a unified method for the design of nonovershooting linear multivariable state feedback tracking controllers we consider the use of linear multivariable feedback control to achieve a nonovershooting step response a method is given for designing a linear time invariant state feedback controller to asymptotically track a constant step reference with zero overshoot and arbitrarily small rise time under some mild assumptions we present a unified design method that can be applied to continuous and discrete time systems square and non square systems minimum and nonminimum phase systems and also strictly proper and nonstrictly proper systems

some new results on easy lambda terms abstract given two closed terms a and b we consider the question whether the equation a b is consistent with the calculus in general the problem is undecidable however if a is a 0 term we can give good sufficient conditions for the consistency of a b this allows us to prove some counterintuitive results such as 1 there is a closed term x which can be consistently equated to every closed term with the exception of the identity 2 there is a closed term which can be consistently equated to every closed normal form but not to the curry fixed point operator y

highlights in infinitary rewriting and lambda calculus we present some highlights from the emerging theory of infinitary rewriting both for first order term rewriting systems and l calculus in the first section we introduce the framework of infinitary rewriting for first order rewrite systems so without bound variables we present a recent observation concerning the continuity of infinitary rewriting in the second section we present an excursion to the infinitary l calculus after the main definitions we mention a recent observation about infinite looping l terms that is terms that reduce in one step to themselves next we describe the fundamental trichotomy in the semantics of l calculus bohm trees levy longo trees and berarducci trees we conclude with a short description of a new refinement of bohm tree semantics called clocked semantics

controller synthesis for sign invariant impulse response in this paper we consider the problem of designing controllers for discrete time linear time invariant lti plants that render the closed loop impulse response nonnegative such systems have a non undershooting and non overshooting step response we first show that the impulse response of any discrete time lti system changes sign at least r times if it has r real positive zeros outside a circular disk centered at the origin and containing all its poles we then show that a necessary and sufficient condition on the plant for the existence of a compensator that makes the closed loop impulse response sign invariant is that there be no real positive nonminimum phase plant zeros finally we show by construction how such a compensator may be synthesized when the plant does satisfy the existence condition

algebraic characterization of controllability subspaces in the current base and its practical computation from the concepts of input chain and controllability chain introduced by heymann and in view of the generalized eigenvector assignment a new algebraic characterization of controllability subspaces css is developed compared with the previous ones based on matrix pencil theory it presents both the advantages of being stated in the current base and of being derived without resorting to use of canonical forms a practical algebraic algorithm is provided in order to compute the controllable structure of a given pair a b this approach is then applied to characterize css contained in a given subspace and span css via eigenvector assignment

applications of infinitary lambda calculus we present an introduction to infinitary lambda calculus highlighting its main properties subsequently we give three applications of infinitary lambda calculus the first addresses the non definability of surjective pairing which was shown by the first author not to be definable in lambda calculus we show how this result follows easily as an application of berry s sequentiality theorem which itself can be proved in the setting of infinitary lambda calculus the second pertains to the notion of relative recursiveness of number theoretic functions the third application concerns an explanation of counterexamples to confluence of lambda calculus extended with non left linear reduction rules adding non left linear reduction rules such as dxx x or the reduction rules for surjective pairing to the lambda calculus yields non confluence as proved by the second author we discuss how an extension to the infinitary lambda calculus where bohm trees can be directly manipulated as infinite terms yields a more simple and intuitive explanation of the correctness of these church rosser counterexamples

an algorithm for pole assignment in high order multivariable systems an efficient computational method is presented for solving the problem of pole assignment by state feedback in linear multivariable systems with large dimensions a given multiinput system is first transformed to an upper block hessenberg form by means of orthogonal state coordinate transformations the state feedback problem is then reformulated in terms of the sylvester equation the transformed system matrices along with certain assumed block forms for unknown matrices enable the sylvester equation to be decomposed and solved effectively a distinct point of the proposed algorithm is that the solution procedure can be tailored to parallel implementation and is therefore fast computational aspects of the algorithm are discussed and numerical examples are provided

