stable inversion of continuous time nonlinear systems by finite difference methods introduces finite difference methods for stable inversion of continuous time nonlinear systems a relationship between the new finite difference methods and the existing picard methods is established a damped newton finite difference method is shown to possess superior convergence properties and its effectiveness is illustrated with an inverted pendulum example

a new approach to inversion based feedforward control design for nonlinear systems the finite time transition between stationary setpoints of nonlinear siso systems is considered as a scenario for the presentation of a new design approach for inversion based feedforward control design techniques which are based on a stable system inversion result in input trajectories with pre and or post actuation intervals the presented approach treats the considered transition task as a two point boundary value problem bvp and yields causal feedforward trajectories which are constant outside the transition interval the main idea of this approach is to provide free parameters in the desired output trajectory to solve the bvp of the internal dynamics thereby a standard matlab function can be used for the numerical solution of the bvp feedforward control design techniques are illustrated by simulation results for a simple example

tracking nonlinear non minimum phase systems using sliding control nonlinear systems affine in the input and having a well defined vector relative degree are considered the invertibility of the input output dynamics can be used to achieve tracking of smooth desired trajectories if the associated zero dynamics are stable we consider tracking in nonlinear systems with unacceptable zero dynamics i e non minimum phase systems the desired trajectories are assumed to be generated by some exosystem we use sliding control to achieve tracking independent of disturbances entering in the channels of the input the main idea is i to do an output redefinition such that the zero dynamics with respect to this new output are acceptable ii to define a modified desired trajectory for the new output to track such that in the process the original output tracks the original desired trajectory asymptotically

on the growth of torsion in the cohomology of arithmetic groups in this paper we consider certain families of arithmetic subgroups of mathrm so 0 p q and mathrm sl 3 mathbb r respectively we study the cohomology of such arithmetic groups with coefficients in arithmetically defined modules we show that for natural sequences of such modules the torsion in the cohomology grows exponentially

lee distance and topological properties of k ary n cubes in this paper we consider various topological properties of a k ary n cube q sub n sup k using lee distance we feel that lee distance is a natural metric for defining and studying a q sub n sup k after defining a q sub n sup k graph using lee distance we show how to find all disjoint paths between any two nodes given a sequence of radix k numbers a function mapping the sequence to a gray code sequence is presented and this function is used to generate a hamiltonian cycle embedding the graph of a mesh and the graph of a binary hypercube into the graph of a q sub n sup k is considered using a k ary gray code we show the embedding of a k n sub 1 spl times k n sub 2 spl times spl times k n sub m dimensional mesh into a q sub n sup k where n spl sigma sub i l sup m n sub i then using a single digit 4 ary reflective gray code we demonstrate embedding a q sub n into q sub n 2 sup 4 we look at how lee distance may be applied to the problem of resource placement in a q sub n sup k by using a lee distance error correcting code although the results in this paper are only preliminary lee distance error correcting codes have not been applied previously to this problem finally we consider how lee distance can be applied to message routing and single node broadcasting in a q sub n sup k in this section we present two single node broadcasting algorithms that are optimal when single port and multi port i o is used

path embedding in star graphs abstract the star graph interconnection network has been introduced as an attractive alternative to the hypercube network in this paper we consider the path embedding problem in star graphs assume that n 4 we prove that paths of all even lengths from d x y to n 2 can be embedded between two arbitrary vertices x and y from the same partite set in the n dimensional star graph in addition paths of all odd lengths from d x y to n 1 can be embedded between two arbitrary vertices x and y from different partite sets in the n dimensional star graph except that if x and y are adjacent there is no path of length 3 between them the result is optimal in the sense that paths of all possible lengths are found in star graphs

hamiltonian path embedding and pancyclicity on the mobius cube with faulty nodes and faulty edges a graph g v e is said to be pancyclic if it contains fault free cycles of all lengths from 4 to v in g let f sub v and f sub e be the sets of faulty nodes and faulty edges of an n dimensional mobius cube mq sub n respectively and let f f sub v spl cup f sub e a faulty graph is pancyclic if it contains fault free cycles of all lengths from 4 to v f sub v in this paper we show that mq sub n f contains a fault free hamiltonian path when f spl les n 1 and n spl ges 1 we also show that mq sub n f is pancyclic when f spl les n 2 and n spl ges 2 since mq sub n is regular of degree n both results are optimal in the worst case

embedding two edge disjoint hamiltonian cycles into locally twisted cubes the n dimensional hypercube network q n is one of the most popular interconnection networks since it has simple structure and is easy to implement the n dimensional locally twisted cube ltq n an important variation of the hypercube has the same number of nodes and the same number of connections per node as q n one advantage of ltq n is that the diameter is only about half of the diameter of q n recently some interesting properties of ltq n have been investigated in the literature the presence of edge disjoint hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the interconnection network the existence of two edge disjoint hamiltonian cycles in locally twisted cubes has remained unknown in this paper we prove that the locally twisted cube ltq n with n 4 contains two edge disjoint hamiltonian cycles based on the proof of existence we further provide an o n2 n linear time algorithm to construct two edge disjoint hamiltonian cycles in an n dimensional locally twisted cube ltq n with n 4 where ltq n contains 2 n nodes and n2 n 1 edges

