perfect and subperfect regulation in linear multivariable control systems this paper is concerned with the synthesis of a high gain feedback control called perfect regulation p r for linear multivariable systems with external signals the existence condition for p r is derived in which the minimum phase property plays an essential role the use of an observer is discussed for achieving p r under restricted state observation some asymptotically ideal feedback properties are demonstrated such as the complete desensitization the complete servo performance with decoupling and the complete disturbance rejection which formulate the loop tightness for multivariable systems a design method for applying p r to non minimum phase systems called subperfect regulation s p r is proposed based on the factorization of the plant transfer function matrix into the minimum phase part and the totally non minimum phase part it is a multivariable extension of a well known design technique for scalar systems to overcome the difficulty of phase non minimality computational procedures for p r and s p r are discussed an illustrative example is shown

biased random walk on the trace of biased random walk on the trace of we study the behaviour of a sequence of biased random walks x scriptscriptstyle i i ge 0 on a sequence of random graphs where the initial graph is mathbb z d and otherwise the graph for the ith walk is the trace of the i 1 st walk the sequence of bias vectors is chosen so that each walk is transient we prove the aforementioned transience and a law of large numbers and provide criteria for ballisticity and sub ballisticity we give examples of sequences of biases for which each x scriptscriptstyle i i ge 1 is transient but not ballistic and the limiting graph is an infinite simple self avoiding path we also give examples for which each x scriptscriptstyle i i ge 1 is ballistic but the limiting graph is not a simple path

biased random walk on critical galton watson trees conditioned to survive we consider the biased random walk on a critical galton watson tree conditioned to survive and confirm that this model with trapping belongs to the same universality class as certain one dimensional trapping models with slowly varying tails indeed in each of these two settings we establish closely related functional limit theorems involving an extremal process and also demonstrate extremal aging occurs

on the asymptotic behaviour of first passage times for transient random walk let x denote the time at which a random walk with finite positive mean first passes into x wherex 0 this paper establishes the asymptotic behaviour of pr x n asn for fixedx in two cases in the first case the left hand tail of the step distribution is regularly varying and in the second the step distribution satisfies a one sided cramer type condition as a corollary it follows that in the first case mathop lim limits n to infty pr x n pr 0 n coincides with the limit of the same quantity for recurrent random walk satisfying spitzer s condition but in the second case the limit is more complicated

escape regimes of biased random walks on galton watson trees we study biased random walk on subcritical and supercritical galton watson trees conditioned to survive in the transient sub ballistic regime by considering offspring laws with infinite variance we extend previously known results for the walk on the supercritical tree and observe new trapping phenomena for the walk on the subcritical tree which in this case always yield sub ballisticity this is contrary to the walk on the supercritical tree which always has some ballistic phase

a law of large numbers for random walks in random environment we derive a law of large numbers for a class of multidimensional random walks in random environment satisfying a condition which first appeared in the work of kalikow the approach is based on the existence of a renewal structure under an assumption of transience in the direction l this extends to a multidimensional context previous work of kesten our results also enable proving the convergence of the law of the environment viewed from the particle toward a limiting distribution

the speed of biased random walk on percolation clusters we consider biased random walk on supercritical percolation clusters in 2 we show that the random walk is transient and that there are two speed regimes if the bias is large enough the random walk has speed zero while if the bias is small enough the speed of the random walk is positive

convergence in the boundary layer for singularly perturbed equations a singularly perturbed linear finite dimensional ordinary differential equation is considered on the half line 0 the reduced system is assumed to have a unique solution in the sense of distributions it is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense and the order of the limiting distribution is computed an application to the optimal linear quadratic regulator with cheap control is described

biased random walks on galton watson trees we consider random walks with a bias toward the root on the family tree t of a supercritical galton watson branching process and show that the speed is positive whenever the walk is transient the corresponding harmonic measures are carried by subsets of the boundary of dimension smaller than that of the whole boundary when the bias is directed away from the root and the extinction probability is positive the speed may be zero even though the walk is transient the critical bias for positive speed is determined

slow movement of a random walk on the range of a random walk in the presence of an external field in this article a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions d ge 5 this demonstrates that unlike in the supercritical percolation setting a slowdown effect occurs as soon as a non trivial bias is introduced the proof applies a decomposition of the underlying simple random walk path at its cut times to relate the associated biased random walk to a one dimensional random walk in a random environment in sinai s regime via this approach a corresponding aging result is also proved

perturbation analysis of a system of quasi variational inequalities for optimal stochastic scheduling optimal scheduling of continuously evolving dynamical systems involves the analysis of certain partial differential inequalities on solution dependent domains these are the quasi variatlonai inequalities qvi s introduced for such problems by a bensoussan and j l lions they arise naturally in such applications as inventory control and unit commitment scheduling in electric energy systems qvi s are in these contexts the analog of the dynamic programming partial differential equations of r bellman for continuous control problems analytical treatment of qvi s involves not only the solution of partial differential inequalities but also the simultaneous analysis of the free boundaries of the domain of the solution in effect the optimal return function is the solution of the inequalities and the optimal control switching policy is defined by the free boundaries this paper considers a system of two singularly perturbed second order quasi variational inequalities with a turning point in a bounded domain in r1 asymptotic approximations for the free boundaries are derived using standard perturbation analysis for boundary value problems also local regularity properties of the limit solution are obtained the results are illustrated by a parametric study of a simple model of commitment scheduling for a single unit in a power generation system