graph easy sets of mute lambda terms among the unsolvable terms of the lambda calculus the mute ones are those having the highest degree of undefinedness in this paper we define for each natural number n an infinite and recursive set m n of mute terms and show that it is graph easy for any closed term t of the lambda calculus there exists a graph model equating all the terms of m n to t alongside we provide a brief survey of the notion of undefinedness in the lambda calculus

a class of bounded functions a database language and an extended lambda calculus abstract we develop an approach of partial computations for the lambda calculus it produces a class of bounded functions i e the co domains are finite while the domains are possibly infinite including self applicable functions we show that the bounded functions are recursive and have to be represented as lambda terms without head normal form in the lambda calculus in parallel we develop a language independently from the lambda calculus it also represents the class of bounded functions and therefore can produce whatever a turing machine produces provided that computation has finite time and space we call such a language a database language because we can use the language to construct and query business objects in database practice with the bounded functions we are able to extend the lambda calculus to effectively reduce terms having weak head normal form in a manner similar to how the standard lambda calculus reduces terms that have normal form

on the mode shapes of the helmholtz equation abstract the differential equation governing the free transverse vibration of a thin membrane the helmholtz equation is also the governing equation for problems of microwave propagation stress waves and acoustics simple analytical solutions may be found in elliptic and parabolic co ordinates the paper is concerned with the nature of the fundamental and higher modes of membranes of arbitrary shape and in particular with the question of whether the level lines contours of the modes do or do not intersect each other i e whether the displacement has or has not saddle points we announce a result proved elsewhere and discuss its implications if the membrane is not circular then any mode with only interior nodal lines has non nodal saddle points

shaping of the output response in a class of linear multivariable systems a state feedback controller is designed to regulate as desired the output response of minimum phase linear multivariable square plants with cb having full rank b input matrix and c output matrix properties of the controller are given and an example is worked out for illustration

robust eigenstructure assignment in geometric control theory in this paper we employ the rosenbrock system matrix pencil for the computation of output nulling subspaces of linear time invariant systems which appear in the solution of a large number of control and estimation problems we also consider the problem of finding friends of these output nulling subspaces i e the feedback matrices that render such subspaces invariant with respect to the closed loop map and output nulling with respect to the output map and which at the same time deliver a robust closed loop eigenstructure we show that the methods presented in this paper offer considerably more robust eigenstructure assignment than the other commonly used methods and algorithms

eigenvalue assignment in a single input linear system a procedure for eigenvalue assignment in a single input linear system in hessenberg form is described the procedure uses real arithmetic throughout and includes a facility for estimating the robustness of the assigned eigenvalues the assigned eigenvalues may be real or complex simple or multiple

transient response control via characteristic ratio assignment this note develops an approach to directly control the transient response of linear time invariant control systems we begin by considering all pole transfer functions of order n for which we introduce a set of parameters spl alpha sub i i 1 n called the characteristic ratios we also introduce a generalized time constant spl tau we prove that spl alpha sub 1 and spl tau can be used to characterize the system overshoot to a step input and the speed of response respectively by independently adjusting spl alpha sub 1 and spl tau in all pole systems arbitrarily small or no overshoot as well as arbitrarily fast speed of response can be achieved these formulas are used to develop a procedure to design feedback controllers with feedforward or two parameter output feedback type for achieving time response specifications for a minimum phase plant we show that arbitrary transient response specifications namely one with independently specified overshoot and specified rise time or speed of response can be exactly attained

an analysis of bo hm s theorem abstract in this article we present a detailed analysis of bohm s theorem explained completely constructively as an algorithmic development in the functional language ml

