subgradient based neural networks for nonsmooth nonconvex optimization problems this paper presents a subgradient based neural network to solve a nonsmooth nonconvex optimization problem with a nonsmooth nonconvex objective function a class of affine equality constraints and a class of nonsmooth convex inequality constraints the proposed neural network is modeled with a differential inclusion under a suitable assumption on the constraint set and a proper assumption on the objective function it is proved that for a sufficiently large penalty parameter there exists a unique global solution to the neural network and the trajectory of the network can reach the feasible region in finite time and stay there thereafter it is proved that the trajectory of the neural network converges to the set which consists of the equilibrium points of the neural network and coincides with the set which consists of the critical points of the objective function in the feasible region a condition is given to ensure the convergence to the equilibrium point set in finite time moreover under suitable assumptions the coincidence between the solution to the differential inclusion and the ldquoslow solutionrdquo of it is also proved furthermore three typical examples are given to present the effectiveness of the theoretic results obtained in this paper and the good performance of the proposed neural network

on resource bounded instance complexity we prove the instance complexity conjecture of ko orponen schoning and watanabe for all recursive tally sets and for all recursive sets which are np hard under honest reductions in particular it holds for all natural np hard problems on the other hand the conjecture is shown to be oracle dependent additional results concern the nonrecursiveness of the instance complexity measure and a comparison of time bounded c and cd complexity

spectral methods for weakly singular volterra integral equations with smooth solutions we propose and analyze a spectral jacobi collocation approximation for the linear volterra integral equations vies of the second kind with weakly singular kernels in this work we consider the case when the underlying solutions of the vies are sufficiently smooth in this case we provide a rigorous error analysis for the proposed method which shows that the numerical errors decay exponentially in the infinity norm and weighted sobolev space norms numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence

stabilizing receding horizon h sub spl infin controls for linear continuous time varying systems in this note new matrix inequality conditions on the terminal weighting matrices are proposed for linear continuous time varying systems under these conditions nonincreasing and nondecreasing monotonicities of the saddle point value of a dynamic game are shown to be guaranteed it is proved that the proposed terminal inequality conditions ensure the closed loop stability of the receding horizon h sub spl infin control rhhc the stabilizing rhhc guarantees the h sub spl infin norm bound of the closed loop system the proposed terminal inequality conditions for the monotonicity of the saddle point value and the closed loop stability include most well known existing terminal conditions as special cases the results for time invariant systems are obtained correspondingly from those in the time varying case

convergence analysis of the multistep legendre pseudo spectral method for volterra integral equations with vanishing delays in this paper we extend the single step pseudo spectral method for second kind volterra integral equations with vanishing variable delays to the multistep pseudo spectral method we also analyze the convergence of the hp version of the multistep pseudo spectral method under the l2 norm and show that the scheme enjoys high order accuracy and can be implemented in a stable and efficient manner in addition it is very suitable for long time calculations and large step size situations numerical results show good agreement with the theoretical analysis

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

a general methodology for designing globally convergent optimization neural networks we present a general methodology for designing optimization neural networks we prove that the neural networks constructed by using the proposed method are guaranteed to be globally convergent to solutions of problems with bounded or unbounded solution sets in contrast with the gradient methods whose convergence is not guaranteed we show that the proposed method contains both the gradient methods and nongradient methods employed in existing optimization neural networks as special cases based on the theoretical results of the proposed method we study the convergence and stability of general gradient models in the case of unisolated solutions using the proposed method we derive some new neural network models for a very large class of optimization problems in which the equilibrium points correspond to exact solutions and there is no variable parameter finally some numerical examples show the effectiveness of the method

multirate and composite control of two time scale discrete time systems the design of stabilizing feedback control of singularly perturbed diserete time systems is decomposed into the design of slow and fast controllers which are combined to form the composite control composite control strategies are developed for the case of single rate measurements all variables are measured at the same rate as well as for the case of multirate measurements slow variables are measured at a rate slower than that of fast variables

