a new recursive identification algorithm for singularity free adaptive control reportedly guaranteeing the controllability of the estimated system is a crucial problem in adaptive control in this paper we introduce a least squares based identification algorithm for stochastic siso systems which secures the uniform controllability of the estimated system and presents closed loop identification properties similar to those of the least squares algorithm the proposed algorithm is recursive and therefore easily implementable its use however is confined to cases in which the parameter uncertainly is highly structured

linear discrete time h sub spl infin optimal tracking with preview the problem of finite time h sub spl infin tracking for linear discrete time varying systems is considered no a prior knowledge of the dynamics of the reference signal is assumed a distinction between three cases is made depending on whether the reference signal is perfectly known in advance measured online or previewed in a fixed interval of time ahead the tracking problem is formulated as a game where the controller plays against nature which may choose the initial condition or the system and any energy bounded driving disturbance and measurement noise inputs necessary and sufficient conditions are derived for the existence of saddle point equilibrium solutions to the three different information structures of the reference and the corresponding tracking controllers are derived

adaptive regulation of mimo linear discrete time systems without requiring a persistent excitation an adaptive regulator which does not require a persistent excitation is developed for multiinput multioutput mimo linear discrete time systems the assumptions on the plant are 1 an upper bound on the system dimension is known 2 the unknown system parameters belong to known bounded intervals 3 the plant is stabilizable for all possible values of the unknown system parameters the stabilizability condition can be tested before the system is put into operation a recursive parameter estimation scheme is given which forces the parameter estimates to converge to the known intervals using this estimator an adaptive regulator is derived which results in a globally stable closed loop system

interval algorithm for random number generation the problem of generating a random number with an arbitrary probability distribution by using a general biased m coin is studied an efficient and very simple algorithm based on the successive refinement of partitions of the unit interval 0 1 which we call the interval algorithm is proposed a fairly tight evaluation on the efficiency is given generalizations of the interval algorithm to the following cases are investigated 1 output sequence is independent and identically distributed i i d 2 output sequence is markov 3 input sequence is markov 4 input sequence and output sequence are both subject to arbitrary stochastic processes

a generalization of peres s algorithm for generating random bits from loaded dice peres s algorithm produces unbiased random bits from biased coin tosses recursively using the famous von neumann s method as its base the algorithm is simple and elegant but at first glance appears to work almost like magic and its generalization is elusive we generalize the method to generate unbiased random bits from loaded dice i e many valued bernoulli source the generalization is asymptotically optimal in its output rate as is the original peres s algorithm three valued case is discussed in detail and then other many faced cases are considered

stable adaptive control of non minimum phase systems abstract an adaptive pole placement design for not necessarily minimum phase systems is analyzed with respect to stability conditions are given for boundedness of closed loop signals when the process is subject to bounded disturbances the most restrictive one can be avoided in a local stability result

design of adaptive pole placement controllers for plants of unknown order by an indirect control approach an adaptive pole placement control problem is considered for a scalar discrete time linear plant assuming the knowledge of an upper bound of the plant order a class of models that can be regarded to be input output equivalent to the plant is first constructed based on the parameter estimate generated by a least squares type identification scheme a minimization problem is then derived that enables one to determine the model s coefficients and the pole placing feedback gains so that the desired closed loop poles are assigned in a limit

on nonsingular sign regular matrices abstract an m n matrix a is sign regular if for each k 1 k min m n all k k submatrices of a have determinant with the same nonstrict sign the zero pattern of nonsingular sign regular matrices is analyzed it is proved that the number of zero entries which can appear in a nonsingular sign regular matrix depends on its signature a matrix is totally nonpositive if all its minors are nonpositive a test for recognizing nonsingular totally nonpositive matrices is also provided

combined matrices of almost strictly sign regular matrices abstract the combined matrix is a very useful concept for many applications almost strictly sign regular assr matrices form an important structured class of matrices with two possible zero patterns which are either type i staircase or type ii staircase we prove that under an irreducibility condition the pattern of zero and nonzero entries of an assr matrix is preserved by the corresponding combined matrix without the irreducibility condition it is proved that type i and type ii staircases are still preserved illustrative numerical examples are included

paper an approach to stable indirect adaptive control stable indirect adaptive control of minimum and nonminimum phase plants is established for cases where a priori bounds on the unknown plant parameters are known and where for each set of parameter values within these bounds the plant has no unstable pole zero cancellation by incorporating this partial parameter knowledge in the adaptive law and using a nonminimal representation of the plant it is shown that the adaptive closed loop control system can be written as an exponentially stable system driven by the identification error the stability of the adaptive control system is then shown using techniques similar to those known from the model reference adaptive control approach