output deadbeat control discrete time multivariate systems an algorithm is presented to compute output deadbeat controls for linear multivariable systems the algorithm based on quadratic optimization with no cost on control cheap control is numerically stable and covers the most general cases the resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback the central part of the algorithm is the construction of the nonunique state cost matrix two alternatives are presented having different complexities and resulting in solutions having different properties

meshless thin plate spline methods for the modified helmholtz equation in this paper we investigate the application of the meshless radial basis function method for solving the helmholtz equation using thin plate splines we use a meshless method mixed with a boundary and a fundamental solution methods the numerical computation is achieved by using the generalized minimal residual gmres the least square lsqr methods associated with tikhonov regularization

approximate pole assignment a novel approach and some new algorithms for the pole assignment problem of a controllable time invariant linear multivariable system with linear state or output feedback are presented the main theme of the approach and the algorithms is to satisfy some constraints in the problem approximately various rank 1 update algorithms can then be derived depending on different extents to which the constraints are approximated functionals have to be minimized when eigenvectors of the closed loop system are chosen a perturbation analysis on the effect of the approximation and several numerical examples will be presented

nonovershooting and monotone nondecreasing step responses of a third order siso linear system this paper presents the necessary and sufficient conditions for a third order single input single output siso linear system to have a nonovershooting or monotone nondecreasing step response if the transfer function of an overall system has real poles a necessary and sufficient condition is found for the nonovershooting or monotone nondecreasing step response in the case of complex poles one sufficient condition and two necessary conditions are obtained the resulting conditions are all in terms of the coefficients of the numerator of the transfer function simple calculations can be used to check a system for the nonovershooting or monotone nondecreasing step response another feature is that the conditions in terms of pole zero configurations can be easily derived from the present results

robust control with pole shifting via performance index modification robust controllers that ensure closed loop eigenvalue placement are designed for linear systems with parametric uncertainties by using an appropriate state weighting matrix choice and a relative stability degree an lmi based algorithm is proposed to provide guaranteed cost controllers that ensure i the closed loop nominal eigenvalues shifting by a pre specified amount ii a prescribed degree of stability for all system uncertainties of a given class a certain level of closed loop performance is also ensured by minimizing the associated guaranteed cost

on sets of solutions to combinator equations abstract we show that every r e set of combinators closed under conversion is the set of solutions to a pattern matching problem

nonovershooting and nonundershooting exact output regulation abstract we consider the classic problem of exact output regulation for a linear time invariant plant under the assumption that either a state feedback or measurement feedback output regulator exists we give design methods to obtain a regulator that avoids overshoot and undershoot in the transient response

inverse spectral problem for the density of a vibrating elastic membrane this paper is concerned with the recovery of an unknown symmetric density function in the weighted helmholtz equation with dirichlet boundary conditions from the lowest few eigenvalues by using the piecewise constant function to approximate the density function and using the rayleigh ritz approach to discretize the differential equation the continuous inverse eigenvalue problem is converted to a related matrix inverse eigenvalue problem and then a least squares problem for the discrete model is formulated the solution of the least squares problem via an iterative method is discussed and then an approximation to the unknown density is recovered numerical experiments are given to confirm its competitiveness

equational programming in l calculus via sl systems part 1 abstract a system of equations in the calculus is a set of formulas of the equations together with a finite set of variables of the unknowns a system s is said to be solvable solvable iff there exists a simultaneous substitution with closed terms for the unknowns that makes the equations of s theorems in the theory a system s can be viewed as a set of specifications the equations for a finite set of programs the unknowns whereas a solution for s yields executable codes for such programs a class g of systems for which the solvability problem is effectively decidable defines an equational programming language and a system solving algorithm for g defines a compiler for such language this leads us to consider separation like systems sl systems i e systems with equations having form x m z wherex is an unknown and z is a free variable which is not an unknown it is known that the solvability problem for sl systems is undecidable here we show that there is a class of sl systems np regular sl systems for which the solvability problem is np complete moreover we show that any sl system s can be transformed into an np regular sl system s this transformation consists of adding abstractions to the lhs occurrences of the rhs variables of s in this sense np regular sl systems isolate the source of undecidability for sl systems namely a shortage of abstractions on the lhs occurrences of the rhs variables np regular sl systems yield an equational programming language in which unrestrained self application is handled constraints on executable code to be generated by the compiler can be specified by the user and properties of data structures can be described in an abstract way however existence of executable code satisfying a specification in such language is an np complete problem this is the price we have to pay for allowing unrestrained self application in our language