brief paper on the equivalence between stable inversion for nonminimum phase systems and reciprocal transfer functions defined by the two sided laplace transform in this paper the two sided laplace transform a classical but not very common mathematical tool is revived to express the stable inversion for linear nonminimum phase systems that was recently proposed from the viewpoint of state space representations it is demonstrated that those two different expressions for the stable inversion are mathematically equivalent simple examples are presented to illustrate the two sided laplace transform as a direct and intuitive approach to stable inversion the two sided laplace transform approach is also applied to the development of an iterative learning control for nonminimum phase systems that needs neither a precise inversion model nor fourier transform computations but instead requires only measuring the system response with time reversals

adaptive neural control of mimo nonlinear systems with a block triangular pure feedback control structure this paper presents adaptive neural tracking control for a class of uncertain multi input multi output mimo nonlinear systems in block triangular form all subsystems within these mimo nonlinear systems are of completely nonaffine purefeedback form and allowed to have different orders to deal with the nonaffine appearance of the control variables the mean value theorem mvt is employed to transform the systems into a block triangular strict feedback form with control coefficients being couplings among various inputs and outputs a systematic procedure is proposed for the design of a new singularityfree adaptive neural tracking control strategy such a design procedure can remove the couplings among subsystems and hence avoids the possible circular control construction problem as a consequence all the signals in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded sguub moreover the outputs of the systems are ensured to converge to a small neighborhood of the desired trajectories simulation studies verify the theoretical findings revealed in this work

embedding of tori and grids into twisted cubes the hypercube is one of the most popular interconnection networks since it has a simple structure and is easy to implement an n dimensional twisted cube tq n is an important variation of hypercube q n and preserves many of its desirable properties the problem of how to embed a family of disjoint meshes or tori into a host graph has attracted great attention in recent years however there is no systematic method proposed to generate the desired meshes and tori in tq n in this paper we develop two systematic linear time algorithms for embedding disjoint multi dimensional tori into tq n n 7 as follows 1 for a positive integer m with email protected email protected email protected n 4 a family of 2 m disjoint k dimensional tori of size 2 s 1x2 s 2x x2 s k each can be embedded with unit dilation where k 2 and i 1 ks email protected n m and 2 for a positive integer m with email protected email protected n 5 a family of 2 m disjoint k dimensional tori of size 2 s 1x2 s 2x x2 s k each can be embedded with unit dilation where k 2 s i 2 i 1 ks email protected n m and max 1 i k s i n 2m moreover we also provide similar embedding results for meshes and hypercubes our results mean that a family of torus structured mesh structured or hypercube structured parallel algorithms can be executed on the same twisted cube efficiently and in parallel

brief paper inversion of sampled data system approximates the continuous time counterpart in a noncausal framework although correspondence between the poles of a continuous time and sampled data system with a piecewise constant input is simple and desirable from the stability viewpoint the relationship between zeros is intricate inversion of a sampled data system is mostly unstable irrespective of the stability of the continuous time counterpart this makes it difficult to apply inversion based control techniques such as perfect tracking transient response shaping or iterative learning control to sampled data systems although recently developed noncausal inversion techniques help us to circumvent unboundedness of the inversion caused by unstable zeros whether the inversion of sampled data systems approximates the continuous time counterpart or not as the sample period is shortened is still to be determined this article gives a positive conclusion to this problem

embedding meshes into crossed cubes crossed cubes are important variants of hypercubes in this paper we consider embeddings of meshes in crossed cubes the major research findings in this paper are 1 for any integer n 1 a 2x2 n 1 mesh can be embedded in the n dimensional crossed cube with dilation 1 and expansion 1 2 for any integer n 4 two node disjoint 4x2 n 3 meshes can be embedded in the n dimensional crossed cube with dilation 1 and expansion 2 the obtained results are optimal in the sense that the dilations of the embeddings are 1 the embedding of the 2x2 n 1 mesh is also optimal in terms of expansion because it has the smallest expansion 1

stable inversion and parameter variations abstract as part of the process of automatically guiding an aircraft we have been successful in using stable inversion to compute a desired bounded state trajectory and corresponding bounded control in addition to this feedforward control we must also construct a regulator to address modeling errors and disturbances with respect to modeling errors we find that the stable inversion procedures used are so accurate that the regulator can assume a simple form say a linear regulator about the desired trajectory we show that under the appropriate assumptions the bounded state trajectory and bounded control computed through stable inversion depend continuously on the parameters of the system this is a consequence of a mathematical result that we prove about the continuous dependence of the particular solution of a time varying nonlinear system driven by a bounded input this is distinct from the usual continuous dependence of the initial value problem for systems

cycle embedding in star graphs with conditional edge faults among the various interconnection networks the star graph has been an attractive one in this paper we consider the cycle embedding problem in star graphs with conditional edge faults we show that there exist cycles of all even lengths from 6 to n in an n dimensional star graph with 4

on torsion in the cohomology of locally symmetric varieties the main result of this paper is the existence of galois representations associated with the mod p or mod p m cohomology of the locally symmetric spaces for gln over a totally real or cm eld proving conjectures of ash and others following an old suggestion of clozel recently realized by harris lan taylor thorne for characteristic 0 cohomology classes one realizes the cohomology of the locally symmetric spaces for gln as a boundary contribution of the cohomology of symplectic or unitary shimura varieties so that the key problem is to understand torsion in the cohomology of shimura varieties thus we prove new results on the p adic geometry of shimura varieties of hodge type namely the shimura varieties become perfectoid when passing to the inverse limit over all levels at p and a new period map towards the ag variety exists on them called the hodge tate period map it is roughly analogous to the embedding of the hermitian symmetric domain which is roughly the inverse limit over all levels of the complex points of the shimura variety into its compact dual the hodge tate period map has several favorable properties the most important being that it commutes with the hecke operators away from p for the trivial action of these hecke operators on the ag variety and that automorphic vector bundles come via pullback from the ag variety

