robust control of cascaded and individually feedback linearizable nonlinear systems abstract feedback linearization technique is applied to design robust controllers for a class of nonlinear uncertain systems every system in the class is a series connection of finite number of nonlinear subsystems which are individually feedback linearizable and have significant but matched nonlinear functional uncertainties the key difference between this work and existing robust results is that the matching conditions and the existence of feedback linearization transformation are only required individually for each subsystem a constructive robust control design procedure is proposed for the unique control in the overall system the procedure is conceptually simple and contains three steps first perform input output feedback linearization for all individual subsystems second design fictitious robust controllers for inputs of each subsystem as if the subsystem had an independent control finally a mapping is developed which maps the individual fictitious controls recursively into the unique control of the overall system since neither the matching conditions nor feedback linearization are required for the overall system this becomes the broadest class of nonlinear uncertain or known systems for which a robust regular tracking control can be constructed using feedback linearization method global stability of the overall system is always guaranteed

state feedback control of non linear systems a design method for state feedback controllers for single input non linear systems is proposed the method makes use of the transformations of the non linear system into controllable like canonical forms the resulting non linear state feedback is designed in such a way that the eigenvalues of the linearized closed loop model are invariant with respect to any constant operating point the method constitutes an alternative approach to the design methodology recently proposed by baumann and rugh also a review of different transformation methods for non linear systems is presented an example and simulation results of different control strategies are provided to illustrate the design technique

parallel adaptive gmres implementations for homotopy methods the success of probability one homotopy methods in solving large scale optimization problems and nonlinear systems of equations on parallel architectures may be significantly enhanced by the accurate parallel solution of large sparse nonsymmetric linear systems iterative solution techniques such as gmres k favor parallel implementations however their straightforward parallelization usually leads to a poor parallel performance because of global communication incurred by processors one variation of gmres k considered here is to adapt the restart value k for any given problem and use householder reflections in the orthogonalization phase coupled with graph based matrix partitioning to achieve high accuracy and reduce the communication overhead this particular gmres implementation is tailored to the uniquely stringent requirements imposed on a linear system solver by probability one homotopy algorithms occasionally unusually high accuracy ability to adapt to problems of widely varying difficulty and parallelism

numerical linear algebra aspects of globally convergent homotopy methods probability one homotopy algorithms are a class of methods for solving nonlinear systems of equations that are globally convergent with probability one these methods are theoretically powerful and if constructed and implemented properly are robust numerically stable accurate and practical the concomitant numerical linear algebra problems deal with rectangular matrices and good algorithms require a delicate balance not always achieved of accuracy robustness and efficiency in both space and time the author s experience with globally convergent homotopy algorithms is surveyed here and some of the linear algebra difficulties for dense and sparse problems are discussed

global state and feedback equivalence of nonlinear systems the problem of finding global state space transformations and global feedback of the form u t x t to transform a given nonlinear system xdot f x g x u to a controllable linear system on rn or on an open subset of rn is considered here we give a complete set of differential geometric conditions which are equivalent to the existence of a solution to the above problem

coset codes for partial response channels or coset codes with spectral nulls known coset codes are adapted for use on partial response channels or to generate signals with spectral nulls by using coset precoding and running digital sum feedback any desired tradeoff can be achieved between the power and spectra of the relevant sequences up to the optimum tradeoff possible a fundamental theorem specifying this optimum tradeoff is given a maximum likelihood sequence estimation mlse decoder for the original code may be used for the adapted code and such a decoder then attains the minimum squared distance of the original code these methods sometimes generate codes with greater minimum squared distance than that of the original code this distance can be attained by augmented decoders although such decoders inherently require long decoding delays and may be subjected to quasi catastrophic error propagation the authors conclude that at least for sequences supporting large numbers of bits per symbol coset codes can be adapted to achieve effectively the same performance and complexity on partial response channels or for sequences with spectral nulls as they do in the ordinary memoryless case

a functional equations approach to nonlinear discrete time feedback stabilization through pole placement abstract the present work proposes a new approach to the nonlinear discrete time feedback stabilization problem with pole placement the problem s formulation is realized through a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived using tools from functional equations theory one can prove that the solution to the above system of nonlinear functional equations is locally analytic and an easily programmable series solution method can be developed under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear discrete time state feedback control law that are both computed through the solution of the system of nonlinear functional equations the feedback stabilization with pole placement design objective can be attained under rather general conditions the key idea of the proposed single step design approach is to bypass the intermediate step of transforming the original system into a linear controllable one with an external reference input associated with the classical exact feedback linearization approach however since the proposed method does not involve an external reference input it cannot meet other control objectives such as trajectory tracking and model matching