approximation of surfaces by modified helmholtz splines abstract we present a smoothing method of a set of points to be approximated from a given boundary value problem for the modified helmholtz equation a solution of such problem will be called mh spline two convergence results are carefully established some numerical and graphic examples are shown in order to test the validity of the method

new approach to robust observer design this paper shows that based on the recent development of observer design solution an observer pole selection method can be formulated to minimize the observer gain to the system input it is proved that this method is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems

a meshless method for some inverse problems associated with the helmholtz equation in this paper a new numerical scheme based on the method of fundamental solutions is proposed for the numerical solution of some inverse boundary value problems associated with the helmholtz equation including the cauchy problem since the resulting matrix equation is badly ill conditioned a regularized solution is obtained by employing truncated singular value decomposition while the regularization parameter for the regularization method is provided by the l curve method numerical results are presented for problems on smooth and piecewise smooth domains with both exact and noisy data and the convergence and stability of the scheme are investigated these results show that the proposed scheme is highly accurate computationally efficient stable with respect to the noise in the data and convergent with respect to decreasing the amount of data noise and increasing the distance between the physical and fictitious boundaries and could be considered as a competitive alternative to existing methods for these problems

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

a new design approach to unknown input observers this paper proposes a fundamentally new unknown input observer uio which has uniquely r decoupled modes provides r linearly independent combinations of plant system states and has zero gain to all p unknown inputs the parameter r is adjustable if the plant system satisfies the conditions of the existing uio then r n plant system order and there is no difference between our uio and the existing regular uio however if the plant system satisfies either of the following two significantly more general conditions m p m is the number of plant output measurements and at least one stable transmission zero then 1 n and our uio can still generate some constrained state feedback control signals hence this new uio can completely unify the regular uio r n and the static output feedback r m the two basic feedback structures of modern control theory far from being unified before

some necessary and sufficient conditions for eigenstructure assignment abstract some necessary and sufficient conditions for closed loop eigenstructure assignment by output feedback in time invariant linear multivariable control systems are presented a simple condition on a square matrix necessary and sufficient for it to be the closed loop plant matrix of a given system with some output feedback is the basis of the paper some known results on entire eigenstructure assignment are deduced from this the concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors

linear matrix inequalities for globally monotonic tracking control this paper addresses the problem of achieving monotonic tracking control for any initial condition also referred to as global monotonic tracking control this property is shown to be equivalent to global non overshooting as well as to global non undershooting i e non overshooting and non undershooting for any initial condition respectively the main objective of this paper is to prove that a stable system is globally monotonic if and only if all the rows of the output matrix are left eigenvectors of the space transition matrix this property allows one to formulate the design of a controller which ensures global monotonic tracking as a convex optimization problem described by a set of linear matrix inequalities lmis

a new approach for computing the state feedback gains of multivariable systems this note presents some new results in linear systems first the relationship between the polynomial matrix description and the state space representation of multivariable systems is clarified then we show that once such a relationship is determined the coprime matrix fraction description can be easily computed and we can further develop a closed form formula to solve the pole assignment problem of multivariable systems such formula can be thought of as an extension of the ackermann s formula for mimo systems thus this note potentially gives us a clearer insight into linear systems from the theoretical viewpoint

robust eigenvalue assignment for generalized systems abstract in this paper we examine the problem of robust pole placement using state feedback in generalized systems we develop a robustness theory for the finite generalized spectrum of the system as a partial problem and for the infinite pole placement problem as a second partial problem where perfect conditioning is always achievable we also give bounds between the complete closed loop robust eigenvalue problem and the two partial ones the basic tool that is exploited in the presented theory is the concept of chordal metric in this paper we take advantage of this notion and present a compact theory for the robust eigenvalue assignment problem in generalized systems the proposed theory is easy to implement retrieves the results for the state variable case as a special case and takes advantage of well known computational results