a one layer recurrent neural network for pseudoconvex optimization subject to linear equality constraints in this paper a one layer recurrent neural network is presented for solving pseudoconvex optimization problems subject to linear equality constraints the global convergence of the neural network can be guaranteed even though the objective function is pseudoconvex the finite time state convergence to the feasible region defined by the equality constraints is also proved in addition global exponential convergence is proved when the objective function is strongly pseudoconvex on the feasible region simulation results on illustrative examples and application on chemical process data reconciliation are provided to demonstrate the effectiveness and characteristics of the neural network

robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks this paper presents a neural network approach to robust model predictive control mpc for constrained discrete time nonlinear systems with unmodeled dynamics affected by bounded uncertainties the exact nonlinear model of underlying process is not precisely known but a partially known nominal model is available this partially known nonlinear model is first decomposed to an affine term plus an unknown high order term via jacobian linearization the linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning the minimax methodology is exploited to deal with bounded uncertainties the minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two layer recurrent neural network the proposed neurodynamic approach to nonlinear mpc improves the computational efficiency and sheds a light for real time implementability of mpc technology simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach

kolmogorov complexity and instance complexity of recursively enumerable sets the way in which way kolmogorov complexity and instance complexity affect properties of recursively enumerable r e sets is studied the well known 2 log n upper bound on the kolmogorov complexity of initial segments of r e sets is shown to be optimal and the turing degrees of r e sets which attain this bound are characterized the main part of the paper is concerned with instance complexity introduced by ko orponen schoning and watanabe in 1986 as a measure of the complexity of individual instances of a decision problem they conjectured that for every r e nonrecursive set the instance complexity is infinitely often at least as high as the kolmogorov complexity the conjecture is refuted by constructing an r e nonrecursive set with instance complexity logarithmic in the kolmogorov complexity this bound is optimal up to an additive constant in the other extreme the conjecture is established for many classes of complete sets such as weak truth table complete wtt complete and q complete sets however there is a turing complete set for which it fails

a projection neural network for constrained quadratic minimax optimization this paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network compared with some of the existing neural networks for quadratic minimax optimization the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems and the designed neural network does not include any parameter moreover the neural network has lower model complexities the number of state variables of which is equal to that of the dimension of the optimization problems the simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

output feedback control of linear two time scale systems output feedback control of linear time invariant singularly perturbed systems is studied the set of all compensators that stabilize a singularly perturbed system while preserving its two time scale structure is parameterized the parameterization is used to show that any two frequency scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure in this procedure a fast high frequency compensator is designed first to stabilize the fast model of the system then a strictly proper slow low frequency compensator is designed to stabilize a modified slow model the parallel connection of the two compensators forms a two frequency scale stabilizing compensator for the singularly perturbed system

a new strategy for the numerical solution of nonlinear volterra integral equations with vanishing delays abstract the aim of this paper is to develop a high order algorithm for nonlinear volterra integral equations with vanishing variable delays the algorithm is a non trivial extension of the single step methods this method is based on the variational form so the algorithm is relatively simple this scheme enjoys high order accuracy and can be implemented in a stable and efficient manner we prove the existence and uniqueness of the numerical solution and derive error estimates of the algorithm numerical results show a good agreement with the theoretical analysis

a one layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints this paper presents a one layer projection neural network for solving nonsmooth optimization problems with generalized convex objective functions and subject to linear equalities and bound constraints the proposed neural network is designed based on two projection operators linear equality constraints and bound constraints the objective function in the optimization problem can be any nonsmooth function which is not restricted to be convex but is required to be convex pseudoconvex on a set defined by the constraints compared with existing recurrent neural networks for nonsmooth optimization the proposed model does not have any design parameter which is more convenient for design and implementation it is proved that the output variables of the proposed neural network are globally convergent to the optimal solutions provided that the objective function is at least pseudoconvex simulation results of numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network

