a modified decomposition abstract the maclaurin series is quite limited in comparison to the adomian series obtained in the decomposition method by adding procedures from the decomposition method and the expansion of nonlinearities using the adomian polynomials as well as a recent result of adomian and rach on transformation of series using the above polynomials the maclaurin series can be made much more useful in its applicability however the convergence is still slower than for adomian s results using decomposition

proper stable bezout factorizations and feedback control of linear time delay systems this paper deals with the existence and construction of proper stable bezout factorizations of transfer function matrices of linear time invariant systems with commensurate time delays existence of factorizations is characterized in terms of spectral controllability or spectral observability of the co canonical or canonical realization of the transfer function matrix an explicit procedure for computing proper stable bezout factorizations is given in terms of a specialized ring of pure and distributed time delays this procedure is utilized to construct finite dimensional stabilizing compensators and to construct feedback systems which assign the characteristic polynomial of the closed loop system

delay independent stability analysis of linear time delay systems based on frequency discretization this paper studies strong delay independent stability of linear time invariant systems it is known that delay independent stability of time delay systems is equivalent to some frequency dependent linear matrix inequalities to reduce or eliminate conservatism of stability criteria the frequency domain is discretized into several sub intervals and piecewise constant lyapunov matrices are employed to analyze the frequency dependent stability condition applying the generalized kalman yakubovich popov lemma new necessary and sufficient criteria are then obtained for strong delay independent stability of systems with a single delay the effectiveness of the proposed method is illustrated by a numerical example

h control via output feedback for state delayed systems a sufficient condition is derived such that the closed loop state delayed system is stable and guarantees a prescribed h norm bound of the closed loop transfer matrix from the disturbance to the controlled output based on this derivation a full order observer based h controller for the stace delayed linear systems is constructed by solving two modified algebraic riccati equations the state feedback h controller for the state delayed linear systems is also obtained by solving a modified algebraic riccati equation an illustrative example is given to show the applicability of the proposed approach

an efficient algorithm for the multivariable adomian polynomials abstract in this article the sum of the series of multivariable adomian polynomials is demonstrated to be identical to a rearrangement of the multivariable taylor expansion of an analytic function of the decomposition series of solutions u 1 u 2 u m about the initial solution components u 1 0 u 2 0 u m 0 of course the multivariable adomian polynomials were developed and are eminently practical for the solution of coupled nonlinear differential equations the index matrices and their simplified forms of the multivariable adomian polynomials are introduced we obtain the recurrence relations for the simplified index matrices which provide a convenient algorithm for rapid generation of the multivariable adomian polynomials another alternative algorithm for term recurrence is established in these algorithms recurrence processes do not require complicated operations such as parametrization expanding and regrouping derivatives etc as practiced in prior art the mathematica program generating the adomian polynomials based on the algorithm in this article is designed

convex separable optimization is not much harder than linear optimization the polynomiality of nonlinear separable convex concave optimization problems on linear constraints with a matrix with small subdeterminants and the polynomiality of such integer problems provided the inteter linear version of such problems ins polynomial is proven this paper presents a general purpose algorithm for converting procedures that solves linear programming problems the conversion is polynomial for constraint matrices with polynomially bounded subdeterminants among the important corollaries of the algorithm is the extension of the polynomial solvability of integer linear programming problems with totally unimodular constraint matrix to integer separable convex programming an algorithm for finding a e accurate optimal continuous solution to the nonlinear problem that is polynomial in log 1 e and the input size and the largest subdeterminant of the constraint matrix is also presented these developments are based on proximity results between the continuous and integral optimal solutions for problems with any nonlinear separable convex objective function the practical feature of our algorithm is that is does not demand an explicit representation of the nonlinear function only a polynomial number of function evaluations on a prespecified grid

on continuous approximate solutions of nonlinear differential equations abstract two recently developed methods for continuous approximate solution of equations involving differential operators the adomian decomposition method and the sarafyan method are compared

observer based h controller design for state delayed linear systems we present two alternative observer based h control design methods for linear dynamic systems with delay in the state based on the riccati equation approach we design observer based feedback control laws that guarantee the asymptotic stability if the closed loop control system and reduce the effect of the disturbance input on the controlled output to a prescribed level

on spl hscr sub spl infin control for dead time systems a mixed sensitivity spl hscr sub spl infin problem is solved for dead time systems it is shown that for a given bound on the spl hscr sub spl infin norm causal stabilizing controllers exist that achieve this bound if and only if a related finite dimensional riccati equation has a solution with a certain nonsingularity property in the case of zero time delay the riccati equation is a standard riccati equation and the nonsingularity condition is that the solution be nonnegative definite for nonzero time delay the nonsingularity condition is more involved but still allows us to obtain controllers all suboptimal controllers are parameterized and the central controller is shown to be a feedback interconnection of a finite dimensional system and a finite memory system both of which can be implemented some spl hscr sub spl infin problems are rewritten as pure rational spl hscr sub spl infin problems using a smith predictor parameterization of the controller

numerical integration analytic continuation and decomposition one step formulas are developed using the decomposition method to explore relationships with numerical integration analytic continuation and numerical continuation analytic continuation in one or multiple dimensions is considered for decomposition solutions and the effects of chaos

a polynomial time algorithm for computing an arrow debreu market equilibrium for linear utilities we provide the first polynomial time exact algorithm for computing an arrow debreu market equilibrium for the case of linear utilities our algorithm is based on solving a convex program using the ellipsoid algorithm and simultaneous diophantine approximation as a side result we prove that the set of assignments at equilibrium is convex and the equilibrium prices themselves are log convex our convex program is explicit and intuitive which allows maximizing a concave function over the set of equilibria on the practical side ye developed an interior point algorithm lecture notes in comput sci 3521 springer new york 2005 pp 3 5 to find an equilibrium based on our convex program we also derive separate combinatorial characterizations of equilibrium for arrow debreu and fisher cases our convex program can be extended for many nonlinear utilities and production models our paper also makes a powerful theorem theorem 6 4 1 in m grotschel l lovasz and a schrijver geometric algorithms and combinatorial optimization 2nd ed springer verlag berlin heidelberg 1993 even more powerful in theorems 12 and 13 in the area of geometric algorithms and combinatorial optimization the main idea in this generalization is to allow ellipsoids to contain not the whole convex region but a part of it this theorem is of independent interest

a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

brief delay dependent robust h control of uncertain linear state delayed systems this paper examines the problems of robust stabilization and robust h control for linear systems with a constant time delay in the state and subject to parameter uncertainty systems with norm bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers we develop methods of robust stabilization and robust h control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities the proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays

h controller synthesis by j lossless coprime factorization this paper develops a coprime factorization approach to the synthesis of internally stabilizing controllers for a given system such that the mathcal h infty norm of the closed loop is strictly less than a given bound by the use of coprime factorizations it is shown that the mathcal h infty control problem is fundamentally related to the so called analytic systems considered by helton et al regional conference series in mathematics 68 1987 such problems admit a solution if and only if a certain j lossless factorization exists interpreted in the mathcal h infty control context this means that for a controller of the requisite type to exist the plant must admit a certain j lossless coprime factorization the full mathcal h infty synthesis problem requires that two nested j lossless factorizations exist the results are independent of whether discrete time or continuous time systems are being considered it is then shown that j lossless factorization is equivalent to the existen

an innovative eigenvalue problem solver for free vibration of uniform timoshenko beams by using the adomian modified decomposition method this paper deals with free vibration problems of uniform timoshenko beams under various supporting boundary conditions the technique we have used is based on applying the adomian modified decomposition method amdm to our vibration problems doing some simple mathematical operations on the method we can obtain ith natural frequencies and mode shapes one at a time the computed results agree well with those analytical and numerical results given in the literature these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is simpler and more straightforward than the other modal analysis

nonlinear transformation of series part ii abstract this paper generalizes the theorem on transformation of series presented in part i to function of several variables the result is valuable in deriving solutions of coupled ordinary differential equations with general nonlinear coupling terms such as u u w or u 1 u n using the modified decomposition method of the authors

adomian decomposition method for solving the volterra integral form of the lane emden equations with initial values and boundary conditions in this paper we use the systematic adomian decomposition method to handle the integral form of the lane emden equations with initial values and boundary conditions the volterra integral form of the lane emden equation overcomes the singular behavior at the origin x 0 we confirm our belief that the adomian decomposition method provides efficient algorithm for analytic approximate solutions of the equation our results are supported by investigating several numerical examples that include initial value problems and boundary value problems as well finally we consider the modified decomposition method of rach adomian and meyers for the volterra integral form

an iterative algorithm for pole placement by output feedback an iterative algorithm is proposed for solving the pole assignment by output feedback problem for an nth order l input m output linear system the algorithm uses a full rank feedback gain matrix and requires only linear equations of low dimension to be solved at each iteration application of the proposed algorithm allows all n closed loop poles to be almost exactly assigned provided that the iterations converge so that deviations of the resulting closed loop poles from the respective desired values become less than some user specified tolerance and m spl times t spl ges n examples are provided to illustrate the applicability of the proposed method

technical communique output feedback stabilizing controller for time delay systems this paper considers the problem of output feedback stabilization of unstable linear time delay systems the major features of the approach are 1 the delay system is characterized by a fixed transfer function matrix that contains just the set of unstable or marginally unstable modes plus an h norm for the stable part 2 the controller design is accomplished by dynamic output feedback and 3 sufficient conditions in the form of two algebraic riccati equations and an upper bound explicitly characterize a stabilizing controller the method is restricted to delay systems that satisfy an upper bound on the stable part

on an estimate of the decay rate for stable linear delay systems in this paper it is shown that for a certain class of stable linear delay systems we can obtain an estimate of the decay rate of the solution by a simple computation

concave generalized flows with applications to market equilibria we consider a nonlinear extension of the generalized network flow model with the flow leaving an arc being an increasing concave function of the flow entering it as proposed by truemper truemper k 1978 optimal flows in nonlinear gain networks networks 8 1 17 36 and by shigeno shigeno m 2006 maximum network flows with concave gains math programming 107 3 439 459 we give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems finding an e approximate solution in o m m log n log mum e arithmetic operations where m and u are upper bounds on simple parameters and is the complexity of a value oracle query for the gain functions this also gives a new algorithm for linear generalized flows an efficient purely scaling variant of the fat path algorithm by goldberg et al goldberg av plotkin sa tardos e 1991 combinatorial algorithms for the generalized circulation problem math oper res 16 2 351 381 not using any cycle cancellations we sho

the theoretical foundation of the adomian method abstract in this paper we work out the theoretical basis of the adomian method this powerful method that g adomian has developed in the beginning of the 1980 s supplies analytical approximations to the solution of many kinds of equations thanks to our decomposition theory we justify the practical method and we generalize the convergence results obtained by y cherruault afterward we explain how to solve rigorously equations with linear nonlinear or composed operator and also equations with several terms or with a second member

numerical algorithms and decomposition abstract relationships are explored between conventional one step methods a new one step version resulting from a discretized adomian decomposition runge kutta and analytic continuation

market equilibrium via a primal dual algorithm for a convex program we give the first polynomial time algorithm for exactly computing an equilibrium for the linear utilities case of the market model defined by fisher our algorithm uses the primal dual paradigm in the enhanced setting of kkt conditions and convex programs we pinpoint the added difficulty raised by this setting and the manner in which our algorithm circumvents it

market equilibrium under separable piecewise linear concave utilities we consider fisher and arrow debreu markets under additively separable piecewise linear concave utility functions and obtain the following results for both market models if an equilibrium exists there is one that is rational and can be written using polynomially many bits there is no simple necessary and sufficient condition for the existence of an equilibrium the problem of checking for existence of an equilibrium is np complete for both market models the same holds for existence of an e approximate equilibrium for e e o n 5 under standard mild sufficient conditions the problem of finding an exact equilibrium is in ppad for both market models finally building on the techniques of chen et al 2009a we prove that under these sufficient conditions finding an equilibrium for fisher markets is ppad hard

α stability of systems governed by a functional differential equation extension of results concerning linear delay systems abstract theorem 1 stated by mori et al 1982 and discussed by hmamed 1985 and mori 1986 is generalized in this note this theorem is extended to the case of a system governed by a more general functional differential equation theorem 3 claimed by hmamed 1986 is erroneous the correct result is established

on the adomian decomposition method and comparisons with picard s method abstract this paper shows that the adomian decomposition method stochastic systems academic press new york 1983 is not to be identified with any of the earlier methods since it solves a wide class of nonlinear and stochastic equations without the often unphysical assumptions which have become customary similarities between the picard method and the decomposition method are purely superficial

taylor series method for solving a class of nonlinear singular boundary value problems arising in applied science abstract taylor series method is applied to a class of nonlinear singular boundary value problems without requiring any specific technique in handling the singularity at the origin for the problems with exponential nonlinearity a variable transformation is introduced to accelerate the convergence of the solution by converting this exponential nonlinearity into a polynomial nonlinearity the efficiency and applicability of the algorithm are assessed and tested on several problems arising in applied science pade approximants are used to verify that the series solutions to these problems converge within the boundaries an error analysis is presented and the results show that the analytical approximate solutions obtained are highly accurate