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates we use reddy s third order plate theory to study buckling and steady state vibrations of a simply supported functionally gradient isotropic polygonal plate resting on a winkler pasternak elastic foundation and subjected to uniform in plane hydrostatic loads young s modulus and the poisson ratio for the material of the plate are assumed to vary only in the thickness direction effects of rotary inertia are considered the problem of determining the critical buckling load or the vibration frequency of the plate is found to be analogous to that of ascertaining the frequency of a membrane clamped at the edges and whose shape coincides with that of the plate the critical buckling load and the vibration frequency are shown to be positive some available results for plates symmetric about the mid plane can be retrieved from the present analysis

non existent statman s double fixed point combinator does not exist indeed we give a negative answer to a problem of r statman concerning the existence in the lambda calculus of a fixed point combinatorysuch thaty si yholds

explicit reference governor for linear systems abstractthe explicit reference governor is a constrained control scheme that was originally introduced for generic nonlinear systems this paper presents two explicit reference governor strategies that are specifically tailored for the constrained control of linear time invariant systems subject to linear constraints both strategies are based on the idea of maintaining the system states within an invariant set which is entirely contained in the constraints this invariant set can be constructed by exploiting either the lyapunov inequality or modal decomposition to improve the performance we show that the two strategies can be combined by choosing at each time instant the least restrictive set numerical simulations illustrate that the proposed scheme achieves performances that are comparable to optimisation based reference governors

effects of using observers on stabilization of uncertain linear systems the effects of observers on robust linear feedback controllers are studied sufficient conditions are obtained that guarantee full recovery of the allowable uncertainty bounds attainable by full state feedback the effects of the resulting high gain observers on the disturbance rejection bounds are also studied it is shown that full recovery of the uncertainty bound leads to possible large degradation in disturbance rejection however if there is only additive plant disturbance and no measurement disturbance this degradation can be prevented

an algorithm for computing state feedback in multiinput linear systems a new algorithm is proposed in this note to compute the state feedback for arbitrary pole placement in multiinput linear systems the algorithm has good numerical behavior it also allows the user to adjust the eigenstructure of the resulting feedback system and therefore improve the condition of the problem and computation

robust pole assignment for synthesizing feedback control systems using recurrent neural networks this paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback the problem is formulated as a pseudoconvex optimization problem with robustness measure i e the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment two coupled recurrent neural networks are applied for solving the formulated problem in real time in contrast to existing approaches the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority

non overshooting output tracking of feedback linearisable nonlinear systems the problem of non overshooting output tracking of feedback linearisable single input single output nonlinear systems is considered we present a controller design procedure which makes use of feedback linearisation and global coordinate transformation techniques and is applicable to the cases with a variety of reference inputs and possibly non zero initial conditions for systems with low relative order the sets of feasible controller parameters are constructed and the presented conditions for determining these sets are sufficient and necessary for systems with higher relative order an approach to construct such sets is proposed where the conditions are sufficient two illustrative examples are provided to show the effectiveness of the results

infinite l calculus and types recent work on infinitary versions of the lambda calculus has shown that the infinite lambda calculus can be a useful tool to study the unsolvable terms of the classical lambda calculus working in the framework of the intersection type disciplines we devise a type assignment system such that two terms are equal in the infinite lambda calculus iff they can be assigned the same types in any basis a novel feature of the system is the presence of a type constant to denote the set of all terms of order zero and the possibility of applying a type to another type we prove a completeness and an approximation theorem for our system our results can be considered as a first step towards the goal of giving a denotational semantics for the lambda calculus which is suited for the study of the unsolvable terms however some noncontinuity phenomena of the infinite lambda calculus make a full realization of this idea namely the construction of a filter model a quite difficult task

