the phase transition of the directed polymer on disordered hierarchical lattices the directed polymer on disordered hierarchical lattices is studied using an exact renormalization scheme the phase transition is studied and a hyperscaling relation is derived the fixed distributions of the renormalized energies are obtained numerically the specific heat and associated exponents are computed from the fixed distributions

an interior point constrained trust region method for a special class of nonlinear semidefinite programming problems in this paper an interior point trust region algorithm for the solution of a class of nonlinear semidefinite programming sdp problems is described and analyzed such nonlinear and nonconvex programs arise e g in the design of optimal static or reduced order output feedback control laws and have the structure of abstract optimal control problems in a finite dimensional hilbert space the algorithm treats the abstract states and controls as independent variables in particular an algorithm for minimizing a nonlinear matrix objective functional subject to a nonlinear sdp condition a positive definiteness condition and a nonlinear matrix equation is considered the algorithm is designed to take advantage of the structure of the problem it is an extension of an interior point trust region method to nonlinear and nonconvex sdps with a special structure which applies sequential quadratic programming techniques to a sequence of barrier problems and uses trust regions to ensure robustness of the iteration some convergence results are given and finally several numerical examples demonstrate the applicability of the considered algorithm

differential migdal kadanoff renormalization group for disordered systems phase transitions in quenched random systems are studied within the migdal kadanoff approximation exact differential recursion relations for the distribution of coupling are derived the q state potts model with random ferromagnetic couplings is studied in two and three dimensions in three dimensions there is a non perturbative random fixed point which exists when the specific heat exponent is either positive or slightly negative if the specific heat exponent is slightly negative a multicritical point separates strong and weak disorder regimes the analytic results are confirmed by numerical simulations of the recursion relations

optimality conditions for nonconvex semidefinite programming this paper concerns nonlinear semidefinite programming problems for which no convexity assumptions can be made we derive first and second order optimality conditions analogous to those for nonlinear programming using techniques similar to those used in nonlinear programming we extend existing theory to cover situations where the constraint matrix is structurally sparse the discussion covers the case when strict complementarity does not hold the regularity conditions used are consistent with those of nonlinear programming in the sense that the conventional optimality conditions for nonlinear programming are obtained when the constraint matrix is diagonal

self avoiding walks in quenched random environments the self avoiding walk in a quenched random environment is studied using realspace and field theoretic renormalization and flory arguments these methods indicate that the system is described for d de by a strong disorder fixed point corresponding to a glass state in which the polymer is confined to the lowest energy path this fixed point is characterized by scaling laws for the size of the walk l n with n the number of steps and the fluctuations in the free energy af l the bound 1 co pore and suggests that this inequality holds for d 2 and 3 although pure cannot be excluded particularly for d 2 for d d c there is a transition between strong and weak disorder phases at which pure the strong disorder fixed point for saws on percolation clusters is discussed the analogy with directed walks is emphasized

h sub infinity control and quadratic stabilization of systems with parameter uncertainty via output feedback the article concerns linear systems which are subject to both time varying norm bounded parameter uncertainty and exogenous disturbance it addresses the robust h sub infinity control problem of designing a linear dynamic output feedback controller such that the closed loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties it is shown that such a problem is equivalent to a scaled h sub infinity control problem

robust spl hscr sub spl infin filtering for uncertain discrete time state delayed systems this paper addresses the problem of robust spl hscr sub spl infin filtering for linear discrete time systems subject to parameter uncertainties in the system state space model and with multiple time delays in the state variables the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain a methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed spl hscr sub spl infin performance for the filtering error irrespective of the uncertainty and the time delays the proposed design is given in terms of linear matrix inequalities which has the advantage in that it can be implemented numerically very efficiently

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

polymers on disordered hierarchical lattices a nonlinear combination of random variables the problem of directed polymers on disordered hierarchical and hypercubic lattices is considered for the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way we present the results of numerical simulations of two hierarchical lattices finding evidence of a phase transition in one case for a limiting case we extend the perturbation theory developed by derrida and griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties overlaps of the model in this limit we obtain an interpolation formula allowing one to obtain the noninteger moments of the partition function from the integer moments we obtain bounds for the transition temperature for hierarchical and hypercubic lattices and some similarities between the problem on the two different types of lattice are discussed

brief rbust control of linear systems with real parametric uncertainty we discuss the problem of robust controller synthesis to provide quadratic stability and a desirable disturbance attenuation level through an appropriately small l 2 gain for systems with time varying real parametric uncertainty through the use of skewsymmetric matrices the conservatism of standard scaled h approach is reduced while the full state feedback problem is convex the output feedback problem is not a set of conditions under which the design of output feedback controllers can be broken into two sequential convex problems is presented the results are compared with recent results concerning the design of parameter varying controllers and a simple result regarding the mixed problem where some of the unknown parameters can be measured on line is discussed