a chain scattering matrix description approach to h sup infinity control chain scattering matrix descriptions and j lossless coprime factorizations are employed to develop a relatively simple method for the synthesis of the continuous time h sup infinity suboptimal control analogously to the youla parameterization of all stabilizing controllers the authors derive an identity to generate all suboptimal controllers the derivation is carried out in terms of transfer function matrices although the final formulas are in state space the approach provides a clear connection at the transfer function level between coprime factorizations and algebraic riccati equations that are associated with the solutions of the problem

polynomial methods for separable convex optimization in unimodular linear spaces with applications we consider the problem of minimizing a separable convex objective function over the linear space given by a system mx 0 with m a totally unimodular matrix in particular this generalizes the usual minimum linear cost circulation and cocirculation problems in a network and the problems of determining the euclidean distance from a point to the perfect bipartite matching polytope and the feasible flows polyhedron we first show that the idea of minimum mean cycle canceling originally worked out for linear cost circulations by goldberg and tarjan j assoc comput mach 36 1989 pp 873 886 and extended to some other problems t r ervolina and s t mccormick discrete appl math 46 1993 pp 133 165 a frank and a v karzanov technical report rr 895 m laboratoire artemis imag universite joseph fourier grenoble france 1992 t ibaraki a v karzanov and h nagamochi private communication 1993 m hadjiat technical report groupe intelligence artificielle faculte des sciences de luminy marseille france 1994 can be generalized to give a combinatorial method with geometric convergence for our problem we also generalize the computationally more efficient cancel and tighten method we then consider objective functions that are piecewise linear pure and piecewise quadratic or piecewise mixed linear and quadratic and we show how both methods can be implemented to find exact solutions in polynomial time strongly polynomial in the piecewise linear case these implementations are then further specialized for finding circulations and cocirculations in a network we finish by showing how to extend our methods to find optimal integer solutions to linear spaces of larger fractionality and to the case when the objective functions are given by approximate oracles

solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach adomian meyers modified decomposition method abstract in this paper we present the generalized adomian rach theorem and the generalized rach adomian meyers modified decomposition method for solving multi order nonlinear fractional ordinary differential equations we consider different classes of initial value problems for nonlinear fractional ordinary differential equations including the case of real valued orders and another case of rational valued orders which are solved by the present method this method can treat any analytic nonlinearity the coefficients of the solution in the form of a generalized power series are determined by a convenient recurrence scheme which does not involve integration operations compared with the classic adomian decomposition method

memoryless stabilization of uncertain dynamic delay systems riccati equation approach the authors present a procedure for obtaining the memoryless linear state feedback control of uncertain dynamic delay systems the uncertainties are time varying and within a given compact set this method is an extension of the riccati equation approach proposed by i r petersen and c v hollot 1986 the extension is straightforward also the uncertainties do not need to satisfy the matching conditions

a perfect price discrimination market model with production and a rational convex program for it recent results showing ppad completeness of the problem of computing an equilibrium for fisher s market model under additively separable piecewise linear concave plc utilities have dealt a serious blow to the program of obtaining efficient algorithms for computing equilibria in traditional market models and has prompted a search for alternative models that are realistic as well as amenable to efficient computation in this paper we show that introducing perfect price discrimination into the fisher model with plc utilities renders its equilibrium polynomial time computable moreover its set of equilibria are captured by a convex program that generalizes the classical eisenberg gale program and always admits a rational solution we also give a combinatorial polynomial time algorithm for computing an equilibrium next we introduce production into our model and again give a rational convex program that captures its equilibria we use this program to obtain surprisingly simple proofs of both welfare theorems for this model finally we also give an application of our price discrimination market model to online display advertising marketplaces

technical communique h state feedback control for generalized continuous discrete time delay system in this paper we consider the problem of designing h state feedback controller for the generalized time delay systems with delayed states and control inputs in continuous and discrete time cases respectively the generalized time delay system problems are solved on the basis of linear matrix inequality lmi technique considering time delays the sufficient condition for the existence of controller and h state feedback controller design methods are presented also using some changes of variables and schur complements the obtained sufficient condition can be rewritten as an lmi form in terms of transformed variables the proposed controller design method can be extended into the problem of robust h state feedback controller design method easily

h control of discrete time linear systems with norm bounded uncertainties and time delay in state this paper deals with h control problem for discrete time linear systems with norm bounded uncertainties and time delay in state in terms of a modified riccati inequality for discrete time linear systems a sufficient condition is presented and a state feedback control law is also given the proposed control law is a memoryless state feedback control law