torsion homology of arithmetic lattices and k_2 of imaginary fields let be a symmetric space of noncompact type a result of gelander provides exponential upper bounds in terms of the volume for the torsion homology of the noncompact arithmetic locally symmetric spaces we show that under suitable assumptions on this result can be extended to the case of nonuniform arithmetic lattices that may contain torsion using recent work of calegari and venkatesh we deduce from this upper bounds in terms of the discriminant for of the ring of integers of totally imaginary number fields more generally we obtain such bounds for rings of integers in f

bipanconnectivity of balanced hypercubes the balanced hypercube proposed by wu and huang is a variant of the hypercube network in this paper paths of various lengths are embedded into balanced hypercubes a bipartite graph g is bipanconnected if for two arbitrary nodes x and y of g with distance d x y there exists a path of length l between x and y for every integer l with d x y l v g 1 and l d x y 0 mod 2 we prove that the n dimensional balanced hypercube bh n is bipanconnected for all n 1 this result is stronger than that obtained by xu et al which shows that the balanced hypercube is edge bipancyclic and hamiltonian laceable

on a nonlinear multivariable servomechanism problem abstract multivariable nonlinear plants with both measured and unmeasured vector disturbance signals are considered output feedback dynamic control laws are designed for the problem of tracking a constant or slowly varying reference input while rejecting constant or slowly varying disturbances

frequency domain computations for nonlinear steady state solutions steady state analysis and fourier analysis play a major role in linear signal processing in response to a bounded input a steady state solution exists if all the poles of the discrete time linear system are inside the unit circle despite the fact that there is no principle of superposition for nonlinear systems under appropriate sufficient conditions including all poles inside the unit circle for the linear part of the nonlinear system there is a bounded solution for all time in response to a bounded input for all time for a time varying nonlinear difference equation all solutions that start sufficiently close to this unique solution converge to it as time goes to infinity this steady state solution can be computed by applying fourier and inverse fourier transforms to each step in a picard process in this paper we develop an algorithm to compute approximate steady state solutions for discrete time nonlinear difference equations by employing fast fourier transforms and inverse fast fourier transforms at each step of the iterative process simulations are provided to illustrate our algorithm

analytic torsion of complete hyperbolic manifolds of finite volume abstract in this paper we define the analytic torsion for a complete oriented hyperbolic manifold of finite volume it depends on a representation of the fundamental group for manifolds of odd dimension we study the asymptotic behavior of the analytic torsion with respect to certain sequences of representations obtained by restriction of irreducible representations of the group of isometries of the hyperbolic space to the fundamental group

inversion of nonlinear time varying systems a procedure for inverting nonlinear systems that presents some computational advantages when applied to flexible robot arms or more generally to mechanical structures is given the procedure is presented in a general setting for nonlinear time varying systems an iterative algorithm that computes a smooth controlled invariant time varying manifold the mathematical properties of which are illustrated and exploited is also proposed an application to a flexible two link manipulator illustrates the algorithm and its computational advantages

stable inversion for nonlinear systems abstract there have been two recent major developments in output tracking for nonlinear systems and our first main contribution is to relate these under appropriate assumptions we show that the bounded solution of the partial differential equation of isidori and byrnes for each trajectory of an exosystem must be given by an integral representation formula of devasia chen and paden under restrictive hypotheses devasia chen and paden develop a picard process that converges to the solution of the integral equation this solution to the integral equation is also a bounded solution to a dynamical equation driven by the desired outputs in aircraft applications our nonlinear systems are perturbations of pure feedback systems with outputs and we find a solution to the stable inversion problem i e finding bounded controls and bounded state trajectories in response to bounded output signals in two steps the first step ignores the perturbation error and computes the major part of the desired control and corresponding state trajectory the second step computes the remaining control and states by finding a noncausal and stable solution to an error driven dynamical equation in other words the method of devasia chen and paden is applied to an error system and not to the full system this two step procedure is the second main contribution of this paper throughout this paper it is assumed that our nonlinear systems have vector relative degree

on embedding cycles into faulty twisted cubes the twisted cube tq n is an alternative to the popular hypercube network recently some interesting properties of tq n were investigated in this paper we study the pancycle problem on faulty twisted cubes let f e and f v be the numbers of faulty edges and faulty vertices in tq n respectively we show that with f e f v 3

paths and cycles identifying vertices in twisted cubes the hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement the twisted cube is an important variation of the hypercube and preserves many of its desirable properties karpovsky et al introduced the concept of identifying codes to model fault detection in multiprocessor systems and honkala et al developed an identifying code by using cycles to identify the faulty processors in the hypercube in this paper we study the vertex identification problem on the twisted cube we first propose an interesting construction scheme to build paths and cycles and furthermore apply a minimum number of paths and cycles to identify the faulty processors of the twisted cube