ising model in an external field on a hierarchical lattice the two dimensional renormalization map of the diamond hierarchical ising model in an external field is given and pictures of the distribution of zeros of the partition function in the complex plane of temperature for varying values of coupling constant and external field are shown critical exponents of the model are found and results are different from those of the ising model on a two or three dimensional regular lattice

h 2 and h_ infty robust filtering for discrete time linear systems this paper investigates robust filtering design problems in h2 and h infty spaces for discrete time systems subjected to parameter uncertainty which is assumed to belong to a convex bounded polyhedral domain it is shown that by a suitable change of variables both design problems can be converted into convex programming problems written in terms of linear matrix inequalities lmi the results generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured then assuming the order of the uncertain system is known the optimal guaranteed performance h2 and h infty filters are proven to be of the same order as the order of the system comparisons with robust filters for systems subjected to norm bounded uncertainty are provided in both theoretical and practical settings in particular it is shown that under the same assumptions the results here are generally better as far as the minimization of a guaranteed cost expressed in terms of h2 or h infty norms is considered some numerical examples illustrate the theoretical results

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

analysis of a slow fast system near a cusp singularity this paper studies a slow fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe our analysis consists of two main parts first we recall a formal normal form suitable for systems as the one studied here afterwards taking advantage of this normal form we investigate the transition near the cusp singularity by means of the blow up technique our contribution relies heavily in the usage of normal form theory allowing us to refine previous results

robust output feedback controller design via local bmi optimization the problem of designing a globally optimal full order output feedback controller for polytopic uncertain systems is known to be a non convex np hard optimization problem that can be represented as a bilinear matrix inequality optimization problem for most design objectives in this paper a new approach is proposed to the design of locally optimal controllers it is iterative by nature and starting from any initial feasible controller it performs local optimization over a suitably defined non convex function at each iteration the approach features the properties of computational efficiency guaranteed convergence to a local optimum and applicability to a very wide range of problems furthermore a fast but conservative lmi based procedure for computing an initially feasible controller is also presented the complete approach is demonstrated on a model of one joint of a real life space robotic manipulator

directed paths on percolation clusters we consider a variant of the problem of directed polymers on a disordered lattice in which the disorder is geometrical in nature in particular we allow a finite probability for each bond to be absent from the lattice we show through the use of numerical and scaling arguments on both euclidean and hierarchical lattices that the model has two distinct scaling behaviors depending upon whether the concentration of bonds on the lattice is at or above the directed percolation threshold we are particularly interested in the exponents and defined by f t and x t describing the free energy and transverse fluctuations respectively above the percolation threshold the scaling behavior is governed by the standard random energy exponents 1 3 and 2 3 in 1 1 dimensions at the percolation threshold we predict and verify numerically in 1 1 dimensions the exponents 1 2 and v v where v and v are the directed percolation exponents in addition we predict the absence of a free phase in any dimension at the percolation threshold

robust performance of systems with structured uncertainties in state space abstract this paper considers robust performance analysis and state feedback design for systems with time varying parameter uncertainties the notion of a strongly robust h performance criterion is introduced and its applications in robust performance analysis and synthesis for nominally linear systems with time varying uncertainties are discussed and compared with the constant scaled small gain criterion it is shown that most robust performance analysis and synthesis problems under this strongly robust performance criterion can be transformed into linear matrix inequality problems and can be solved through finite dimensional convex programming the results are in general less conservative than those using small gain type criteria

minimal path on the hierarchical diamond lattice we consider the minimal paths on a hierarchical diamond lattice where bonds are assigned a random weight depending on the initial distribution of weights we find all possible asymptotic scaling properties the different cases found are the small disorder case the analog of levy s distributions with a power law decay at and finally a limit of large disorder which can be identified as a percolation problem the asymptotic shape of the stable distributions of weights of the minimal path are obtained as well as their scaling properties as a side result we obtain the asymptotic form of the distribution of effective percolation thresholds for finite size hierarchical lattices

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

renormalisation group study of a disordered model we study the potts model on a diamond hierarchical lattice with random interactions using weak disorder expansions we calculate analytically the position and the exponents of the random fixed point which appears when the specific heat exponent ap of the pure system becomes positive at ap 0 we find how the logarithmic singularity is modified by the disorder lastly we suggest that this model should present griffiths like singularities

global optimization for h sub spl infin control with constant diagonal scaling this paper considers the h sub spl infin control problem with constant diagonal scaling related to the robust control synthesis for systems with structured time varying uncertainties the problem is not convex in general and hence it is difficult to find a global solution the purpose of this paper is to provide an algorithm to find a suboptimal solution with any specified small tolerance from the globally optimal solution for the optimization problem the algorithm based on the triangle covering method is proposed the computational complexity analysis shows that its worst case order is polynomial in the inverse of the tolerance and the size of an a priori given interval of scaling with a fixed number of uncertainty blocks