combination of the estimates at all time the weighting functions of the individual estimates are provided at each time by a suboptimization scheme for a quadratic loss function the robust stability of the overall adaptive scheme is ensured by an adaptation relative dead zone which takes into account the contribution of the unmodeled dynamics and bounded noise

a note on an algebraic version of cochran s theorem we characterize complex square matrices with the property that each of their orthogonal decompositions is rank additive

an approach to adaptive control of fuzzy dynamic systems this paper discusses adaptive control for a class of fuzzy dynamic models the adaptive control law is first designed in each local region and then constructed in the global domain it is shown that the resulting fuzzy adaptive control system is globally stable robustness issues of the adaptive control system are also addressed a simulation example is given for demonstration of the application of the approach