generalized laguerre pseudospectral method based laguerre interpolation abstract in this paper we develop the generalized laguerre pseudospectral method for the second order ordinary differential equation based on the modified generalized laguerre approximation which is very efficient for the long time numerical simulations of dynamical systems the numerical solution possesses the spectral accuracy the global convergence of the proposed algorithm is proved numerical results demonstrate the effectiveness of the proposed method and coincide well with theoretical analysis

parametric eigenstructure assignment in second order descriptor linear systems this note considers eigenstructure assignment in second order descriptor linear systems via proportional plus derivative feedback it is shown that the problem is closely related with a type of so called second order sylvester matrix equations through establishing two general parametric solutions to this type of matrix equations two complete parametric methods for the proposed eigenstructure assignment problem are presented both methods give simple complete parametric expressions for the feedback gains and the closed loop eigenvector matrices the first one mainly depends on a series of singular value decompositions and is thus numerically simple and reliable the second one utilizes the right factorization of the system and allows the closed loop eigenvalues to be set undetermined and sought via certain optimization procedures an example shows the effect of the proposed approaches

a neural network for a class of convex quadratic minimax problems with constraints in this paper we propose a neural network for solving a class of convex quadratic minimax problems with constraints four sufficient conditions are provided to ensure the asymptotic stability of the proposed network furthermore the exponential stability of the proposing network is also proved under certain conditions the results obtained here can be further extended to the globally projected dynamical system in addition some new stability conditions for the system are also obtained since our stability conditions can be easily checked in practice these results becomes more attractive in real applications

a multistep legendre pseudo spectral method for volterra integral equations in this paper we extend the single step pseudo spectral method for volterra integral equations of the second kind to the multistep pseudo spectral method we also analyze the convergence of the hp version of the multistep pseudo spectral method under the l2 norm and show that the scheme enjoys high order accuracy and can be implemented in a stable and efficient manner in addition it is very suitable for long time calculations and large step size situations numerical experiments confirm theoretical expectations

neurodynamics based robust pole assignment for high order descriptor systems in this paper a neurodynamic optimization approach is proposed for synthesizing high order descriptor linear systems with state feedback control via robust pole assignment with a new robustness measure serving as the objective function the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem a neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high order singular systems with guaranteed optimality and exact pole assignment two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach

a two time scale neurodynamic approach to constrained minimax optimization this paper presents a two time scale neurodynamic approach to constrained minimax optimization using two coupled neural networks one of the recurrent neural networks is used for minimizing the objective function and another is used for maximization it is shown that the coupled neurodynamic systems operating in two different time scales work well for minimax optimization the effectiveness and characteristics of the proposed approach are illustrated using several examples furthermore the proposed approach is applied for h infty model predictive control

a generalized block by block method for solving linear volterra integral equations abstract one of the numerical methods for solving linear volterra integral equations is block by block method which is explained in l m delves j l mohamed computational methods for integral equations cambridge university press 1985 l m delves j walsh numerical solution of integral equations oxford university press 1974 and p k kyte p puri computational methods for linear integral equations birkhauser boston 2002 in this article we explain a general method for constructing block by block systems for solving volterra integral equations then we deduce some of the special cases especially the linz s block by block method which explained in these references

a dynamical model for solving degenerate quadratic minimax problems with constraints this paper presents a new neural network model for solving degenerate quadratic minimax dqm problems on the basis of the saddle point theorem optimization theory convex analysis theory lyapunov stability theory and lasalle invariance principle the equilibrium point of the proposed network is proved to be equivalent to the optimal solution of the dqm problems it is also shown that the proposed network model is stable in the sense of lyapunov and it is globally convergent to an exact optimal solution of the original problem several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper

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

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

a novel neural network for a class of convex quadratic minimax problems based on the inherent properties of convex quadratic minimax problems this article presents a new neural network model for a class of convex quadratic minimax problems we show that the new model is stable in the sense of lyapunov and will converge to an exact saddle point in finite time by defining a proper convex energy function furthermore global exponential stability of the new model is shown under mild conditions compared with the existing neural networks for the convex quadratic minimax problem the proposed neural network has finite time convergence a simpler structure and lower complexity thus the proposed neural network is more suitable for parallel implementation by using simple hardware units the validity and transient behavior of the proposed neural network are illustrated by some simulation results

