a note on parameterization of the class of deadbeat controllers the problem of parameterizing the class of deadbeat controllers for a given discrete time system through the minimum number of parameters was solved by schlegel 1 this note shows how to utilize the above solution to study some problems in designing deadbeat controllers first an algorithm is developed to compute a controller which minimizes in an average sense a given objective function second a necessary and sufficient condition is given for the existence of an output deadbeat controller finally the problem of parameterizing the set of deadbeat controllers for those systems transformable to the phase variable block canonical form is reconsidered

frechet differentiability for a damped sine gordon equation abstract we consider a damped sine gordon equation with a variable diffusion coefficient the goal is to derive necessary conditions for the optimal set of parameters minimizing the objective function j first we show that the solution map is continuous under a weak assumption on the topology of the admissible set p then the solution map is shown to be weakly g teux differentiable on p implying the g teux differentiability of the objective function finally we show the frechet differentiability of j the optimal set of parameters is shown to satisfy a bang bang control law

robust numerical algorithm to the european option with illiquid markets abstract in this paper we consider illiquid european call option which is arisen in nonlinear black scholes equation in this respect we apply the newton s method to linearize it based on the obtained linear equation we obtain the approximate solutions recursively in two steps finally based on the conditions of kantorovich theorem we investigate the convergence analysis of the newton s method on the proposed problem finally the positivity of the solution is discussed

the design of deadbeat controllers by state transition graph two kinds of deadbeat control problems are considered one is the state deadbeat control problem and the other is the pointwise minimum time deadbeat control problem a simple graph called the state transition graph of a matrix is introduced and simple algorithms based on it giving deadbeat controllers are presented the set of pointwise minimum time deadbeat controllers is characterized the set of output feedback deadbeat controller is also considered

comments on design of optimal dead beat controllers it is shown that the system considered in the numerical example of the above paper belongs to a class of systems with n states and r inputs for which the set of all minimum time dead beat mtdb controllers is parameterized by an arbitrary matrix of order lambda 1 r n x n lambda r where is the greatest integer less than the ratio n r since the example treats the case of n 3 r 2 the mdtb controller is parameterized by a single scalar element

influence of solitons in the initial state on chaos in the driven damped sine gordon system abstract the appearance of chaos in the a c driven damped sine gordon equation is studied numerically several transitions from periodic to chaotic behaviour are investigated in detail for flat initial conditions spatial structures breather kink in the initial conditions smooth out many of these transitions and give rise to an interesting symbiosis of time and spatial intermittency this symbiosis appears to be due to the competition between the background tendency towards chaos and the system s preference to maintain a spatial pattern the way that this competition is relieved is also found to depend very strongly on symmetry in the initial conditions

frechet differentiability of solution mappings for semilinear second order evolution equations in this paper we establish the strong frechet differentiability of maps from the set of initial values and forcing terms into the set of solutions for semilinear second order evolution equations also under the weaker conditions of nonlinear terms we establish the strong g teaux differentiability of the solution maps an application of results to semilinear strongly damped wave equations is given

discontinuity of the percolation density in one dimensional 1 x y 2 percolation models we consider one dimensional percolation models for which the occupation probability of a bond kx y has a slow power decay as a function of the bond s length for independent models and with suitable reformulations also for more general classes of models it is shown that i no percolation is possible if for short bondskx y p 1 this dichotomy resembles one for the magnetization in 1 x y 2 ising models which was first proposed by thouless and further supported by the renormalization group flow equations of anderson yuval and hamann the proofs of the above percolation phenomena involve rigorous renormalization type arguments of a different sort

poisson point processes cascades and random coverings ofr n the generalized random energy model grem is formulated in terms of hierarchies of poisson point processes this allows one to relate the high temperature region with a random covering ofr n

analyticity of the partition function of the random energy model we consider the random energy model with complex temperature for beta lying in a suitable set the function zn beta ezn beta is at the thermodynamic limit an analytic function of beta analytic properties of the high temperature free energy follow directly

identification of discontinuous parameters in flow equations a problem of identifying possibly discontinuous diffusion coefficients in parabolic equations is considered general theorems on existence and convergence of galerkin approximations are proved in l 1 setting classes of functions of bounded variation are discussed and the variation estimates are obtained a double discretization method with the variations constraints is used in two and three dimensional problems and the numerical experiments are presented