h control of discrete time linear systems with time varying delays in state this paper deals with the h control problems for discrete time linear systems with time varying delays in state in this paper the h control law is assumed to be a memoryless state feedback and the size of time varying delays considered is upper bounded the solution of the h control problem for discrete time linear systems with time varying delays in state can be obtained by solving an h control problem for auxiliary discrete time linear systems with no time delays

recurrence triangle for adomian polynomials in this paper a recurrence technique for calculating adomian polynomials is proposed the convergence of the series for the adomian polynomials is discussed and the dependence of the convergent domain of the solution s decomposition series n 0 u n on the initial component function u 0 is illustrated by introducing the index vectors of the adomian polynomials the recurrence relations of the index vectors are discovered and the recurrence triangle is given the method simplifies the computation of the adomian polynomials in order to obtain a solution s decomposition series with larger domain of convergence we illustrate by examples that the domain of convergence can be changed by choosing a different u 0 and a modified iteration

on polyhedral approximations of the second order cone we demonstrate that a conic quadratic problem is polynomially reducible to linear programming we demonstrate this by constructing for every an lp program explicitly given in terms of e and the data of cqp with the following properties i the number dimx dimu of variables and the number dimp of constraints in lp do not exceed ii every feasible solutionx to cqp can be extended to a feasible solution x u to lp iii if x u is feasible for lp thenx satisfies the e relaxed constraints of cqp namely

new higher order numerical one step methods based on the adomian and the modified decomposition methods abstract we develop new higher order numerical one step methods and apply them to several examples to investigate approximate discrete solutions of nonlinear differential equations these new algorithms are derived from the adomian decomposition method adm and the rach adomian meyers modified decomposition method mdm to present an alternative to such classic schemes as the explicit runge kutta methods for engineering models which require high accuracy with low computational costs for repetitive simulations in contrast to a one size fits all philosophy this new approach incorporates the notion of analytic continuation which extends the region of convergence without resort to other techniques that are also used to accelerate the rate of convergence such as the diagonal pade approximants or the iterated shanks transforms hence global solutions instead of only local solutions are directly realized albeit in a discretized representation we observe that one of the difficulties in applying explicit runge kutta one step methods is that there is no general procedure to generate higher order numeric methods it becomes a time consuming tedious endeavor to generate higher order explicit runge kutta formulas because it is constrained by the traditional picard formalism as used to represent nonlinear differential equations the adm and the mdm rely instead upon adomian s representation and the adomian polynomials to permit a straightforward universal procedure to generate higher order numeric methods at will such as a 12th order or 24th order one step method if need be another key advantage is that we can easily estimate the maximum step size prior to computing data sets representing the discretized solution because we can approximate the radius of convergence from the solution approximants unlike the runge kutta approach with its intrinsic linearization between computed data points we propose new variable step size variable order and variable step size variable order algorithms for automatic step size control to increase the computational efficiency and reduce the computational costs even further for critical engineering models

a derivation of the glover doyle algorithms for general h control problems abstract we show that the glover doyle algorithm can be formulated simply by using the j j lossless factorization method and chain scattering matrix description this algorithm was first stated by glover and doyle in 1988 because the corresponding diagonal block of the j j lossless matrix in the general 4 block h control problem of the glover doyle algorithm is not square a new type of chain scattering matrix description is developed with this description in hand we obtain two types of state space solution which are similar to each other thus a similarity transformation between these solutions in the 4 block h control problem can also be obtained the main idea of the solution is illustrated by means of block diagrams

a sufficiently large time delay in feedback loop must destroy exponential stability of any decay rate a linear time invariant system with time delays is considered it is assumed that the delays are nontrivial in the sense that they affect the characteristic equation i e the characteristic quasi polynomial is not a polynomial of one complex variable it is proved that if any of such delays grows to infinity then either the system becomes unstable or at least some of its eigenvalues approach the imaginary axis in the latter case of course the system may become extremely sensitive to changes of other parameters which means practical instability the theoretical results of this paper support well known real world observations concerning the stability of systems with large delays in the feedback loop