rvccc a new variational network of cube connected cycles and its topological properties abstract the ccc r n network is an extension of the hypercube which replaces each vertex with a cycle of length n providing that the hypercube is r dimensional when n r the ccc r n network contains more vertices than that of ccc r r which makes it more useful in the construction of a large scale interconnection network however the ccc r n is irregular when n r which makes their properties difficult to be analyzed in this paper we propose a new variational network of the cube connected cycles rvccc the rvccc networks have the properties of regularity vertex symmetry and low diameter compared with the general ccc networks the rvccc networks are more suitable for constructing a large scale interconnection network after the shortest internode distance between any two vertices in the rvccc was determined the exact diameter of this network was calculated and the communication algorithms including the routing algorithm and the broadcasting algorithm were also developed

embedding of meshes in mobius cubes the hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement mobius cubes form a class of hypercube variants that give better performance with the same number of edges and vertices in this paper we consider embedding of meshes in mobius cubes the main results obtained in this paper are 1 for n 1 there exists a 2x2 n 1 mesh that can be embedded in the n dimensional mobius cube with dilation 1 and expansion 1 2 for n 4 there exists a 4x2 n 2 mesh that can be embedded in the n dimensional mobius cube with dilation 2 and expansion 1 3 for n 4 there are two disjoint 4x2 n 3 meshes that can be embedded in the 0 type n dimensional mobius cube with dilation 1 4 for n 4 there are two disjoint 4x2 n 3 meshes that can be embedded in the 1 type n dimensional mobius cube with dilation 2 results of 1 and 3 are optimal in the sense that the dilations of the embeddings are 1

on the torsion in the cohomology of arithmetic hyperbolic 3 manifolds in this paper we consider the cohomology of a closed arithmetic hyperbolic 3 manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of sl 2 c the cohomology is defined over the integers and is a finite abelian group we show that the order of the 2nd cohomology grows exponentially as the local system grows we also consider the twisted ruelle zeta function of a closed arithmetic hyperbolic 3 manifold and we express the leading coefficient of its laurent expansion at the origin in terms of the orders of the torsion subgroups of the cohomology

geodesic pancyclicity of twisted cubes the hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement an n dimensional twisted cube tq n is an important variation of the hypercube q n and preserves many of its desirable properties the problem of embedding linear arrays and cycles into a host graph has attracted substantial attention in recent years the geodesic cycle embedding problem is for any two distinct vertices to find all the possible lengths of cycles that include a shortest path joining them in this paper we prove that tq n is geodesic 2 pancyclic for each odd integer n 3 this result implies that tq n is edge pancyclic for each odd integer n 3 moreover tq nxk 2 is also demonstrated to be geodesic 4 pancyclic

dvcube a novel compound architecture of disc ring graph and hypercube like graph in this paper we first introduce a family of interconnection network topologies named disc ring graphs disc ring graphs possess many desirable topological properties in building parallel machines such as fixed degree small diameter hamiltonian decomposition etc we first examine the topological properties of disc ring graphs and give an efficient routing algorithm for disc ring graphs we then bring forward a novel interconnection network of dqcube which is a compound graph of disc ring graph and hypercube that is it uses the hypercube as a unit cluster and connects many such clusters by means of a disc ring graph at the cost that only one additional link is added to any node in each hypercube the topological benefits of both basic graphs are preserved in the compound network it utilizes the topological properties of hypercube to conveniently embed parallel algorithms into each cluster and the short diameter of disc ring graph to support an efficient inter cluster communication the proposed methodologies for dqcube are further applied to many other compound graphs of disc ring graph and hypercube like graphs including locally twisted cube twisted cube crossed cube and mobius cube with diameter being a half of that of hypercube we also give and analyze an efficient routing algorithm for the proposed compound networks in this article

output regulation of non linear systems with more inputs than outputs abstract the necessary and sufficient conditions for the existence of a solution of the non linear regulator problem given by isidori and byrnes 1990 for square systems are extended to the case of systems with more inputs than outputs some examples that stress specific aspects of the solution of the nonlinear regulator problem are given

guaranteed performance in semi global trajectory tracking for matched disturbance nonlinear systems in this article we present a semi global trajectory tracking approach that guarantees a priori computable l 2 and l performance bounds for matched disturbance control affine systems the proposed controller is derived by combining a standard inverse control technique with an extended nonlinear robust state feedback the latter is based on a control lyapunov function used for stabilising one operating point inside the considered state space a difference gradient formulation of this lyapunov function is then applied to prove stabilisation along any trajectory in the considered state space results for l 2 and l bounded disturbances will be presented and further extended to the case of actuator uncertainties and disturbance offsets the theoretical contributions are verified applying them to a numerical example

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

restricted connectivity for three families of interconnection networks vertex connectivity and edge connectivity are two important parameters in interconnection networks even though they reflect the fault tolerance correctly they undervalue the resilience of large networks by the concept of conditional connectivity and super connectivity the concept of restricted vertex connectivity and restricted edge connectivity of graphs was proposed by esfahanian a h esfahanian generalized measures of fault tolerance with application to n cube networks ieee transactions on computers 38 1989 1586 1591 such measures take the resilience of large networks into consideration in this paper we propose three families of interconnection networks and discuss their restricted vertex connectivity and restricted edge connectivity in particular the hypercubes twisted cubes crossed cubes mobius cubes star graphs pancake graphs recursive circulant graphs and k ary n cubes are special cases of these families

