exact and inexact lqg model matching problems the design of discrete time lqg linear quadratic gaussian controllers that yield closed loop systems that match a provided model is addressed the solution is in the form of a two degree of freedom controller having feedback and feedforward paths that independently provide the optimal actions for disturbance rejection and model matching exact and approximate model matching cases are discussed in a unified fashion

arbitrary adaptive pole placement for linear multivariable systems this paper presents a methodology for adaptively assigning the closed loop poles of either continuous or discrete time linear mnltivariable systems the scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified rather the control parameters and an equivalent plant parameterization are simultaneously estimated from input output data using linear parameter estimation procedures implementation of the scheme requires only knowledge of the system controllability indexes and an upper bound on the observabilily index

growth rate of binary words avoiding xxxr consider the set of those binary words with no non empty factors of the form x x x r du mousavi schaeffer and shallit asked whether this set of words grows polynomially or exponentially with length in this paper we demonstrate the existence of upper and lower bounds of the form n lg n o lg n on the number of such words of length n where lg n denotes the base 2 logarithm of n

decision algorithms for fibonacci automatic words ii we use a decision procedure for the fibonacci automatic words to solve problems about a number of different sequences in particular we prove that there exists an aperiodic infinite binary word avoiding the pattern x x x r this is the first avoidability result concerning a nonuniform morphism proven purely mechanically

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

the design of a precompensator for multivariable adaptive control a network theoretic approach a network theoretic approach to the design of a dynamic precompensator c s for a multiinput multioutput plant t s is considered the design is based on the relative degree of each element of t s specifically an efficient algorithm is presented for determining whether a given plant t s has a diagonal precompensator c s such that for almost all cases t s c s has a diagonal interactor the algorithm also finds any optimal precompensator in the sense that the total relative degree is minimal the algorithm can be easily modified to work even when a t s represented by a nonsquare matrix is given

frequency domain conditions for parameter convergence in multivariable recursive identification abstract a multivariable adaptive identifier is designed on the basis of a canonical form leading to a unique set of parameters to identify frequency domain conditions for parameter convergence are derived the sufficient condition to guarantee convergence in all cases is that n v distinct frequency components be present in each input of the plant where v is the maximum of the observability indices and n the order of the plant on the other hand the necessary condition requires n mv distinct frequency components distributed over the inputs where m is the number of inputs and at least v frequency components are in each separate input through examples it is shown that convergence may or may not occur for intermediate numbers of frequency components depending on their location and on the plant parameters

a multivariable self tuning controller based on pole placement design abstract the design problem of controller for discrete time linear multi input output systems is discussed the basic idea is to use pole placement approach a new pole placement tracking problem formulation and its solution is given the design of controller requires no a priori information either about stability or minimum phase of controlled plants the designed controller consists of a feedback part a feedforward part and a new precompensator and is suitable for self tuning control of continuous systems with differing and unknown dead times in each path the controller can have integral action the number of outputs can be different from the number of inputs of the controlled system a reference vector sequence and an effect of the initial state on the system output are given as a left matrix fraction the self tuning algorithm is based on identification of explicit plant model the self tuning algorithm is illustrated by examples

the canonical diophantine equations with applications a fundamental relationship between appropriate pairs of polynomial matrices is presented this relationship termed canonical diophantine equations can be used to resolve a number of standard polynomial matrix problems here the general diophantine equation is constructively resolved in a unique minimal way in addition prime canonical factorizations of a system transfer matrix are derived from knowledge of any dual factorization

avoiding three consecutive blocks of the same size and same sum we show that there exists an infinite word over the alphabet 0 1 3 4 containing no three consecutive blocks of the same size and the same sum this answers an open problem of pirillo and varricchio from 1994

an algorithm for the calculation of a nilpotent interactor matrix for linear multivariable systems a new algorithm for the calculation of the delay structure for a linear multivariable system is presented the algorithm evaluates a nilpotent interactor matrix from the matrix of coefficients of the numerator of a right matrix fraction description of the system the resulting nilpotent interactor is a product of first degree nilpotent polynomial matrices

on the least number of palindromes contained in an infinite word we investigate the least number of palindromic factors in an infinite word we first consider general alphabets and give answers to this problem for periodic and non periodic words closed or not under reversal of factors we then investigate the same problem when the alphabet has size two

