paper low order control design for lmi problems using alternating projection methods computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities lmis in particular we concentrate on the stabilization and the suboptimal h output feedback control design problems these problems can be described by a pair of lmis and an additional coupling condition this coupling condition is convex for the full order control design problem but convexity is lost for the control problem of order strictly less than the plant order we formulate these problems as feasibility problems with matrix constraint sets of simple geometry and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets full order and low order controllers are designed using alternating projection methods for the full order controller case global convergence of the alternating projection methods to a feasible solution is guaranteed however for the low order control case only local convergence is guaranteed an example is provided to illustrate the use of these methods for the full order and the low order controller design

robust control with structure perturbations the problem of making a given stabilizing controller robust so that the closed loop system remains stable for prescribed ranges of variations of a set of physical parameters in the plant the problem is treated in the state space and transfer function domains in the state space domain a stability hypersphere is determined in the parameter space using lyapunov theory the radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere in the transfer function domain a corresponding stability margin is defined and optimized on the basis of the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed loop characteristic polynomial the design algorithms are illustrated by examples

an asymptotic preserving automatic domain decomposition method for the vlasov poisson bgk system with applications to plasmas in this work we present an efficient strategy to deal with plasma physics simulations in which localized departures from thermodynamical equilibrium are present the method is based on the introduction of intermediate regions which allows smooth transitions between kinetic and fluid zones in this paper we extend domain decomposition techniques obtained through dynamic coupling and buffer zones to the study of plasmas and moreover we combine them with asymptotic preserving and asymptotically accurate strategies for the time integration we use a hybrid scheme in which both kinetic and fluid descriptions are considered and coupled together while the kinetic model is solved by asymptotic preserving and accurate methods in order to guarantee high efficiency and accuracy in all regimes the numerical scheme is validated and its performances are analyzed by numerical simulations

high order imex spectral schemes for computing the dynamics of systems of nonlinear schrodinger gross pitaevskii equations the aim of this paper is to build and validate some explicit high order schemes both in space and time for simulating the dynamics of systems of nonlinear schrodinger gross pitaevskii equations the method is based on the combination of high order implicit explicit imex schemes in time and fourier pseudo spectral approximations in space the resulting imexsp schemes are highly accurate efficient and easy to implement they are also robust when used in conjunction with an adaptive time stepping strategy and appear as an interesting alternative to time splitting pseudo spectral tssp schemes finally a complete numerical study is developed to investigate the properties of the imexsp schemes in comparison with tssp schemes for one and two components systems of gross pitaevskii equations

the dual iteration for fixed order control this paper proposes a new heuristic algorithm for fixed order control problems using linear matrix inequalities the authors call the algorithm the dual iteration because it is based on the iteration of two design steps state feedback and filtering which are dual to each other extensive numerical experiments show that the algorithm has a decent performance

high order exponential integrators for nonlinear schrodinger equations with application to rotating bose einstein condensates this article deals with the numerical integration in time of nonlinear schrodinger equations the main application is the numerical simulation of rotating bose einstein condensates the authors perform a change of unknown so that the rotation term disappears and they obtain as a result a nonautonomous nonlinear schrodinger equation they consider exponential integrators such as exponential runge kutta methods and lawson methods they provide an analysis of the order of convergence and some preservation properties of these methods in a simplified setting and they supplement their results with numerical experiments with realistic physical parameters moreover they compare these methods with the classical split step methods applied to the same problem

direct search for exact solutions to the nonlinear schrodinger equation a five dimensional symmetry algebra consisting of lie point symmetries is firstly computed for the nonlinear schrodinger equation which together with a reflection invariance generates two five parameter solution groups three ansatze of transformations are secondly analyzed and used to construct exact solutions to the nonlinear schrodinger equation various examples of exact solutions with constant trigonometric function type exponential function type and rational function amplitude are given upon careful analysis a bifurcation phenomenon in the nonlinear schrodinger equation is clearly exhibited during the solution process

an alternate numerical solution to the linear quadratic problem this note proposes a new method based on convex programming for solving the linear quadratic problem lqp directly on the parameter space generated by the feedback control gain all stabilizing controllers are mapped into a convex set the problem is then formulated as a minimization of a linear function over this convex set its optimal solution furnishes under certain conditions the same feedback control gain obtained from the classical riccati equation generalizations to decentralized control and output feedback control design are included the theory is illustrated by some numerical examples

practical symplectic partitioned runge kutta and runge kutta nystrom methods we present new symmetric fourth and sixth order symplectic partitioned runge kutta and runge kutta nystrom methods we studied compositions using several extra stages optimising the efficiency an effective error ef is defined and an extensive search is carried out using the extra parameters the new methods have smaller values of ef than other methods found in the literature when applied to several examples they perform up to two orders of magnitude better than previously known method which is in very good agreement with the values of ef

