system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

brief new results for analysis of systems with repeated nonlinearities this work presents new results for analysis of systems with repeated monotonic or slope restricted nonlinearities we first give new integral quadratic constraints iqcs that are satisfied by the inputs and outputs of diagonal operators with equal monotonic or slope restricted diagonal entries then we present new analysis results for systems with repeated nonlinearities obtained using the new iqcs for the type of nonlinearities considered in this work the new results are less conservative than previously known results the computation of the new conditions is discussed the results in this paper apply also to problems with nonrepeated nonlinearities whenever these are representable as the interconnection of multiple repeated nonlinearities and a constant matrix

graded witt kernels of the compositum of multiquadratic extensions with the function fields of pfister forms abstract let f be a field of characteristic 2 and w q f be the witt group of nonsingular quadratic forms over f let be a bilinear pfister form over f and l be a multiquadratic extension of f of separability degree less than of equal to 2 in this paper we compute the kernel of the natural homomorphism h 2 m 1 f h 2 m 1 l where h 2 m 1 f is the cokernel of the artin schreier operator f m f m d f m 1 given by x d x 1 x 1 d x m x m x 2 x d x 1 x 1 d x m x m where f m is the space of m differential forms over f and f is the function field of the affine quadric given by the diagonal quadratic form associated to the bilinear form as a consequence we deduce the kernel of the natural homomorphisms i q m 1 f i q m 1 l and i q m 1 f i q m 1 l where i q m 1 f denotes the quotient i q m 1 f i q m 2 f such that i q m 1 f i m f w q f and i m f is the m th power of the fundamental ideal if of the witt ring of f bilinear forms we also include some results concerning the case where is replaced by a bilinear pfister neighbor or a quadratic pfister form

bayesian system identification in bayesian statistics the concept of probability is interpreted as a rational measure of belief which is used to describe mathematically the uncertain relation between the statistician and the external world the statistical inference is understood as a correction of prior subjective probability distribution by objective data the paper shows that on this bayesian basis it is possible to build a consistent theory of system identification the following problems are considered one shot and real time identification estimation and prediction in closed control loop redundant and unidentifiable parameters time varying parameters and adaptivity

symmetric bilinear forms quadratic forms and milnor k theory in characteristic two is bijective for any field f of characteristic two and for any n 0 here k f is the k group of milnor defined in 11 and i is the unique maximal ideal of the witt ring w f of non degenerate symmetric bilinear forms over f on the other hand sah studied quadratic forms in characteristic two in 15 let f be a field of characteristic two wq f the witt group of non degenerate quadratic forms over f and define i wq f n o by the canonical w f module structure on wq f then he proved that wq f iwq f is isomorphic to the group of quadratic cyclic extensions of f and iwq f i2wq f is isomorphic to the subgroup br f 2 of the brauer group br f of f consisting of elements annihilated by 2 in this paper we prove the above milnor s conjecture and describe the precise structures of w f and wq f generalizing the result of sah for any field f of characteristic p 0 let be the n th exterior power over f of the absolute differential module n t g21 let d 2 1 be the f z f fp image of the exterior derivation d f2 t f2 and let v n v resp h 1 f be the kernel resp cokernel of the homomorphism

brief paper factorization of multipliers in passivity and iqc analysis multipliers are often used to find conditions for the absolute stability of lur e systems they can be used either in conjunction with passivity theory or within the more recent framework of integral quadratic constraints iqcs we compare the use of multipliers in both approaches passivity theory requires that the multipliers have a canonical factorization and it has been suggested in the literature that this represents an advantage of the iqc theory we consider sufficient conditions on the nonlinearity class for the associated multipliers to have a canonical factorization

brief paper multipliers for model predictive control with structured input constraints the stability and robustness of input constrained model predictive control can be analyzed using the theory of integral quadratic constraints we demonstrate the existence of improved multipliers when there are only staged input or box input constraints this can significantly reduce the conservatism of any stability analysis and we illustrate the improved performance with a simple numerical example

all multipliers for repeated monotone nonlinearities we have derived the largest class of bounded linear time invariant operators that preserve positivity of repeated monotone nonlinearities it reduces conservativeness of integral quadratic constraint iqc stability analysis of systems having repeated monotone nonlinearities to the minimum possible utility of this characterization stems from the fact that such nonlinearities are typically encountered in stability analysis of anti windup schemes among other applications we have also derived the time varying counterpart of this class of operators