a schur method for pole assignment in this paper a new numerical algorithm for pole assignment of linear time invariant systems is presented the proposed algorithm uses reliable numerical techniques based on the schur form of the state matrix and on the use of orthogonal transformations only the bad eigenvalues of the system are modified by a sequential pole shifting procedure and the resulted gains in the feedback matrix are minimized

numerically robust pole assignment for second order systems we propose two new methods for solution of the eigenvalue assignment problem associated with the second order control system global hsize 30pc specifically the methods construct feedback matrices f 1 and f 2 such that the closed loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned method 1 is a modification of the singular value decomposition based method proposed by juang and maghami which is a second order adaptation of the well known robust eigenvalue assignment method by kautsky et al for first order systems method 2 is an extension of the recent non modal approach of datta and rincon for feedback stabilization of second order systems robustness to numerical round off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed loop second order pencil control robustness to large plant uncertainty will not be explicitly considered in this paper numerical results for both the two methods are favourable a compara

nonovershooting control of strict feedback nonlinear systems a means of obtaining a nonovershooting output tracking response for single input single output siso strict feedback nonlinear systems is introduced with the proposed method arbitrary reference trajectories can be tracked from below for arbitrary initial conditions as long as the initial value of the plant output is strictly below the initial value of the reference trajectory in addition a design is presented for approximately nonovershooting control in the presence of disturbances where the amount of overshoot can be made arbitrarily small by appropriately choosing the control gains finally an output feedback example shows the ability of our approach to ensure arbitrarily small overshoot where the overshoot is caused by the initial condition of the unmeasured part of the state

on the jacopini technique the general concern of the jacopini technique is the question is it consistent to extend a given lambda calculus with certain equations the technique was introduced by jacopini in 1975 in his proof that in the untyped lambda calculus omega is easy i e omega can be assumed equal to any other closed term without violating the consistency of the lambda calculus the presentations of the jacopini technique that are known from the literature are difficult to understand and hard to generalise in this paper we generalise the jacopini technique for arbitrary lambda calculi we introduce the concept of proof replaceability by which the structure of the technique is simplified considerably we illustrate the simplicity and generality of our formulation of the technique with some examples we apply the jacopini technique to the lambda mu calculus and we prove a general theorem concerning the consistency of extensions of the lambda mu calculus of a certain form many well known examples e g the easi ness of omega are immediate consequences of this general theorem

a unified closed loop stability measure for finite precision digital controller realizations implemented in different representation schemes a computationally tractable unified finite word length closed loop stability measure is derived which is applicable to fixed point floating point and block floating point representation schemes both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure for each arithmetic scheme the optimal controller realization problem is defined and a numerical optimization approach is adopted to solve it numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes

on overshoot and nonminimum phase zeros it is widely known that real nonminimum phase zeros lead to step response undershoot and that the size of the undershoot necessarily tends to infinity as the settling time tends to zero in this note we show that the presence of two or more real nonminimum phase zeros can lead to step response overshoot in addition to undershoot a lower bound on the overshoot is derived and it is shown that the overshoot like the undershoot necessarily tends to infinity as the settling time tends to zero the results are derived for single input single output linear time invariant continuous time systems and apply to both open loop control and general two degree of freedom closed loop control

an algorithm for pole assignment of time invariant linear systems an algorithm is suggested for the computation of a linear state feedback for a single input system such that the resultant closed loop system has specified eigenvalues the algorithm is more efficient than many comparable techniques and has some desirable numerical properties it is closely related to the qr algorithm for the eigenproblem and extends to descriptor systems