brief parameter variations relative degree and stable inversion motivated by our prior research on automatic aircraft guidance we address stable inversion for output tracking and prove that this process is continuous with respect to parameter variations even when these variations cause a change in relative degree our earlier simulations indicated that the stable inversion process is extremely accurate and that only a linear regulator about the desired trajectory is required in the face of reasonable modeling error the principal novelty in our technique is that a differential equations point of view is taken as opposed to a state space approach on the driven zero dynamics of the system this is the situation that arises in many applications and it also enables handling the question of changes in relative degree without having to be encumbered by the change in state space dimension as the parameters change linear systems are first studied since the corresponding result is unknown next a corresponding theorem for nonlinear systems proved by using the picard process in conjunction with the result for the linear case the principal contribution of this paper is a result concerning the continuous dependence of a generalized steady state solution of nonlinear driven differential equations with respect to parameter variations which cause the order of the differential equation to change since the notion of steady state is of paramount importance to innumerable engineering situations the contents of this paper have wider scope

embedding meshes into twisted cubes the n dimensional twisted cube tn n is a variation of the hypercube in this paper we study embedding of meshes into tn n we prove three major results in this paper 1 for any integer n 1 a 2x2 n 1 mesh can be embedded into tn n with dilation 1 and expansion 1 2 for any integer n 4 an mxk m 3 k 3 mesh cannot be embedded into tn n with dilation 1 3 for any integer n 4 two node disjoint 4x2 n 3 meshes can be embedded into tn n with dilation 2 and expansion 1

nonlinear observers for two classesof perturbed systems in this paper we study two important classes of nonlinear systems with perturbation namely perturbation with output injection and perturbation of pure feedback systems with sufficiently good initial error estimates and sufficiently restricted external inputs and perturbation parameter nonlinear observers for each class of perturbed systems are designed so that the error between the exact states and the estimated states goes to zero our simulation results illustrate the applicability of our technique in building nonlinear observers for these two classes of perturbed systems

a fast diagnosis algorithm for locally twisted cube multiprocessor systems under the mm model comparison based diagnosis is a practical approach to the system level fault diagnosis of multiprocessors the locally twisted cube is a newly introduced hypercube variant which not only possesses lower diameter and better graph embedding capability as compared with a hypercube of the same size but retains some nice properties of hypercubes this paper addresses the fault diagnosis of locally twisted cubes under the mm comparison model by utilizing the existence of abundant cycles within a locally twisted cube we present a new diagnosis algorithm with elaborately organized data this algorithm can run in o nlog 2 2n time where n stands for the total number of nodes in comparison the classical sengupta dahbura diagnosis algorithm takes as much as o n 5 time to achieve the same goal as a consequence the proposed algorithm is remarkably superior to the sengupta dahbura algorithm in terms of the time overhead

the torsion in symmetric powers on congruence subgroups of bianchi groups in this paper we prove that for a fixed neat principal congruence subgroup of a bianchi group the order of the torsion part of its second cohomology group with coefficients in an integral lattice associated to the m th symmetric power of the standard representation of sl 2 c grows exponentially in m 2 we give upper and lower bounds for the growth rate our result extends a a result of w muller and s marshall who proved the corresponding statement for closed arithmetic 3 manifolds to the finite volume case we also prove a limit multiplicity formula for combinatorial reidemeister torsions on higher dimensional hyperbolic manifolds

the g good neighbor conditional diagnosability of hypercube under pmc model abstract processor fault diagnosis plays an important role in multiprocessor systems for reliable computing and the diagnosability of many well known networks has been explored for example hypercubes crossed cubes mobius cubes and twisted cubes of dimension n all have diagnosability n the conditional diagnosability of n dimensional hypercube q n is proved to be 4 n 2 1 under the pmc model in this paper we study the g good neighbor conditional diagnosability of q n under the pmc model and show that it is 2 g n g 2 g 1 for 0 g n 3 the g good neighbor conditional diagnosability of q n is several times larger than the classical diagnosability

optimal inversion based control for the set point regulation of nonminimum phase uncertain scalar systems we propose an optimal inversion based control for the set point constrained regulation of nonminimum phase uncertain scalar systems this approach is based on a new control architecture where the main purpose of the feedback is to reduce the sensitivity to parametric plant uncertainties permitting in such a way the effective use of a feedforward action determined via a stable dynamic inversion essential constituents of the architecture are a parameterized family of transition polynomials to shape ideal output transfers and a parameterized controller ensuring the internal model principle the methodology is then centered on the optimal combined design of the feedback controller and of the inversion based command signal in order to minimize the worst case settling time subject to an amplitude constraint on the control variable and to arbitrarily assigned overshoot and undershoot bounds finally an approximate or suboptimal solution to the resulting nonlinear optimization problem can be obtained by genetic algorithms a worked example highlights the effectiveness of the overall methodology

brief optimal noncausal set point regulation of scalar systems this paper presents a novel system inversion approach to the set point regulation of linear scalar minimum phase systems this approach uses closed form expressions of cause effect pairs that make possible an arbitrarily smooth transition between two given output set points the cause effect pairs are based on the introduced concept of transition polynomials simple optimization procedures are then proposed to solve the relevant optimal output synthesis and optimal input synthesis the potentiality of the method is highlighted by the examples presented namely a synthesis of elevator velocity profiles and the performance improving of a pid controller

a canonical expansion for nonlinear systems the importance of differential geometry in particular lie brackets of vector fields in the study of nonlinear systems is well established under very mild assumptions we show that a real analytic nonlinear system has an expansion in which the coefficients are computed in terms of lie brackets this expansion occurs in a special coordinate system we also explain the concept of a pure feedback system for control design involving a nonlinear system one approach is to put the system in its canonical expansion and approximate by that part having only feedback paths