fourier splitting methods for the dynamics of rotating bose einstein condensates abstract we present a new method to propagate rotating bose einstein condensates subject to explicitly time dependent trapping potentials using algebraic techniques we combine magnus expansions and splitting methods to yield any order methods for the multivariate and nonautonomous quadratic part of the hamiltonian that can be computed using only fourier transforms at the cost of solving a small system of polynomial equations the resulting scheme solves the challenging component of the nonlinear hamiltonian and can be combined with optimized splitting methods to yield efficient algorithms for rotating bose einstein condensates the method is particularly efficient for potentials that can be regarded as perturbed rotating and trapped condensates e g for small nonlinearities since it retains the near integrable structure of the problem for large nonlinearities the method remains highly efficient if higher order p 2 is sought furthermore we show how it can be adapted to the presence of dissipation terms numerical examples illustrate the performance of the scheme

some new additive runge kutta methods and their applications we propose some new additive runge kutta methods of orders ranging from 2 to 4 that may be used for solving some nonlinear system of odes especially for the temporal discretization of some nonlinear systems of pdes with constraints only linear odes or pdes need to be solved at each time step with these new methods

an efficient algorithm based on splitting for the time integration of the schrodinger equation we present a practical algorithm based on symplectic splitting methods intended for the numerical integration in time of the schrodinger equation when the hamiltonian operator is either time independent or changes slowly with time in the later case the evolution operator can be effectively approximated in a step by step manner first divide the time integration interval in sufficiently short subintervals and then successively solve a schrodinger equation with a different time independent hamiltonian operator in each of these subintervals when discretized in space the schrodinger equation with the time independent hamiltonian operator obtained for each time subinterval can be recast as a classical linear autonomous hamiltonian system corresponding to a system of coupled harmonic oscillators the particular structure of this linear system allows us to construct a set of highly efficient schemes optimized for different precision requirements and time intervals sharp local error bounds are obtained for the solution of the linear autonomous hamiltonian system considered in each time subinterval our schemes can be considered in this setting as polynomial approximations to the matrix exponential in a similar way as methods based on chebyshev and taylor polynomials the theoretical analysis supported by numerical experiments performed for different time independent hamiltonians indicates that the new methods are more efficient than schemes based on chebyshev polynomials for all tolerances and time interval lengths the algorithm we present automatically selects for each time subinterval the most efficient splitting scheme among several new optimized splitting methods for a prescribed error tolerance and given estimates of the upper and lower bounds of the eigenvalues of the discretized version of the hamiltonian operator

multidimensional integrable schrodinger operators with matrix potential the schrodinger operators with matrix rational potential which are d integrable i e can be intertwined with the pure laplacian are investigated corresponding potentials are uniquely determined by their singular data which are a configuration of the hyperplanes in cn with prescribed matrices we describe some algebraic conditions matrix locus equations on these data which are sufficient for d integrability as the examples some matrix generalizations of the calogero moser operators are considered

the xy centring algorithm for the dual lmi problem a new approach to fixed order control design many fixed order suboptimal control problems with stability performance and robustness specifications can be reduced to a search for a matrix x 0 satisfying a linear matrix inequality lmi while x 1 satisfies another lmi this paper defines a certain class of these problems we shall call the dual lmi problem and a computational algorithm to solve our dual lmi problem is given properties and limitations of the algorithm are discussed in comparison with the existing algorithm the min max algorithm an extension to optimal control problems is provided numerical examples for the fixed order stabilization problem and the static output feedback linear quadratic optimal control problem demonstrate the applicability of the proposed algorithm

splitting methods for non autonomous separable dynamical systems a large number of splitting methods for autonomous separable systems exist in the literature which have been designed for many different structures of the vector field however the performance of most of these methods is diminished and their orders of accuracy are frequently reduced when applied to non autonomous problems based on the formal solution obtained from the magnus series expansion we show how to modify a standard splitting method for autonomous problems to treat non autonomous systems with similar or better efficiency we illustrate this technique to build new fourth and sixth order schemes whose performance is then illustrated on several numerical examples

the optimal projection equations for fixed order dynamic compensation first order necessary conditions for quadratically optimal steady state fixed order dynamic compensation of a linear time invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form in contrast to the pair of matrix riccati equations for the full order lqg case the optimal steady state fixed order dynamic compensator is characterized by four matrix equations two modified riccati equations and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains the coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced order controller case

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

computational complexity of a problem arising in fixed order output feedback design this paper is concerned with a matrix inequality problem which arises in fixed order output feedback control design this problem involves finding two symmetric and positive definitive matrices x and y such that each satisfies a linear matrix inequality and that xy i it is well known that many control problems such as fixed order output feedback stabilization h control guaranteed h2 control and mixed h2 h control can all be converted into the matrix inequality problem above including static output feedback problems as a special case we show however that this matrix inequality problem is np hard

from structured data to evolution linear partial differential equations abstract this paper is devoted to the derivation of computational methods for constructing partial differential equations from data following some recent works 7 14 15 20 we propose a methodology based on symbolic calculus 8 9 13 pseudospectral methods 2 3 and stochastic processes 6 in order to determine non constant coefficients of linear evolution partial differential equations pdes from a set of structured data constituted by solutions at given times and positions of an unknown linear pde

splitting methods for non autonomous hamiltonian equations abstract we present an algorithm for numerically integrating non autonomous hamiltonian differential equations special attention is paid to the separable case and in particular a new fourth order splitting method is presented which in a certain measure is optimal in combination with a new way of handling non autonomous problems the schemes we present are based on magnus expansions and they show very promising results when applied to hamiltonian odes and pdes