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

on adomian s decomposition method and some comparisons with picard s iterative scheme abstract we consider the general mathematical framework of adomian s decomposition method g adomian stochastic systems academic press new york 1983 for a large class of nonlinear operator equations picard s iterative scheme is considered for the same class for equations and compared with the decomposition method the paper identifies carefully all substantial differences between the two methods and shows that various advantages exist for the decomposition method

memoryless stabilization of linear delay differential systems sufficient conditions for memoryless feedback stabilization of linear time invariant delay differential systems are derived for both constant and time dependent delays

a comparison of the iterative method and picard s successive approximations for deterministic and stochastic differential equations a comparison of adomian s iterative method for stochastic differential equations and the picard method of successive approximations shows interesting differences for both deterministic and stochastic differential equations the iterative procedure is more efficient and computationally useful even in the deterministic case in the stochastic case the picard method has no value while the iterative procedure is useful and simple

stability criteria for linear systems with uncertain delays new delay independent and delay dependent stability criteria for linear systems with multiple uncertain delays are established by using both the time domain and the frequency domain methods the results are derived based on the established new preliminary lemmas and by using new type stability theorems for general retarded dynamical systems and new analysis techniques in the time domain and the frequency domain all the established stability criteria depend only on the eigenvalues related to the coefficient matrices of the systems and do not involve any free tuning parameters in addition some remarks are given to explain in detail the obtained results and to point out the limitations of the existing results in the literature

a polynomial algorithm for minimum quadratic cost flow problems abstract network flow problems with quadratic separable costs appear in a number of important applications such as approximating input output matrices in economy projecting and forecasting traffic matrices in telecommunication networks solving nondifferentiable cost flow problems by subgradient algorithms it is shown that the scaling technique introduced by edmonds and karp 1972 in the case of linear cost flows for deriving a polynomial complexity bound for the out of kilter method may be extended to quadratic cost flows and leads to a polynomial algorithm for this class of problems the method may be applied to the solution of singly constrained quadratic programs and thus provides an alternative approach to the polynomial algorithm suggested by helgason kennington and lall 1980

robust stability of uncertain time delay systems and its stabilization by variable structure control in this paper two main results for uncertain time delay systems are derived the first result is the presentation of a new robust stability criterion for uncertain time delay systems the second result is the successful application of the concept of variable structure control to the stabilization problem of uncertain time delay systems the robustness and stability degree of perturbed systems in the sliding mode are also discussed last some examples are included to illustrate our results

new recurrence algorithms for the nonclassic adomian polynomials in this article we present new algorithms for the nonclassic adomian polynomials which are valuable for solving a wide range of nonlinear functional equations by the adomian decomposition method and introduce their symbolic implementation in mathematica beginning with rach s new definition of the adomian polynomials we derive the explicit expression for each class of the adomian polynomials e g a email protected k 1 mf k u 0 z m k for the class ii iii and iv adomian polynomials where the z m k are called the reduced polynomials these expressions provide a basis for developing improved algorithmic approaches by introducing the index vectors the recurrence algorithms for the reduced polynomials are suitably deduced which naturally lead to new recurrence algorithms for the class ii and class iii adomian polynomials mathematica programs generating these classes of adomian polynomials are subsequently presented computation shows that for computer generation of the class iii adomian polynomials the new algorithm reduces the running times compared with the definitional formula we also consider the number of summands of these classes of adomian polynomials and obtain the corresponding formulas finally we demonstrate the versatility of the four classes of adomian polynomials with several examples which include the nonlinearity of the form f t u explicitly depending on the argument t

memoryless h controllers for discrete time systems with time delay this paper considers the problem of h stabilization of discrete time systems with state delays and exogenous bounded energy l 2 disturbances specifically an h state feedback control design problem for discrete time systems with time delay is addressed the principal result involves sufficient conditions in terms of a modified riccati equation for characterizing state feedback controllers that enforce a bound on h performance and guarantee closed loop stability in the face of system state delay

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

a chain scattering matrix approach to the h output feedback control for state delayed systems a state space coprime factorization approach to the h controllers design for state delayed systems is developed the coprime factors that are generated by the present factorization possess the same delayed state as that of the original system this property together with the well known youla parameterization and the chain scattering matrix description provides a relatively simple method to obtain a family of the internally stabilizing h output feedback controllers a numerical example is given to demonstrate the validity and the applicability of the proposed approach

a convenient computational form for the adomian polynomials abstract recent important generalizations by g adomian stochastic systems academic press 1983 have extended the scope of his decomposition method for nonlinear stochastic operator equations see also iterative method inverse operator method symmetrized method or stochastic green s function method very considerably so that they are now applicable to differential partial differential delay and coupled equations which may be strongly nonlinear and or strongly stochastic or linear or deterministic as subcases thus for equations modeling physical problems solutions are obtained rapidly easily and accurately the methodology involves an analytic parametrization in which certain polynomials an dependent on the nonlinearity are derived this paper establishes simple symmetry rules which yield adomian s polynomials quickly to high orders