combined matrices in special classes of matrices abstract the combined matrix of a nonsingular matrix a is the matrix a a 1 t where means the hadamard entrywise product it has simple properties its row as well as column sums are always one and it is not changed if a is multiplied from either side by a nonsingular diagonal matrix although it is usually difficult to compute its further properties deserve attention in the paper we concentrate on the sequence of the diagonal entries of combined matrices in various classes of matrices

design of a deadbeat adaptive tracking system using an orthogonal decomposition technique a matrix pseudo in version lemma is presented to derive recursive algorithms for computing the best approximate solution to the sequential estimation problem a deadbeat convergence property of the algorithms is shown and is applied to the design of a deadbeat adaptive tracking system simulations illustrate perfect tracking of the system output to the periodic reference trajectory in finite steps

some applications of doubly stochastic matrices abstract we discuss primarily two applications of doubly stochastic matrices and related matrices the first concerns a topic in communication theory called satellite switched time division multiple access systems and we attempt to illuminate some results which have occured in the engineering literature the second concerns a recent notion of a doubly stochastic automorphism of a graph we prove several new theorems about doubly stochastic automorphisms of certain classes of graphs and in particular obtain a theorem of which birkhoff s theorem for doubly stochastic matrices is a special case

an adaptive lq controller for non minimum phase systems abstract the paper studied the problem of the adaptive tracking of a reference signal by the output of any deterministic discrete siso linear system with unknown parameters an adaptive control scheme based on the lq control solution is proposed the stability of the resulting adaptively controlled system and conditions for a good tracking are studied several simulations illustrate the proposal

matrix fraction solution to the discrete time lq stochastic tracking and servo problems a novel matrix fraction solution to the discrete time lq linear quadratic stochastic tracking and servo problems is presented the resulting control law is based on the knowledge at time t of the output reference up to time t gamma if gamma is positive and large enough the optimal feedforward input can be tightly approximated without requiring any stochastic model for the reference if the latter is known the optimal feedforward input is obtained by solving a bilateral diophantine equation

a generalized lqg approach to self tuning control part i aspects of design implicit self tuners based on single stage cost function minimization schemes require exact knowledge of the dead time of the controlled plant explicit pole placement self tuners on the other hand though robust against variations of the time delay are very sensitive to the assumptions made about the model order of the plant wrong assumptions may result in very poor performance an explicit method based on minimization of a multistage cost function and a carima plant model formulated in state space is presented the method extends the design features of the generalized minimum variance scheme to the multistage case these can be used to tailor the closed loop response of the system the approach is shown to be robust against wrong a priori assumptions made about the plant dead time or order thus maintaining good servo and disturbance rejection properties see part ii

binarization trees and random number generation an m extracting procedure produces unbiased random bits from a loaded dice with m faces and its output rate the average number of output per input is bounded by the shannon entropy of the source this information theoretic upper bound can be achieved only asymptotically as the input size increases by certain extracting procedures that we call asymptotically optimal although a computationally efficient asymptotically optimal 2 extracting procedure has been known for a while its counterparts for m ary input m 2 was found only recently and they are still relatively complicated to describe a binarization takes inputs from an m faced dice and produce bit sequences to be fed into a binary extracting procedure to obtain random bits thus binary extracting procedures give rise to an m extracting procedure via a binarization a binarization is to be called complete if it preserves the asymptotic optimality and such a procedure has been proposed by zhou and bruck we show that a complete binarization naturally arises from a binary tree with m leaves therefore there exist complete binarizations in abundance and zhou bruck scheme is an instance of them we now have a relatively simple way to obtain an asymptotically optimal and computationally efficient m extracting procedure from a binary one because these binarizations are both conceptually and computationally simple the well known leaf entropy theorem and a closely related structure lemma play important roles in the arguments

nonsingular almost strictly sign regular matrices abstract the class of nonsingular almost strictly totally positive matrices has been characterized m gasca j m pena characterizations and decompositions of almost strictly positive matrices siam j matrix anal appl 28 2006 1 8 in this paper we discuss the class of almost strictly sign regular matrices that includes almost strictly totally positive matrices a characterization is provided for these matrices in terms of their nontrivial minors using consecutive rows and consecutive columns in particular we present a characterization of certain almost strictly sign regular matrices in terms of a very reduced number of boundary almost trivial minors

combined matrices of sign regular matrices abstract the combined matrix of a nonsingular matrix a is the hadamard entry wise product c a a a 1 t since each row and column sum of c a is equal to one the combined matrix is doubly stochastic when it is nonnegative in this work we study the nonnegativity of the combined matrix of sign regular matrices based upon their signature in particular a few coordinates of the signature e of a play a crucial role in determining whether or not c a is nonnegative

a stable iterative adaptive control an adaptive control algorithm that carries out the online controller design iteratively is formulated a set of conditions is provided under which the closed loop system is stable in particular the controller iterations must satisfy certain convergence and continuity assumptions but only one step iteration is required for each parameter update resulting in a considerable reduction in computation time the iteration algorithm is applied to an adaptive linear quadratic regulator