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

a parameter adaptive control structure for linear multivariable systems this paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous time linear multivariable system represented by an m times m strictly proper transfer matrix t s provided t s has no right half plane zeros the controller parameters can be directly estimated from input output data the paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design this information is a natural extension of that required in the scalar case

a division algorithm for polynomial matrices a new algorithm is presented for directly determining both the quotient and the remainder associated with the division of one polynomial matrix by another the procedure requires that the denominator matrix be column proper with nonzero column degrees however unlike earlier algorithms only real matrix multiplications are employed i e there is no need for matrix inversions either explicit or implicit

stable robust tracking by sliding mode control sliding mode control is examined from the perspective of obtaining stable and robust tracking of an arbitrary time varying reference by a multi input output linear time invariant system driven by a certain class of bounded errors nonlinearities and disturbances most existing schemes for such systems are subsumed by the one presented here the results are developed via the use of inverse models and make clear the constraints imposed by the finite and infinite zero structure of the system in particular stable and robust tracking is shown to be obtained by the scheme in this paper if and only if the system is minimum phase

minimax lq exact and inexact model matching problems abstract a mixed h 2 h optimal problem is presented for both disturbance attenuation and model mismatching minimization its solution is in the form of a two degrees of freedom controller whose feedback and feedforward paths can be independently designed if the conditions for exact model matching are not met an inexact model matching problem is addressed this solution provides an effective model matching design methodology for non minimum phase plants

paper parameterization issues in multivariable adaptive control this paper gives both an overview of multivariable adaptive control algorithms which have evolved to date and presents some new approaches to the design of indirect multivariable adaptive control systems all algorithms are presented using a unified pole placement approach furthermore the emphasis is on parameterization issues such as types of control structures necessary for implementation required prior information necessary for implementation and techniques for reducing the size of the resulting parameter estimation problem

a multivariable self tuning pid controller abstract a multivariable self tuning controller with a proportional plus integral plus derivative pid structure is derived the algorithm features a combination of the self tuning property in which the controller parameters are tuned automatically on line and also the structure of a multivariable pid controller making it more favourable to be used in industry a stability proof of the algorithm is also presented here comparison of the performance of the algorithm with a fixed tuned multivariable pid controller in the simulation examples demonstrates the effectiveness of the proposed algorithm

a generalization of automatic sequences abstract we generalize the uniform tag sequences of cobham which arise as images of fixed points of k uniform homomorphisms to the case where the homomorphism is not necessarily uniform but rather satisfies the analogue of an algebraic equation we show that these sequences coincide with 1 a the class of sequences accepted by a finite automaton with generalized digits as input and 2 b generalizations of the locally catenative formula of rozenberg and lindenmayer examples include the infinite fibonacci word which is generated as the fixed point of the homomorphism a ab b a and sequences of rauzy and de bruijn

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

a multivariable self tuning controller with integral action abstract in this paper a novel stochastic self tuning control algorithm for multivariable linear systems described by controlled autoregressive integrating moving average carima models is proposed in particular the presence of an integral action on each component of the error vector ensures the robust offset rejection for any constant load disturbance acting on the plant the leading assumption is made that the system interactor matrix is known a priori the algorithm is derived by resorting to the generalized minimum variance approach two simulation examples illustrate the main features of the method

on some generalizations of abelian power avoidability we prove that 2 abelian cubes are avoidable over a binary alphabet and that 3 abelian squares are avoidable over a ternary alphabet answering positively to two questions of karhumaki et al we also show the existence of infinite additive cube free words on several ternary alphabets to achieve this we give sufficient conditions for a morphism to be k abelian n power free resp additive n power free and then we give several morphisms which respect these conditions additionally all our constructions show that the number of such words grows exponen tially as a corollary we get a new lower bound of 3 1 19 1 059526 for the growth rate of abelian cube free words

nonnegative persymmetric matrices with prescribed elementary divisors abstract the nonnegative inverse elementary divisors problem niedp is the problem of finding conditions for the existence of an n n entrywise nonnegative matrix a with prescribed elementary divisors we consider the case in which the solution matrix a is required to be persymmetric persymmetric matrices are common in physical sciences and engineering they arise for instance in the control of mechanical and electric vibrations in this paper we solve the niedp for n n matrices assuming that i there exists a partition of the given list 1 n in sublists k along with suitably chosen perron eigenvalues which are realizable by nonnegative matrices a k with certain of the prescribed elementary divisors and ii a nonnegative persymmetric matrix exists with diagonal entries being the perron eigenvalues of the matrices a k with certain of the prescribed elementary divisors our results generate an algorithmic procedure to compute the structured solution matrix

reduced order adaptive pole placement for multivariable systems a method is suggested for adaptively assigning the closed loop poles of a continuous time linear multivariable system the resulting design significantly reduces the complexity in comparison to any other known multivariable scheme for implementation one needs to know the order of the system and an upper bound on the observability index

two infinite families of polyominoes that tile the plane by translation in two distinct ways it has been proved that among the polyominoes that tile the plane by translation the so called squares tile the plane in at most two distinct ways in this paper we focus on double squares that is the polyominoes that tile the plane in exactly two distinct ways our approach is based on solving equations on words which allows us to exhibit properties about their shape moreover we describe two infinite families of double squares the first one is directly linked to christoffel words and may be interpreted as segments of thick straight lines the second one stems from the fibonacci sequence and reveals some fractal features