constructing edge disjoint spanning trees in twisted cubes the use of edge disjoint spanning trees or independent spanning trees in a network for data broadcasting has the benefits of increased of bandwidth and fault tolerance in this paper we propose an algorithm which constructs n edge disjoint spanning trees in the n dimensional twisted cube denoted by tq n because the n dimensional twisted cube is n regular the result is optimal with respect to the number of edge disjoint spanning trees constructed furthermore we also show that n2 of the n edge disjoint spanning trees constructed are independent spanning trees this algorithm runs in time o nlogn and can be parallelized to run in time o logn where n is the number of nodes in tq n

on normal forms of nonlinear systems affine in control the nonlinear equivalences of both finite and infinite zero structures of linear systems have been well understood for single input single output systems and have found many applications in nonlinear control theory the extensions of these notions to multiple input multiple output systems have proven to be highly sophisticated in this paper we propose constructive algorithms for decomposing a nonlinear system that is affine in control these algorithms require modest assumptions on the system and apply to general multiple input multiple output systems that do not necessarily have the same number of inputs and outputs they lead to various normal form representations and reveal the structure at infinity the zero dynamics and the invertibility properties all of which represent nonlinear equivalences of relevant linear system structural properties

a new approach to the zero dynamics assignment problem for nonlinear discrete time systems using functional equations the present research work aims at the development of a systematic method to arbitrarily assign the zero dynamics of a nonlinear discrete time real analytic system by constructing the requisite synthetic output maps the problem under consideration is motivated by the need to adequately address the control problem of nonminimum phase nonlinear discrete time systems since the latter represent a rather broad class of systems due to the well known effect of sampling on the stability of zero dynamics in the proposed approach the above control objective can be attained through i a systematic computation of synthetic output maps that induce minimum phase behavior while being statically equivalent to the original output maps both vanish on the equilibrium manifold and ii the subsequent integration into the methodological framework of currently available nonminimum phase compensation schemes for nonlinear discrete time systems that rely on output redefinition the mathematical formulation of the zero dynamics assignment problem is realized via a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived the solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a solution method that is easily programmable with the aid of a symbolic software package the synthetic output maps that induce the prescribed zero dynamics for the original nonlinear discrete time system can be explicitly computed on the basis of the solution to the aforementioned system of functional equations

the diagnosability of the matching composition network under the comparison diagnosis model the classical problem of diagnosability is discussed widely and the diagnosability of many well known networks has been explored we consider the diagnosability of a family of networks called the matching composition network mcn a perfect matching connects two components the diagnosability of mcn under the comparison model is shown to be one larger than that of the component provided some connectivity constraints are satisfied applying our result the diagnosability of the hypercube qn the crossed cube cq sub n the twisted cube tq sub n and the mobius cube mq sub n can all proven to be n for n spl ges 4 in particular we show that the diagnosability of the four dimensional hypercube q sub 4 is 4 which is not previously known

flexible cycle embedding in the locally twisted cube with nodes positioned at any prescribed distance abstract a hamiltonian graph g is panpositionably hamiltonian if for any two distinct vertices x and y of g it contains a hamiltonian cycle c such that d c x y l for any integer l satisfying d g x y l v g 2 where d g x y respectively d c x y denotes the distance between vertices x and y in g respectively on c and v g is the total number of vertices in g as the importance of hamiltonian properties for data communication between units in parallel and distributed systems the panpositionable hamiltonicity involves more flexible cycle embedding for message transmission this paper shows that for two arbitrary nodes x and y of the n dimensional locally twisted cube ltq n n 4 and for any integer l d d 2 d 3 d 4 2 n 1 where d d ltq n x y there exists a hamiltonian cycle c of ltq n such that d c x y l

edge disjoint hamiltonian cycles in k ary n cubes and hypercubes solutions for decomposing a higher dimensional torus to edge disjoint lower dimensional tori in particular edge disjoint hamiltonian cycles are obtained based on the coding theory approach first lee distance gray codes in z sub k sup n are presented and then it is shown how these codes can directly be used to generate edge disjoint hamiltonian cycles in k ary n cubes further some new classes of binary gray codes are designed from these lee distance gray codes and using these new classes of binary gray codes edge disjoint hamiltonian cycles in hypercubes are generated

exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds for d 2n 1 a positive odd integer we consider sequences of arithmetic subgroups of text so 0 d 1 and yielding corresponding hyperbolic manifolds of finite volume and show that under appropriate and natural assumptions the torsion of the associated cohomology groups grows exponentially

embedding meshes into locally twisted cubes as a newly introduced interconnection network for parallel computing the locally twisted cube possesses many desirable properties in this paper mesh embeddings in locally twisted cubes are studied let ltq n v e denote the n dimensional locally twisted cube we present three major results in this paper 1 for any integer n 1 a 2x2 n 1 mesh can be embedded in ltq n with dilation 1 and expansion 1 2 for any integer n 4 two node disjoint 4x2 n 3 meshes can be embedded in ltq n with dilation 1 and expansion 2 3 for any integer n 3 a 4 x 2 n 2 1 mesh can be embedded in ltq n with dilation 2 the first two results are optimal in the sense that the dilations of all embeddings are 1 the embedding of the 2x2 n 1 mesh is also optimal in terms of expansion we also present the analysis of 2px2q mesh embedding in locally twisted cubes