parameterization of the class of deadbeat controllers this technical note deals with the problem of parameterizing the class of deadbeat controllers for a given system through the minimum of parameters it is shown that if n and m are dimensions of the state vector and control vector respectively and the i s are the controllability indexes then almost the whole class of deadbeat controllers is explicitly parameterizable through mn mu 1 3 mu 2 2m 1 mu m parameters

parametric time optimal control of linear discrete time systems by state feedback part 2 irregular kronecker invariants in an earlier paper part 1 a parametric state feedback time optimal control law was devised for the regular kronecker invariants on the basis of parametrization of the vector companion form the present paper describes a straight forward technique for obtaining the parametric feedback matrix by exploiting the parametric vector companion forms in the case of irregular kronecker invariants hidden properties of vector companion forms are also given which result in entirely different and interesting techniques for parametrization of the control law an illustrative example is presented

minimal time minimal order deadbeat regulator with internal stability this paper is concerned with the output deadbeat finite settling time regulation with internal stability for linear discrete time multivariable systems the two cases are treated separately the one is the regulation by state feedback and the other is the regulation through function observers for both cases the basic solvability conditions the minimal settling time and the characterizations of the minimal time regulators are derived throughout the paper the well posedness condition plays a fundamental role a deterministic version of the so called separation theorem in lqg problem is derived namely the minimal time state feedback regulator combined with the minimal time minimal order function observer yields the overall minimal time minimal order regulator by output feedback

finite size effects in random energy models and in the problem of polymers in a random medium by the use of traveling wave equations we calculate the finite size corrections to the free energy of random energy models in their low temperature phases and in the neighborhood of the transition temperature we find that although the extensive part of the free energy does not show any critical behavior when the temperature approaches its transition value the finite size corrections signal the transition by becoming singular we obtain a scaling form for these finite size corrections valid in the limitn andt t c by considering a generalized random energy model in the limit of a very large number of steps we obtain results for the finite size corrections in the problem of a polymer in a random medium

parameterization of the class of deadbeat controllers via the theory of decoupling a novel approach is presented for parameterizing the class of minimum time deadbeat controllers mtdc through the minimum number of parameters the approach is based on the theory of decoupling and the properties of square decouplable systems the main result is a compact parametric form for the class of mtdc of a discrete time system contrary to many existing techniques no special assumption on the invertibility of the transition matrix is required

the set of real numbers left uncovered by random covering intervals random covering intervals are placed on the real line in a poisson manner lebesgue measure governs their random locations and an arbitrary measure governs their random lengths the uncovered set is a regenerative set in the sense of hoffmann jorgensen s generalization of regenerative phenomena introduced by kingman thus as has previously been obtained by mandelbrot it is the closure of the image of a subordinator one that is identified explicitly well known facts about subordinators give shepp s necessary and sufficient condition on for complete coverage and when the coverage is not complete a formula for the hausdorff dimension of the uncovered set the method does not seem to be applicable when the covering is not done in a poisson manner or if the line is replaced by the plane or higher dimensional space

on the general solution of the state deadbeat control problem in this note the state deadbeat control problem is considered it is shown that after appropriate change of basis of input and state spaces the general solution of the state deadbeat control problem can be expressed completely by the rows of the powers of system matrix this result yields a very simple procedure for the calculation of a state feedback deadbeat control gain it also provides the number of free parameters which could be used for further design purposes the results are illustrated by an example at the end of the note

on deadbeat controllers the possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way a detailed analysis of the control sequence generated by any deadbeat controller is then presented

a random covering interpretation for the phase transition of the random energy model the random energy model is related to a random covering of the real line the phase transition is interpreted as the passage from a regime where a family of random intervals covers the line high temperature to a noncovering regime low temperature

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

thermodynamics for the zero level set of the brownian bridge the random set of instants where the brownian bridge vanishes is constructed in terms of a random branching process the hausdorff measure supported by this set is shown to be equivalent to the partition function of a special class of disordered systems this similarity is used to show rigorously the existence of a phase transition for this particular class of disordered systems moreover it is shown that at high temperature the specific free energy has the strong self averaging property and that at low temperature it has no self averaging property the unicity at high temperature and the existence of many limits at low temperature are established almost surely in the disorder

pole assignment by state transition graph the pole assignment problem is considered using the graph representation of a matrix the parametrization of controllers which have a specified characteristic polynomial is given a simple algorithm based on graphs is presented and two examples are given