orthogonal functions for cross directional control of web forming processes the cross directional behaviour of web forming processes can be represented in terms of orthogonal basis functions by choosing a suitable basis set it is possible to separate controllable and uncontrollable components of the profile into low and high order spectral components and hence obtain a parsimonious representation in most cases if there are sufficient actuators to control all low order spectral components then the interaction matrix is likely to be ill conditioned which necessitates the incorporation of input constraints into the control design the representation in terms of orthogonal functions allows the design of finite horizon predictive controllers with hard inequality constraints on the input that are computationally feasible for commercial machines it is also possible to exploit such a representation to construct efficient estimators for the process

the behavior of quadratic and differential forms under function field extensions in characteristic two abstract let f be a field of characteristic 2 let n f be the f space of absolute differential forms over f there is a homomorphism n f n f d n 1 f given by x d x 1 x 1 d x n x n x 2 x d x 1 x 1 d x n x n mod d f n 1 let h n 1 f coker we study the behavior of hn 1 f under the function field f f where b1 bn is an n fold pfister form and f is the function field of the quadric 0 over f we show that ker h n 1 f h n 1 f f d b 1 b 1 d b n b n using kato s isomorphism of hn 1 f with the quotient inwq f in 1wq f where wq f is the witt group of quadratic forms over f and i w f is the maximal ideal of even dimensional bilinear forms over f we deduce from the above result the analogue in characteristic 2 of knebusch s degree conjecture i e inwq f is the set of all classes q with deg q n

quadratic forms and pfister neighbors in characteristic 2 we study pfister neighbors and their characterization over fields of characteristic 2 where we include the case of singular forms we give a somewhat simplified proof of a theorem of fitzgerald which provides a criterion for when a nonsingular quadratic form q is similar to a pfister form in terms of the hyperbolicity of this form over the function field of a form which is dominated by q from this we derive an analogue in characteristic 2 of a result by knebusch saying that in characteristic 2 a form is a pfister neighbor if its anisotropic part over its own function field is defined over the base field our result includes certain cases of singular forms but we also give examples which show that knebusch s result generally fails in characteristic 2 for singular forms as an application we characterize certain forms of height 1 in the sense of knebusch whose quasi linear parts are of small dimension we also develop some of the basics of a theory of totally singular quadratic forms this is used to give a new interpretation of the notion of the height of a standard splitting tower as introduced by the second author in an earlier paper

a direct proof of the discrete time multivariate circle and tsypkin criteria this technical note presents a new proof of the circle criterion for multivariate discrete time systems with time varying feedback nonlinearities a new proof for the multivariate tsypkin criterion for time invariant monotonic feedback nonlinearities is derived as well both integrator and non integrator systems are considered the proofs are direct in the sense that they do not resort to any existing result in systems theory such as lyapunov theory passivity theory or the small gain theorem instead the proofs refer to the asymptotic properties of block toeplitz matrices one major advantage of the new proof is that it elegantly handles integrator systems without resorting to loop transformation pole shifting techniques additionally less conservative stability bounds are derived by making stronger assumptions on the sector bound conditions on the feedback nonlinearities in particular it is exemplified how this technique relaxes stability conditions of i a model predictive control mpc rule and ii an integrator system

a framework for multivariable algebraic loops in linear anti windup implementations abstract this brief paper addresses the implementation and well posedness aspects of multivariable algebraic loops which arise naturally in many anti windup control schemes using the machinery of linear complementarity problems a unified framework is developed for establishing well posedness of such algebraic loops enforcing well posedness is reduced to a linear matrix inequality feasibility problem that can be solved during the anti windup design stage several existing anti windup implementations appear as special cases of the unified framework presented in this brief paper

all stability multipliers for repeated mimo nonlinearities for block structured monotone or incrementally positive n dimensional nonlinearities the largest class of convolution operators stability multipliers that preserve positivity is derived these multipliers can be used in conjunction with positivity and iqc stability criteria to evaluate stability and robustness of mimo feedback systems