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

recurrent neural network for non smooth convex optimization problems with application to the identification of genetic regulatory networks a recurrent neural network is proposed for solving the non smooth convex optimization problem with the convex inequality and linear equality constraints since the objective function and inequality constraints may not be smooth the clarke s generalized gradients of the objective function and inequality constraints are employed to describe the dynamics of the proposed neural network it is proved that the equilibrium point set of the proposed neural network is equivalent to the optimal solution of the original optimization problem by using the lagrangian saddle point theorem under weak conditions the proposed neural network is proved to be stable and the state of the neural network is convergent to one of its equilibrium points compared with the existing neural network models for non smooth optimization problems the proposed neural network can deal with a larger class of constraints and is not based on the penalty method finally the proposed neural network is used to solve the identification problem of genetic regulatory networks which can be transformed into a non smooth convex optimization problem the simulation results show the satisfactory identification accuracy which demonstrates the effectiveness and efficiency of the proposed approach

simplified reproducing kernel method and convergence order for linear volterra integral equations with variable coefficients abstract this paper proposes a simplified reproducing kernel method to solve the linear volterra integral equations with variable coefficients the main idea of the method is to establish a reproducing kernel direct space that can be used in volterra integral equations and in the first time this paper analyzes the convergence order and stability of the approximate solution then the uniform convergence of the numerical solution is proved and the time consuming schmidt orthogonalization process is avoided the proposed method is proved to be stable and is not less than the second order convergence the algorithm is proved to be feasible and stable through some numerical examples

working with strong reducibilities above totally omega c e and array computable degrees we investigate the connections between the complexity of a c e set as calibrated by its strength as an oracle for turing computations of functions in the ershov hierarchy and how strong reducibilities allow us to compute such sets for example we prove that a c e degree is totally w c e iff every set in it is weak truth table reducible to a hypersimple or ranked set we also show that a c e degree is array computable iff every left c e real of that degree is reducible in a computable lipschitz way to a random left c e real an number

arnoldi methods for large sylvester like observer matrix equations and an associated algorithm for partial spectrum assignment abstract we propose an arnoldi based numerical method for solving a sylvester type equation arising in the construction of the luenberger observer given an n n matrix a and an n m matrix g the method simultaneously constructs an m m hessenberg matrix h with a preassigned spectrum and an n m orthonormal matrix x such that ax xh g we consider the case when a is large and sparse so that the standard techniques such as the well known hessenberg schur method for solving a sylvester equation cannot be easily applied as a byproduct we propose an algorithm for the partial pole assignment problem for large matrices

convergence analysis of the jacobi spectral collocation methods for volterra integral equations with a weakly singular kernel in this paper a jacobi collocation spectral method is developed for volterra integral equations of second kind with a weakly singular kernel we use some function transformation and variable transformations to change the equation into a new volterra integral equation deflned on the standard interval i1 1 so that the solution of the new equation possesses better regularity and the jacobi orthogonal polynomial theory can be applied conveniently in order to obtain high order accuracy for the approx imation the integral term in the resulting equation is approximated by using jacobi spectral quadrature rules the convergence analysis of this novel method is based on the lebesgue constants corresponding to the lagrange interpolation polynomials poly nomials approximation theory for orthogonal polynomials and the operator theory the spectral rate of convergence for the proposed method is established in the l 1 norm and weighted l 2 norm numerical results are presented to demonstrate the efiectiveness of the proposed method

fractional linear multistep methods for abel volterra integral equations of the second kind fractional powers of linear multistep methods are suggested for the numerical solution of weakly singular volterra integral equations the proposed methods are convergent of the order of the underlying multistep method also in the generic case of solutions which are not smooth at the origin the stability properties stability region a stability a a stability are closely related to those of the underlying linear multistep method