complete path embeddings in crossed cubes crossed cubes are popular variants of hypercubes in this paper we study path embeddings between any two distinct nodes in crossed cubes we prove two important results in the n dimensional crossed cube a for any two nodes all paths whose lengths are greater than or equal to the distance between the two nodes plus 2 can be embedded between the two nodes with dilation 1 b for any two integers n 2 and l with 1

k restricted edge connectivity for some interconnection networks abstract k restricted edge connectivity is an important parameter in measuring the reliability and fault tolerance of large interconnection networks in this paper we present two families of graphs similar with the networks proposed by chen et al y c chen j j m tan l h hsu s s kao super connectivity and super edge connectivity for some interconnection networks applied mathematics and computation 140 2003 245 254 and study the k k 2 3 restricted edge connectivity of these graphs in particular as the applications of our results the k k 2 3 restricted edge connectivity of the recursive circulant graphs and the n ary k cubes is given

approximation of trajectories of non linear systems by iterates of systems with linear state dynamics abstract a modification of an iterative picard process is proposed to approximate the output of a non linear system by a concatenation of systems with linear state dynamics and non linear outputs a local uniform convergence result is given the motivating example is a non linear system that arises in surface plasmon resonance experiments to determine protein protein interaction constants we show with simulations that for this example the approximants converge not only locally but over the full time interval of interest in the application

the analytic torsion and its asymptotic behaviour for sequences of hyperbolic manifolds of finite volume abstract in this paper we study the regularized analytic torsion of finite volume hyperbolic manifolds we consider sequences of coverings x i of a fixed hyperbolic orbifold x 0 our main result is that for certain sequences of coverings and strongly acyclic flat bundles the analytic torsion divided by the index of the covering converges to the l 2 torsion our results apply to certain sequences of arithmetic groups in particular to sequences of principal congruence subgroups of so 0 d 1 z and to sequences of principal congruence subgroups or hecke subgroups of bianchi groups

on the construction of all shortest vertex disjoint paths in cayley graphs of abelian groups cayley graphs provide a group theoretic model for designing and analyzing symmetric interconnection networks in this paper we give a sufficient condition for the existence of m vertex disjoint shortest paths from one source vertex to other m not necessarily distinct destination vertices in a cayley graph of an abelian group where m n and n is the cardinality of a group generator of the abelian group in addition when the condition holds the m vertex disjoint shortest paths can be constructed in o m n time which is optimal in the worst case when o n the order of diameter by applying our results we can easily obtain the necessary and sufficient conditions which can be verified in nearly optimal time for the existence of all shortest vertex disjoint paths in generalized hypercubes and odd tori in the situation that all of the source vertex and destination vertices are mutually distinct brute force computations show that the probability of the existence of the m vertex disjoint shortest paths in an r dimensional generalized hypercube with r coordinates each of order k is greater than 94 70 96 99 and 99 for k r m 2 7 7 3 4 8 4 3 6 5 3 6 and 6 3 6 respectively

should model based inverse inputs be used as feedforward under plant uncertainty bounds on the size of the plant uncertainties are found such that the use of the inversion based feedforward input improves the output tracking performance when compared to the use of feedback alone the output tracking error is normalized by the size of the desired output and used as a measure of the output tracking performance the worst case performance is compared for two cases 1 with the use of feedback alone and 2 with the addition of the feedforward input it is shown that inversion based feedforward controllers can lead to performance improvements at frequencies w where the uncertainty spl delta jw in the nominal plant is smaller than the size of the nominal plant g sub 0 jw divided by its condition number k sub g0 jw i e spl par spl delta jw spl par sub 2 spl par g sub 0 jw spl par sub 2 k sub g0 jw a modified feedforward input is proposed that only uses the model information in frequency regions where plant uncertainty is sufficiently small the use of this modified inverse with any feedback results in improvement of the output tracking performance when compared to the use of the feedback alone

vertex bipancyclicity of the generalized honeycomb tori assume that m n and s are integers with m 2 n 4 email protected s 6 and is even besides ght m n s is vertex bipancyclic in some special cases the result is optimal in the sense that the absence of cycles of certain lengths on some ght m n s s is inevitable due to their hexagonal structure

stable inversion for nonlinear discrete time systems we solve the exact output tracking problem for square nonlinear discrete time systems through stable inversion this stable inversion problem involves finding a bounded solution of a dynamical system driven by a bounded signal such a solution is given by a difference representation formula whose existence under the proper assumptions can be proven using a picard process

topological properties of twisted cube twisted cube tq n is derived by changing some connections of hypercube q n according to specific rules recently many topological properties of this variation cube are studied in this paper we prove that its connectivity is n its wide diameter and fault diameter are n 2 2 furthermore we show that tq n is a pancyclic network that is cycles of an arbitrary length at least four

edge disjoint hamiltonian cycles in gaussian networks gaussian networks are degree four symmetric networks and these are designed based on the concept of gaussian integers the gaussian network can be described in terms of a generator alpha a bi where a and b are integers and i sqrt 1 when gcd a b 1 how to find edge disjoint hamiltonian cycles has been shown before in this paper for any generator alpha a bi even when gcd a b d 1 how to obtain two edge disjoint hamiltonian cycles in these networks is described

fault free hamiltonian cycles in twisted cubes with conditional link faults the n dimensional twisted cube denoted by tq n a variation of the hypercube possesses some properties superior to the hypercube in this paper assuming that each vertex is incident with at least two fault free links we show that tq n can tolerate up to 2n 5 edge faults while retaining a fault free hamiltonian cycle the result is optimal with respect to the number of edge faults tolerated