h sub spl infin memoryless control with an spl alpha stability constraint for time delay systems an lmi approach focuses on the design of h sub spl infin memoryless state feedback controllers satisfying some spl alpha stability constraints on the closed loop poles for a class of linear systems with delayed state subject to disturbance inputs a sufficient condition for feasibility is derived in terms of linear matrix inequalities furthermore we also consider a particular optimization problem the maximal bound allowed on time delay such that the prescribed level on disturbance attenuation and the spl alpha stability constraints are still preserved this problem is converted into a linear matrix inequality lmi optimization problem and we give a suboptimal bound on the delay

nonlinear h sub spl infin control a j dissipative approach this paper applies the chain scattering approach for linear h sub spl infin control to input affine nonlinear plants with general output structure the nonlinear h sub spl infin control problem is reformulated in terms of the chain representation of a given plant the state space characterization of j dissipative j lossless systems together with two special types of coprime factorizations are used to provide a class of controllers which solve locally the h sub spl infin control problem the problems considered correspond to the general two and four block problems in the linear case the results are given in terms of two uncoupled nonlinear partial differential inequalities with a coupling condition on their solutions

memoryless h sup spl infin controllers for state delayed systems in this note a memoryless h sup spl infin controller for the state delayed system is presented the controller is a delay independent stabilizer for the state delayed system which also reduces the h sup spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level the controller can be obtained by solving a modified riccati equation

spending constraint utilities with applications to the adwords market the notion of a market has undergone a paradigm shift with the internet totally new and highly successful markets have been defined and launched by internet companies which already form an important part of today s economy and are projected to grow considerably in the future another major change is the availability of massive computational power for running these markets in a centralized or distributed manner in view of these new realities the study of market equilibria an important though essentially nonalgorithmic theory within mathematical economics needs to be revived and rejuvenated via an inherently algorithmic approach such a theory should not only address traditional market models but also define new models for some of the new markets we present a new natural class of utility functions that allow buyers to explicitly provide information on their relative preferences as a function of the amount of money spent on each good these utility functions offer considerable expressivity especially in google s adwords market in addition they lend themselves to efficient computation while retaining some of the nice properties of traditional models the latter include weak gross substitutability and the uniqueness and continuity of equilibrium prices and utilities

α stability and robustness of large scale interconnected systems abstract the a stability or the stability with degree of large scale interconnected systems is studied a general stability theorem is established that applies even when the subsystems are governed by a functional differential equation rather than by an o d e this theorem is then applied to robustness the result obtained is a generalization of the well known properties of lq regulators an algorithm enabling the design of a robust controller for a large scale interconnected system is indicated

the standard h sub spl infin problem in systems with a single input delay the standard h sub spl infin problem is solved for lti systems with a single pure input lag the solution is based on state space analysis mixing a finite dimensional and an abstract evolution model utilizing the relatively simple structure of these distributed systems the associated operator riccati equations are reduced to a combination of two algebraic riccati equations and one differential riccati equation over the delay interval the results easily extend to finite time and time varying problems where the algebraic riccati equations are substituted by differential riccati equations over the process time duration

h spl infin output feedback controller design for linear systems with time varying delayed state this paper considers the h spl infin controller design problem for linear systems with time varying delays in states the authors obtain sufficient conditions for the existence of h spl infin controllers in terms of three linear matrix inequalities lmis these sufficient conditions are dependent on the maximum value of the time derivative of time varying delay furthermore they briefly explain how to construct such controllers from the positive definite solutions of their lmis and give an example

synthesis of controllers for continuous time delay systems with saturating controls via lmis the stabilization of linear continuous time systems with time delay in the state and subject to saturating controls is addressed sufficient conditions obtained via a linear matrix inequality lmi formulation are stated to guarantee both the local stabilization and the satisfaction of some performance requirements the method of synthesis consists in determining simultaneously a state feedback control law and an associated domain of safe admissible states for which the stability of the closed loop system is guaranteed when control saturations effectively occur

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

an e relaxation method for separable convex cost generalized network flow problems cover title the extended abstract of this article appeared in the proceedings of the 5th international ipco conference vancouver june 1996 p 1