deterministic feedback linearization girsanov transformations and finite dimensional filters the problem of extending state feedback linearization methods of deterministic control theory to stochastic systems is addressed for stratonovitch stochastic differential equations with smooth vector fields necessary and geffucient geometric conditions for local and global linearization by diffeomorphism and absolutely continuous change of probability law are obtained using the interpretation of girsanov transformations as state feedback on brownian motions for stochastic systems with single with single input or onde dimensional brownian motion and single output or one dimensional observation process necessary and sufficient geometric conditions to transform the duncan mortensen zakai dmz equation of filtering into that of an affine prime system are obtained as well as interpretation of gauge transformation as girsanov change of probability law

punctured turbo codes for bpsk qpsk channels we discuss a procedure for designing high rate turbo codes via puncturing with applications to bpsk qpsk channels rates in the form k k 1 2 spl les k spl les 16 are considered for constituent encoders with memory sizes m 3 and 4 the algorithm includes the selection of constituent encoder generator polynomials puncture patterns and interleavers with the goal of maximizing the minimum codeword weight for weight two and weight three inputs the performance of the proposed codes are found via computer simulation and are observed in each case to be less than 0 9 db m 3 and 0 75 db m 4 from their respective channel capacity limits at a bit error rate of 10 sup 5 we consider two applications of punctured turbo codes

the effect of a precoder on serially concatenated coding systems with an isi channel the performance of a serially concatenated system which includes a channel with memory preceded by a precoder as a rate 1 inner coder is presented the effect of different precoders on the maximum likelihood bit error performance is analyzed the precoder weight gain which explains the good bit error rate ber performance is identified through a union bound analysis precoders are divided into two groups based on an analysis of the euclidean distance and its multiplicity and each precoder group shows a distinct ber curve behavior it is shown that the ber curves for two precoder groups cross over each other convolutional codes are considered as outer codes in simulations on various intersymbol interference channels several important design considerations for the choice of precoders are derived based on the analysis and these are confirmed through simulations with an iterative decoding algorithm

preconditioned iterative methods for sparse linear algebra problems arising in circuit simulation the dc operating point of a circuit may be computed by tracking the zero curve of an associated artificial parameter homotopy homotopy algorithms exist that are globally convergent with probability one for the dc operating point problem these algorithms require computing the one dimensional kernel of the jacobian matrix of the homotopy mapping at each step along the zero curve and hence the solution of a linear system of equations at each step these linear systems are typically large highly sparse non symmetric and indefinite several iterative methods which are applicable to such problems including craig s method gmres k bicgstab qmr kacz and lsqr are applied to a suite of test problems derived from simulations of actual bipolar circuits preconditioning techniques considered include incomplete lu factorization ilu sparse submatrix ilu and ilu allowing restricted fill in bands or blocks timings and convergence statistics are given for each iterative method and preconditioner

concatenated codes for class iv partial response channels we present the design and analysis of parallel and serial concatenated codes with iterative decoding for class iv partial response pr4 signaling code rates of the form k sub 0 k sub 0 1 for k sub 0 4 8 16 32 and 64 are considered we show that the 1 1 spl oplus d sup 2 tomlinson precoder first proposed by wolf and ungerboeck 1991 for trellis coded pr4 channels is effective for both parallel and serial concatenations but the error rate floor is relatively high for the serial case this leads to new interleaver and precoder designs for serial concatenations the latter involving an examination of the conditional distance enumerator of each precoded pr4 channel the new precoders substantially reduce the floors of the serial concatenated codes but degrade the performance of the parallel concatenated codes for a bit error rate of 10 sup 5 the best parallel and serial concatenated codes come within 1 7 db of a lower bound on the capacity limit for pr4 signaling on an additive white gaussian noise channel

trellis coding for partial response channels we consider trellis coding techniques for improving the reliability of digital transmission over noisy partial response channels such channels are commonly encountered in digital communication systems and also play a role in devices for data recording concentrating on the channels with characteristics 1 mp d we study methods to obtain codes which increase free euclidean distance between permitted sequences of channel outputs and avoid the occurrence of unlimited runs of identical outputs at the expense of some loss in data rate one technique employs the concept of set partitioning the other is based on using convolutional codes designed for maximum free hamming distance in conjunction with a precoder both methods lead to essentially equivalent codes

unique characterization of conditional distributions in nonlinear filtering on definit un probleme de martingale filtree pour un generateur a et on montre etant donne des hypotheses appropriees sur a que la distribution conditionnelle est la solution unique au probleme

reduced state representations for trellis codes using constellation symmetry this paper presents a symmetry based technique for trellis code state diagram reduction that has more general applicability than the quasi regularity technique of rouanne et al and zehavi et al for trellis codes using standard constellations and labelings for a 2 sup spl nu x state trellis code the new technique reduces the 2 sup 2 spl nu x state diagram to 2 sup spl nu x spl nu q state diagram where 0 spl les spl nu sub q spl les spl nu sub x the particular value of spl nu sub q depends on the constellation labeling and the convolutional encoder for standard rate k k 1 set partitioned trellis codes spl nu sub q 0 and the overall number of states is the same with the new technique as with quasi regularity for codes that are not quasi regular and thus not amenable to the quasi regularity technique the new technique often provides some improvement when spl nu sub q spl nu sub x for 8 phase shift keying trellis codes the new technique always yields spl nu sub q 0