bloch functions and asymptotic tail variance let p denote the bergman projection on the unit disk dd p z d w 1 zw 2da w z d where dada is normalized area measure we prove that if z 1 z 1 on dd then the integral i a r 02 exp ar4 p rei 2log 11 r2 d 2 0 r 1 has the bound i a r c a 10 1 a 3 2i a r c a 10 1 a 3 2 for 0 1a 1 no such uniform bound is possible we interpret the theorem in terms the asymptotic tail variance of such a bergman projection p p by the way the asymptotic tail variance induces a seminorm on the bloch space this improves upon earlier work of makarov which covers the range 0 a 264 0 1542 we then apply the theorem to obtain an estimate of the universal integral means spectrum for conformal mappings with a k quasiconformal extension for 0 k 10 k 1 the estimate reads for t ct c and 0 k 10 k 1 b k t 14k2 t 2 1 7k 2 for t 2k 1 7k 2 k t 1 1 7k 2 for t 2k 1 7k 2 which should be compared with the conjecture by prause and smirnov to the effect that for real t with t 2 k t 2 k we should have b k t 14k2t2

brief the analysis of optimization based controllers many control techniques employ on line optimization in the determination of a control policy we develop a framework which provides sufficient convex conditions in the form of linear matrix inequalities for the analysis of constrained quadratic based optimization schemes these results encompass standard robustness analysis problems for a wide variety of receding horizon control schemes including those with polytopic and structured uncertainty a simple example illustrates the methodology

annihilators of quadratic and bilinear forms over fields of characteristic two abstract let f be a field with 2 0 w f the witt ring of symmetric bilinear forms over f and w q f the w f module of quadratic forms over f let i f w f be the maximal ideal we compute explicitly in i f m and i m w q f the annihilators of n fold bilinear and quadratic pfister forms thereby answering positively in the case 2 0 certain conjectures stated by kruskemper in m kruskemper on annihilators in graded witt rings and in milnor s k theory in b jacob et al eds recent advances in real algebraic geometry and quadratic forms in contemp math vol 155 1994 pp 307 320

cohomological kernels of mixed extensions in characteristic 2 abstract let f be a field of characteristic 2 f m the space of m differential forms over f d f m 1 f m the differential operator and h 2 m 1 f the cokernel of the artin schreier operator f m f m d f m 1 given on generators by x d x 1 x 1 d x m x m x 2 x d x 1 x 1 d x m x m d f m 1 it was shown in 8 that given a multiquadratic purely inseparable extension l f and a separable quadratic extension k f then the kernel of the natural homomorphism h 2 m 1 f h 2 m 1 k l is equal to the sum of the kernels of the extensions l f and k f in this paper we extend this result to the compositum of a finite purely inseparable multiquadratic extension with a separable biquadratic extension and we prove that this splitting property of kernels is no longer true by computing the kernel of the compositum of a separable quadratic or biquadratic extension with a simple purely inseparable extension of arbitrary degree

les formes bilineaires et quadratiques bonnes de hauteur 2 en caracteristique 2 our aim is to give a complete classification of bilinear and quadratic forms which are good of height 2 over a field of characteristic 2 i e those whose anisotropic parts over their function fields are similar to bilinear pfister forms which are definable over the ground field we include other related results

adaptive cross direction control of paper basis weight abstract the initial setting and maintaining of the desired paper basis weight in machine direction and cross direction is to be ensured adaptively for several given paper grades technical equipment includes usual traversing gauge at the output of the paper machine special traversing robot for shaping the headbox lip sequential setting of screws control computer adaptive multivariate lqg control with recursive identification generalized to distributed parameter system has been designed with the following features integral convolution type model of the process respecting the continuous nature of all signals and kernels involved by means of spline approximation repetitive control synthesis via riccati equation with periodical solutions

zames falb multipliers for quadratic programming in constrained linear model predictive control a quadratic program must be solved on line at each control step and this constitutes a nonlinearity if zero is a feasible point for this quadratic program then the resultant nonlinearity is sector bounded we show that if the nonlinearity is static then it is also monotone and slope restricted hence we show the existence of zames falb multipliers for such a nonlinearity the multipliers may be used in a general and versatile analysis of the robust stability of input constrained model predictive control