inversion of nonlinear stochastic operators abstract the operator theoretic method adomian and malakian j math anal appl 76 1 1980 183 201 recently extended adomian s solutions of nonlinear stochastic differential equations g adomian stochastic systems analysis in applied stochastic processes nonlinear stochastic differential equations j math anal appl 55 1 1976 441 452 on the modeling and analysis of nonlinear stochastic systems in proceeding international conf on mathematical modeling vol 1 pp 29 40 to provide an efficient computational procedure for differential equations containing polynomial exponential and trigonometric nonlinear terms n y the procedure depends on the calculation of certain quantities an and bn this paper generalizes the calculation of the an and bn to much wider classes of nonlinearities of the form n y y essentially the method provides a systematic computational procedure for differential equations containing any nonlinear terms of physical significance this procedure depends on a recurrence rule from which explicit general formulae are obtained for the quantities an and bn for any order n in a convenient form this paper also demonstrates the significance of the iterative series decomposition proposed by adomian for linear stochastic operators in 1964 and developed since 1976 for nonlinear stochastic operators since both the nonlinear and stochastic behavior is quite general the results are extremely significant for applications processes need not for example be limited to either gaussian processes white noise or small fluctuations

the notion of a rational convex program and an algorithm for the arrow debreu nash bargaining game we introduce the notion of a rational convex program rcp and we classify the known rcps into two classes quadratic and logarithmic the importance of rationality is that it opens up the possibility of computing an optimal solution to the program via an algorithm that is either combinatorial or uses an lp oracle next we define a new nash bargaining game called adnb which is derived from the linear case of the arrow debreu market model we show that the convex program for adnb is a logarithmic rcp but unlike other known members of this class it is nontotal our main result is a combinatorial polynomial time algorithm for adnb it turns out that the reason for infeasibility of logarithmic rcps is quite different from that for lps and quadratic rcps we believe that our ideas for surmounting the new difficulties will be useful for dealing with other nontotal rcps as well we give an application of our combinatorial algorithm for adnb to an important fair throughput allocation problem on a wireless channel finally we present a number of interesting questions that the new notion of rcp raises

new ideas for decomposing nonlinearities in differential equations abstract in this paper we consider the decomposition for the nonlinearity in a differential equation for the solution by decomposition by analyzing and transforming the taylor expansion of the nonlinearity about the initial solution component the decomposition of the nonlinearity is converted to the partitions of the solution sets for a class of diophantine equations this conversion simplifies the discussion and presents a new idea for decompositions we enumerate five types of partitions and their corresponding decomposition polynomials each of the last four types contains infinitely many kinds of decomposition polynomials in the form of finite sums in types 2 3 and 4 there is a parameter q and each value of q corresponds to a class of decomposition polynomials in type 5 each positive integer sequence c j satisfying 1 c 1 c 2 and j c j for j 2 3 corresponds to a class of decomposition polynomials four classes of the adomian polynomials r rach a new definition of the adomian polynomials kybernetes 37 2008 910 955 are derived as particular cases

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

convenient analytic recurrence algorithms for the adomian polynomials abstract in this article we present four analytic recurrence algorithms for the multivariable adomian polynomials as special cases we deduce the four simplified results for the one variable adomian polynomials these algorithms are comprised of simple orderly and analytic recurrence formulas which do not require time intensive operations such as expanding regrouping parametrization and so on they are straightforward to implement in any symbolic software and are shown to be very efficient by our verification using mathematica 7 0 we emphasize that from the summation expressions a n k 1 n u n k for the multivariable adomian polynomials and an k 1 n f k u 0 c n k for the one variable adomian polynomials we obtain the recurrence formulas for the u n k and the c n k these provide a theoretical basis for developing new algorithmic approaches such as for parallel computing in particular the recurrence process of one particular algorithm for the one variable adomian polynomials does not involve the differentiation operation but significantly only the arithmetic operations of multiplication and addition are involved precisely c n 1 u n n 1 and c n k 1 n j 0 n k j 1 u j 1 c n 1 j k 1 2 k n we also discuss several other algorithms previously reported in the literature including the adomian rach recurrence algorithm 1 and this author s index recurrence algorithm 23 36

h disturbance attenuation for state delayed systems in this note the differential game and dissipation inequality are applied to the disturbance attenuation or h control for linear systems with delayed state firstly a simple sufficient condition on the existence of a suboptimal h state feedback controller is given which is independent of delay and an observer based dynamic output feedback solution is presented in terms of riccati inequalities or riccati equations secondly a sufficient condition on the existence of a delay dependent state feedback is presented and the criterion is presented by a matrix inequality which can be solved by numerical methods

anharmonic oscillator systems abstract the anharmonic oscillator is solved quickly easily and elegantly by adomian s methods for solution of nonlinear stochastic differential equations emphasizing its applicability to nonlinear deterministic equations as well as stochastic equations no difficulty is encountered in treating the case of the forced anharmonic oscillator or the stochastic case or of any nonlinear oscillating system such as the duffing or van der pol oscillators for example with coefficients as well as forcing functions which are stochastic processes since statistical separability is inherent in the adomian method