on the largest feedback linearizable subsystem abstract a feedback invariant set of integers is associated with any nonlinear multivariable system which is linear with respect to the inputs it is shown to be the set of controllability indices of the largest feedback linearizable subsystem i e the largest subsystem which can be made locally linear and controllable by means of nonsingular feedback transformations

design of protograph ldpc codes for partial response channels we investigate the performance of the protograph low density parity check ldpc codes which have been shown to possess simple structures and outstanding error performance over additive white gaussian noise awgn channels over partial response pr channels using the finite length extrinsic information transfer exit algorithm due to the intersymbol interference isi caused by the pr channels we observe that the conventional protograph ldpc codes do not perform well in terms of error rates we further propose a new design scheme and construct three new types of protograph ldpc codes unlike conventional protograph ldpc codes in which the highest degree variable nodes are punctured the new protograph ldpc codes have their lowest degree variable nodes punctured moreover some edge re connections are made in one of the proposed codes the exit chart analysis the convergence analysis and the bit error rate simulation have shown that all three new codes outperform the conventional protograph ldpc codes moreover two of the proposed codes are superior to the regular column weight 3 ldpc code and thus they are good alternatives compared to other error correction codes for use in data storage systems

the superlinear convergence behaviour of gmres abstract gmres is a rather popular iterative method for the solution of nonsingular nonsymmetric linear systems it is well known that gmres often has a so called superlinear convergence behaviour i e the rate of convergence seems to improve as the iteration proceeds for the conjugate gradients method this phenomenon has been related to a modest degree of convergence of the ritz values it has been observed in experiments that for gmres too changes in the convergence behaviour seem to be related to the convergence of ritz values in this paper we prove that as soon as eigenvalues of the original operator are sufficiently well approximated by ritz values gmres from then on converges at least as fast as for a related system in which these eigenvalues and their eigenvector components are missing

on the performance evaluation of trellis codes generating function techniques for analyzing the error event and the bit error probabilities for trellis codes are considered the conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes and instead a state diagram where the number of states is equal to the square of the number of trellis states must be used it is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states em is equal to the number of trellis states the class of codes considered includes trellis codes of rate r n 1 n based upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same configuration matrix i e the same ordered set of mutual distances the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states bounds on the performance of some interesting codes are given based upon this method

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

on the linear equivalents of nonlinear systems this paper studies feedback equivalence of nonlinear systems an equivalence relation is established for the systems x f x u a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained

an extended direct scheme for robust adaptive nonlinear control abstract the proposed adaptive scheme achieves regulation for a class of nonlinear systems with unknown constant parameters and unmodeled dynamics the scheme does not employ overparametrization and does not restrict the class of nonlinearities by any growth conditions instead the dependence on the unknown parameters is restricted by an extended matching condition which however is satisfied in many systems of practical importance such as most types of electric motors

binary convolutional codes with application to magnetic recording calderbank heegard and ozarow 1 have suggested a method of designing codes for channels with intersymbol interference such as the magnetic recording channel these codes are designed to exploit intersymbol interference the standard method is to minimize intersymbol interference by constraining the input to the channel using run length limited sequences calderbank heegard and ozarow considered an idealized model of an intersymbol interference channel that leads to the problem of designing codes for a partial response channel with transfer function 1 d n 2 where the channel inputs are constrained to be pm 1 this problem is considered here channel inputs are generated using a nontrivial coset of a binary convolutional code the coset is chosen to limit the zero run length of the output of the channel and so maintain clock synchronization the minimum squared euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code which we call the magnitude code an interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic

large sparse continuation problems we study and develop efficient and versatile predictor corrector continuation methods for large sparse problems the first object is to show how special solving methods for a large sparse linear systems can be incorporated into the basic steps of a continuation method next we describe how to use a special nonlinear conjugate gradient method to perform the corrector phase it is shown how such methods can be used to detect bifurcation points and how to trace bifurcating solution branches by using local perturbations finally a numerical example involving bifurcating branches of a nonlinear eigenvalue problem is given

canonical forms of decouplable and controllable linear systems in this paper we present the canonical forms of decouplable and controllable linear systems some of the non zero elements in gilbert s canonically decoupled structure which remain undetermined are explicitly determined by a complete set of invariances our result constitutes the key step to characterization of the whole class of nonlinear systems that are feedback equivalent to decouplable and controllable linear systems

experiments with conjugate gradient algorithms for homotopy curvetracking there are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points i e with probability one the essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map hompack is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve and has separate routines for dense and sparse jacobian matrices the hompack algorithms for sparse jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernal of the homotopy jacobian matrix a required linear algebra step for homotopy curve tracking here variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with craig s preconditioned conjugate gradient method used in hompack the test problems used include actual large scale sparse structural mechanics problems