adaptive control for a class of uncertain strict feedback nonlinear systems based on a generalized fuzzy hyperbolic model in this study we propose an effective method for designing an adaptive controller for a class of uncertain strict feedback nonlinear systems with unknown bounded disturbances during the controller design process all of the unknown functions are accumulated at the intermediate steps to approximate the last step in addition only one generalized fuzzy hyperbolic model is used to approximate the total unknown functions for the system thus only the actual control law needs to be implemented and one adaptive law is proposed for the overall controller design process as a result the controller design is much simpler and the computational burden is reduced greatly using lyapunov techniques we obtain the uniformly ultimately bounded stability of all the signals for the closed loop system our simulation results verified the theoretical analysis and they illustrated the superior performance of the method proposed in this study

adaptive neural control of high order uncertain nonaffine systems a transformation to affine systems approach abstract this brief investigates the adaptive neural network nn control of a class of high order nonaffine nonlinear systems with completely unknown dynamics since the control terms appear within the unknown nonlinearity traditional control schemes and stability analysis are usually rendered extremely complicated our main contribution includes a novel system transformation that converts the nonaffine system into an affine system through a combination of a low pass filter and state transformation as a result the state feedback control of the nonaffine system can be viewed as the output feedback control of an affine system in normal form the transformed system becomes linear with respect to the new input while the traditional backstepping approach is not needed thus allowing the synthesis to be extremely simplified it is theoretically proven that all the signals in the closed loop system are uniformly ultimately bounded uub simulation results are provided to demonstrate the performance of the developed controller

the strong rainbow connection numbers of cayley graphs on abelian groups a path in an edge colored graph g whose adjacent edges may have the same color is called a rainbow path if no two edges of the path are colored the same the rainbow connection number rc g of g is the minimum integer i for which there exists an i edge coloring of g such that every two distinct vertices of g are connected by a rainbow path the strong rainbow connection number src g of g is the minimum integer i for which there exists an i edge coloring of g such that every two distinct vertices u and v of g are connected by a rainbow path of length d u v in this paper we give upper and lower bounds of the strong rainbow connection numbers of cayley graphs on abelian groups moreover we determine the strong rainbow connection numbers of some special cases

conditional edge fault hamiltonicity of augmented cubes the augmented cube is a variation of hypercubes it possesses many superior properties in this paper we show that for any n dimensional augmented cube n 3 with faulty edges up to 4n 8 in which each vertex is incident to at least two fault free edges there exists a fault free hamiltonian cycle our result is optimal with respect to the number of faulty edges tolerated

hamiltonian properties of honeycomb meshes meshes are widely used topologies for networks on chip noc honeycomb meshes have better topological properties than meshes in order to communicate efficiently in a linear or cyclic manner it is benefited that there is a hamiltonian path or hamiltonian cycle in noc in this paper we give a necessary and sufficient condition for the existence of hamiltonian path between any pair of vertices in a honeycomb mesh and for the existence of hamiltonian path in a honeycomb mesh with one faulty vertex besides we give a systematic method to construct a hamiltonian path in honeycomb meshes

on the growth of l 2 invariants for sequences of lattices in lie groups we study the asymptotic behaviour of betti numbers twisted torsion and other spectral invariants of sequences of locally symmetric spaces our main results are uniform versions of the degeorge wallach theorem of a theorem of delorme and various other limit multiplicity theorems a basic idea is to adapt the notion of benjamini schramm convergence bs convergence originally introduced for sequences of finite graphs of bounded degree to sequences of riemannian manifolds and analyze the possible limits we show that bs convergence of locally symmetric spaces g k implies convergence in an appropriate sense of the normalized relative plancherel measures associated to l2 g this then yields convergence of normalized multiplicities of unitary representations betti numbers and other spectral invariants on the other hand when the corresponding lie group g is simple and of real rank at least two we prove that there is only one possible bs limit i e when the volume tends to infinity locally symmetric spaces always bs converge to their universal cover g k this leads to various general uniform results when restricting to arbitrary sequences of congruence covers of a fixed arithmetic manifold we prove a strong quantitative version of bs convergence which in turn implies upper estimates on the rate of convergence of normalized betti numbers in the spirit of sarnak xue an important role in our approach is played by the notion of invariant random subgroups for higher rank simple lie groups g we exploit rigidity theory and in particular the nevo stuck zimmer theorem and kazhdan s property t to obtain a complete understanding of the space of irs s of g 2017 department of mathematics princeton university

constructing edge disjoint spanning trees in locally twisted cubes the use of edge disjoint spanning trees for data broadcasting and scattering problem in networks provides a number of advantages including the increase of bandwidth and fault tolerance in this paper we present an algorithm for constructing n edge disjoint spanning trees in an n dimensional locally twisted cube since the n dimensional locally twisted cube is regular with the common degree n the number of constructed trees is optimal

generalized hypercubes edge disjoint hamiltonian cycles and gray codes some new classes of hamming metric gray codes over zpn where p is a prime and n is an integer power of 2 are described then how these gray codes can be used to generate the maximum number of edge disjoint hamiltonian cycles in an n dimensional generalized hypercube ghc qpn is shown for qpn the number of edge disjoint hamiltonian cycles generated using these methods is n p 1 2 which is the maximum possible since the degree of each node in qpn is n p 1 in addition for any integers p and n p not necessarily a prime and n not necessarily a power of 2 how to generate the maximum number of edge disjoint hamiltonian cycles in qnp is also described