singular perturbational model reduction in the frequency domain singular perturbational approximations for linear continuous time and discrete time systems are developed in the frequency domain it is shown that the familiar singular perturbational result is an approximation at the origin in the complex plane however if the system has multiple time scale effects other approximations can be obtained at different locations on the negative real axis to emphasize such behavior the relationship between singular perturbational approximations and direct subsystem elimination is also investigated

phase transition for the speed of the biased random walk on the supercritical percolation cluster we prove the sharpness of the phase transition for the speed in biased random walk on the supercritical percolation cluster on d that is for each d 2 and for any supercritical parameter p pc we prove the existence of a critical strength for the bias such that below this value the speed is positive and above the value it is zero we identify the value of the critical bias explicitly and in the subballistic regime we find the polynomial order of the distance moved by the particle each of these conclusions is obtained by investigating the geometry of the traps that are most effective at delaying the walk a key element in proving our results is to understand that on large scales the particle trajectory is essentially one dimensional we prove such a dynamic renormalization statement in a much stronger form than was previously known 2013 wiley periodicals inc

brief paper singular perturbation analysis of a receding horizon controller a new receding horizon approach to the linear regulator problem is presented at each instant of time the control strategy is based on the minimization of a quadratic performance index extending over an interval of fixed length into the future connections with standard results are discussed and under general assumptions the closed loop system is shown to be asymptotically stable a potential advantage of our method lies in the fact that a singular perturbation analysis is well posed this indicates that for plants containing slow and fast modes the design procedure can be split up into two stages the resulting composite control exhibits attractive engineering properties use and effectiveness of the proposed techniques are demonstrated by investigating a practical example

on the anisotropic walk on the supercritical percolation cluster we investigate in this work the asymptotic behavior of an anisotropic random walk on the supercritical cluster for bond percolation on d d 2 in particular we show that for small anisotropy the walk behaves in a ballistic fashion whereas for strong anisotropy the walk is sub diffusive for arbitrary anisotropy we also prove the directional transience of the walk and construct a renewal structure

asymptotic stability of nonlinear multiparameter singularly perturbed systems sufficient conditions are derived to guarantee the asymptotic stability of a class of nonlinear singularly perturbed systems with several perturbation parameters of the same order estimates of the region of attraction and bounds on the small parameters are obtained

generalized biderivations of nest algebras let n be a nest on a complex separable hilbert space h and n be the associated nest algebra in this paper we prove that every biderivation of n is an inner biderivation if and only if dim 0 1 or dimh 1 and that every generalized biderivation of n is an inner generalized biderivation if dim 0 1 and dimh 1

a reduction process for perturbed markov chains given a perturbed markov chain with generator a varepsilon a 0 varepsilon a 1 varepsilon 2 a 2 cdots it is shown that to each time scale t t varepsilon t varepsilon 2 cdots is associated a reduced markov chain this process of reduction has only finitely many steps it is given in a recursive way and each reduced chain admits as state space the recurrent classes of the reduced chain defined at the previous stage it is shown that if lambda is an eigenvalue different from zero of the generator of the kth reduced chain with multiplicity p then a varepsilon admits p eigenvalues lambda varepsilon such that lambda varepsilon varepsilon k lambda o varepsilon k a basis of ker a 0 resp ker a 0 which is robust to the perturbation is constructed

a singular perturbation approach to modeling and control of markov chains finite state continuous time markov processes with weak interactions are modeled as singularly perturbed systems aggregate states are obtained using a grouping algorithm two time scale expansions simplify cost equations and lead to decentralized optimization algorithms

a multimodel approach to stochastic nash games a decentralized filtering and control scheme is presented for obtaining low order nash equilibrium strategies for decision makers using different models of the same large scale system multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables the small parameters are appropriately scaled so that the variables in both time scales are well defined the decision makers have decentralized information structures and are constrained to use only finite dimensional compensators of a specified dimension it is shown that the proposed scheme is in fact the asymptotic limit of the exact solution as the small parameters go to zero

biased random walks on galton watson trees with leaves we consider a biased random walk xn on a galton watson tree with leaves in the sub ballistic regime we prove that there exists an explicit constant 0 1 depending on the bias such that xn is of order n denoting n the hitting time of level n we prove that n n1 is tight moreover we show that n n1 does not converge in law at least for large values of we prove that along the sequences n k k n n1 converges to certain infinitely divisible laws key tools for the proof are the classical harris decomposition for galton watson trees a new variant of regeneration times and the careful analysis of triangular arrays of i i d heavy tailed random variables

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods