distributed control for identical dynamically coupled systems a decomposition approach we consider the problem of designing distributed controllers for a class of systems which can be obtained from the interconnection of a number of identical subsystems if the state space matrices of these systems satisfy a certain structural property then it is possible to derive a procedure for designing a distributed controller which has the same interconnection pattern as the plant this procedure is basically a multiobjective optimization under linear matrix inequality constraints with system norms as performance indices the explicit expressions for computing these controllers are given for both h infin or h 2 performance and both for static state feedback and dynamic output feedback in discrete time at the end of the paper two application examples illustrate the effectiveness of the approach

ensemble control of bloch equations in this article we study a class of control problems which involves controlling a continuum of dynamical systems with different values of parameters characterizing the system dynamics by using the same control signal we call such problems control of ensembles the motivation for looking into these problems comes from the manipulation of an ensemble of nuclear spins in nuclear magnetic resonance nmr spectroscopy and imaging mri with dispersions in natural frequencies and the strengths of the applied radio frequency rf field from the standpoint of mathematical control theory the challenge is to simultaneously steer a continuum of systems between points of interest with the same control input this raises some new and unexplored questions about controllability of such systems we show that controllability of an ensemble can be understood by the study of the algebra of polynomials defined by the noncommuting vector fields that govern the system dynamics a systematic study of these systems has immediate applications to broad areas of control of ensembles of quantum systems as arising in coherent spectroscopy and quantum information processing the new mathematical structures appearing in such problems are excellent motivation for new developments in control theory

a method for solving exact controllability problems governed by closed quantum spin systems the liouville von neumann master equation models closed quantum spin systems that arise in nuclear magnetic resonance applications in this paper an efficient and robust computational framework to solve exact controllability problems governed by the liouville von neumann master equation is presented the proposed control framework is based on a new optimisation formulation of exact controllability quantum spin problems that allows the application of efficient computational techniques this formulation results in an optimality system with four differential equations and an optimality condition the differential equations are approximated with an appropriate modified crank nicholson scheme and the resulting discretised optimality system is solved with a matrix free krylov newton scheme combined with a cascadic nonlinear conjugate gradient initialisation results of numerical experiments demonstrate the ability of the proposed framework to solve quantum spin exact controllability control problems

ensemble observability of linear systems we address the observability problem for ensembles that are described by probability distributions the problem is to reconstruct a probability distribution of the initial state from the time evolution of the probability distribution of the output under a classical finite dimensional linear system we present two solutions to this problem one based on formulating the problem as an inverse problem and the other one based on reconstructing all the moments of the distribution the first approach leads us to a connection between the reconstruction problem and mathematical tomography problems in the second approach we use the framework of tensor systems to describe the dynamics of the moments which leads to a more systems theoretic treatment of the reconstruction problem furthermore we show that both frameworks are inherently related the appeal of having two dual viewpoints the first being more geometric and the second one being more systems theoretic is illuminated in several examples of theoretical or practical importance

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

on a system of two nonlinear difference equations abstract in this paper we study the oscillatory behavior the boundedness of the solutions and the global asymptotic stability of the positive equilibrium of the system of two nonlinear difference equationsxn 1 a yn xn p yn 1 a xn yn q n 0 1 p qare positive integers

minimum time frictionless atom cooling in harmonic traps frictionless atom cooling in harmonic traps is formulated as a time optimal control problem and a synthesis of optimal controlled trajectories is obtained

on some solvable systems of difference equations abstract we show that the following systems of difference equations x n 1 u n 1 v n y n 1 w n 1 s n n n 0 where u n v n w n s n are some of the sequences x n or y n with real initial values x 0 and y 0 are solvable in fourteen out of sixteen possible cases two cases are left unsolved probably the most interesting is the result in the case u n x n v n x n w n x n s n y n where a fascinating formula is obtained in an elegant way by using some ad hoc ideas

controllability of a quantum particle in a moving potential well we consider a nonrelativistic charged particle in a 1d moving potential well this quantum system is subject to a control which is the acceleration of the well it is represented by a wave function solution of a schrodinger equation the position of the well together with its velocity we prove the following controllability result for this bilinear control system given 0 close enough to an eigenstate and f close enough to another eigenstate the wave function can be moved exactly from 0 to f in finite time moreover we can control the position and the velocity of the well our proof uses moment theory a nash moser implicit function theorem the return method and expansion to the second order

growth of sobolev norms and controllability of the schrodinger equation in this paper we obtain a stabilization result for both linear and nonlinear schrodinger equations under generic assumptions on the potential then we consider the schrodinger equations with a potential which has a random time dependent amplitude we show that if the distribution of the amplitude is sufficiently non degenerate then any trajectory of the system is almost surely non bounded in sobolev spaces

domains of undefinable solutions of some equations and systems of difference equations for some classes of difference equations and systems of difference equations we find the sets of initial values for which solutions of these equations and systems are not well defined so called domains of undefinable solutions

geometric optimal control of the contrast imaging problem in nuclear magnetic resonance the objective of this article is to introduce the tools to analyze the contrast imaging problem in nuclear magnetic resonance optimal trajectories can be selected among extremal solutions of the pontryagin maximum principle applied to this mayer type optimal problem such trajectories are associated to the question of extremizing the transfer time hence the optimal problem is reduced to the analysis of the hamiltonian dynamics related to singular extremals and their optimality status this is illustrated by using the examples of cerebrospinal fluid water and grey white matter of cerebrum

more on a rational second order difference equation abstract here we give natural explanations for some recent relations for the solutions of the following difference equation z n 2 z n 1 3 z n 2 2 z n 1 2 n n 0 and extend them for the case of complex initial values we also present some other properties related to solutions of the equation as well as some properties of the solutions of an associate difference equation of first order

on fourteen solvable systems of difference equations abstract in this paper we mainly consider the systems of difference equations x n 1 1 p n q n y n 1 1 r n s n n n 0 where each of the sequences p n q n r n and s n represents either the sequence x n or the sequence y n with nonzero real initial values x 0 and y 0 then we solve fourteen out of sixteen possible systems it is noteworthy to depict that the solutions are presented in terms of fibonacci numbers for twelve systems of these fourteen systems

local controllability of a one dimensional beam equation we prove that the beam equation with clamped ends is locally controllable in a h 5 epsilon times h 3 epsilon 0 1 mathbb r neighborhood of a particular trajectory of the free system with epsilon 0 and with control functions in h 1 0 0 t mathbb r ball marsden and slemrod already proved that this equation is not controllable in h 2 0 times l 2 0 1 mathbb r with control functions in l r text loc mathbb r mathbb r r 1 this article justifies that their negative result is due to a choice of functional spaces which does not allow controllability our proof uses moment theory and the nash moser theorem

on some systems of difference equations abstract in this note we show that the following systems of difference equations u n 1 v n 1 v n v n 1 u n 1 u n u n 1 v n 1 u n v n 1 u n 1 v n u n 1 u n 1 v n v n 1 v n 1 u n with n n 0 and complex initial values u 0 and v 0 are solvable explicitly by means of riccati equations and based on the formulae for the general solutions we present the behaviour of their solutions as n while the result is natural for the first system it is a bit surprising for the other two systems

performance measures independent of adjustment an explanation and extension of taguchi s signal to noise ratios parameter design is a method popularized by japanese quality expert g taguchi for designing products and manufacturing processes that are robust to uncontrollable variations in parameter design taguchi s stated objective is to find the settings of product or process design parameters that minimize average quadratic loss that is the average squared deviation of the response from its target value yet in practice to choose the settings of design parameters he maximizes a set of measures called signal to noise ratios in general he gives no connection between these two optimization problems in this article we show that for certain underlying models for the product or process response maximization of the signal to noise ratio leads to minimization of average quadratic loss the signal to noise ratios take advantage of the existence of special design parameters called adjustment parameters when these parameters exist use of the signal to noise ratio allows the parameter design optimization procedu

robust controllability assessment via semi definite programming abstract this paper presents a new framework for systematic assessment of the controllability of uncertain linear time invariant lti systems the objective is to evaluate controllability of an uncertain system with norm bounded perturbation over the entire uncertain region the method is based on a singular value minimization problem over the entire complex plane to solve the problem first a necessary and sufficient condition is proposed to avert the difficulties of griding over the complex plane and to verify the controllability of directed and undirected networks in a single step secondly the results are utilized to formulate the problem as two lyapunov based linear matrix inequalities lmis for undirected networks and four lmis for directed ones the proposed approach is subsequently extended to evaluate the maximum guaranteed distance to uncontrollability of a system through a quasi convex optimization problem whose solution is guaranteed to be globally optimal by duality analogous results are established for robust observability of directed and undirected networks the proposed framework is implemented efficiently using lmi tools and provides a fast and reliable tool for the assessment of robust controllability and by duality robust observability it is also extendable to robust control system design problems such as control node selection for uncertain systems

a moment based approach to ensemble controllability of linear systems abstract in this paper we introduce a new perspective on the l 2 ensemble controllability problem of linear time invariant systems using an l 2 framework the reformulation results from focussing on the controllability of the ensemble s moments which evolve under a linear system defined on the space of square summable sequences for a specific class of ensembles a necessary and sufficient condition can be stated in terms of truncations of infinite kalman matrices we illustrate the analysis in this framework on several examples which highlight the possibility of using elementary structural arguments in proving or disproving the controllability of an ensemble s moments as well as essential differences to the uniform ensemble controllability property which is mostly considered in the literature

on the difference equation xn xn 2 bn cnxn 1xn 2 abstract we prove that the difference equation x n x n 2 b n c n x n 1 x n 2 n n 0 where b n n n 0 and c n n n 0 are sequences periodic with period two and the initial values x 2 x 1 are real numbers can be solved explicitly some applications of obtained formulae are given

ensemble control of finite dimensional time varying linear systems in this article we investigate the problem of simultaneously steering an uncountable family of finite dimensional time varying linear systems with the same control signal this class of control problems motivates further research in the new subject of control theory called ensemble control a notion coming from the study of complex spin dynamics in nuclear magnetic resonance spectroscopy and imaging we derive the necessary and sufficient controllability conditions and an accompanying analytical optimal control law for an ensemble of finite dimensional time varying linear systems we show that ensemble controllability is in connection with singular values of the operator characterizing the system dynamics in addition the problem of optimal ensemble control of harmonic oscillators is studied to demonstrate the controllability results we show that the optimal solutions are pertinent to the study of time frequency limited signals and prolate spheroidal wave functions a systematic study of ensemble control systems has immediate applications to dynamical systems with parameter uncertainty as well as to wide ranging areas such as neuroscience and quantum control the work in ensemble control will foster further developments in mathematical control and systems theory

controllability issues for continuous spectrum systems and ensemble controllability of bloch equations we study the controllability of the bloch equation for an ensemble of non interactinghalf spins inastaticmagneticfield withdispersioninthelarmorfrequency this system may be seen as a prototype for infinite dimensional bilinear systems with continuous spectrum whose controllability is not well understood we provide several mathematical answers with discrimination between approximate and exact controlla bility and between finite time or infinite time controllability this system is not exactly controllable in finite time t with bounded controls in l 2 0 t but it is approximately controllable in l in finite time with unbounded controls in l 0 moreover we propose explicit controls realizing the asymptotic exact controllability to a uniform state of spin 1 2o r 1 2

stabilization of an arbitrary profile for an ensemble of half spin systems we consider the feedback stabilization of a variable profile for an ensemble of non interacting half spins described by the bloch equations we propose an explicit feedback law that stabilizes asymptotically the system around a given arbitrary target profile the convergence proof is done when the target profile is entirely in the south hemisphere or in the north hemisphere of the bloch sphere the convergence holds for initial conditions in a h1 neighbourhood of this target profile this convergence is shown for the weak h1 topology the proof relies on an adaptation of the lasalle invariance principle to infinite dimensional systems numerical simulations illustrate the efficiency of these feedback laws even for initial conditions far from the target profile

on the difference equation xn xn kb cxn 1 xn k abstract we describe the behavior of well defined solutions of the difference equation x n x n k b cx n 1 x n k n n 0 where k n parameters b c and the initial values x k x 1 are real numbers these results among others improve and extend our results in s stevic more on a rational recurrence relation appl math e notes 4 2004 80 85

stabilization for an ensemble of half spin systems feedback stabilization of an ensemble of non interacting half spins described by the bloch equations is considered this system may be seen as an interesting example for infinite dimensional systems with continuous spectra we propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin 1 2 or 1 2 the proof of the convergence is done locally around the equilibrium in the h 1 topology this local convergence is shown to be a weak asymptotic convergence for the h 1 topology and thus a strong convergence for the c 0 topology the proof relies on an adaptation of the lasalle invariance principle to infinite dimensional systems numerical simulations illustrate the efficiency of these feedback laws even for initial conditions far from the equilibrium

joint estimation of location dispersion and random effects in robust design this article presents a methodology for simultaneously modeling three components of a general mixed model approach to robust design location fixed effects dispersion effects and random effects control noise and random factors can be accommodated with this approach parameters associated with all three are estimated jointly using residual maximum likelihood and assuming normality simulated and real datasets illustrate the key concepts and advantages over previously proposed approaches

on a solvable system of difference equations of fourth order it is shown that the next system of k difference equationsx n j a n j x n k j b n j i 1 kx n i s j i 1 c n j n n 0 j 1 k where a n j b n j c n j n n 0 j 1 k and initial values x i j i j 1 k are real numbers and where s n 1 k is defined by s km j j 1 j 1 k 1 s km k 1 m n 0 can be solved in closed form in an elegant way some applications of obtained formulas for the case when the sequences a n j b n j and c n j are k periodic are also given

sampled observability and state estimation of linear discrete ensembles we consider the problem of reconstructing the initial states of a finite group of structurally identical linear systems in the situation that output measurements of the individual systems are received at discrete time steps and in an anonymized manner while we do know all output measurements of the individual systems in the group we do not know which output measurement corresponds to which system this state estimation problem addresses the essence of state estimation problems for populations in which the output measurements of the individual systems are given only as statistics we adopt a measure theoretical approach in which the group is modelled by an lti system describing the structure of the individual systems and an initial state which is expressed by a discrete measure in this framework we derive a geometric characterization for the state estimation to admit a unique solution which combined with a result on the observability of linear systems under irregular sampling yields a sufficient condition for the sampled observability of discrete ensembles as a supplement to our theoretical findings we provide illustrations by means of simulation examples furthermore we consider the practical state estimation problem under noisy output measurements

boundedness character of a class of difference equations abstract a complete picture regarding the boundedness character of positive solutions to the following difference equation x n max a x n 1 p x n k p n n 0 where k 2 and the parameters a and p are positive real numbers is given in particular for the case p k 1 0 k k k 1 k 1 we prove that all solutions to the equation are bounded we also present corresponding results concerning the following closely related difference equation x n a x n 1 p x n k p n n 0

singular trajectories and the contrast imaging problem in nuclear magnetic resonance in this article the contrast imaging problem in nuclear magnetic resonance is modeled as a mayer problem in optimal control whose solutions can be parameterized using pontryagin s maximum principle and analyzed using geometric optimal control in particular the optimal problem can be mainly reduced to the analysis of the hamiltonian dynamics describing the singular trajectories and encoding their optimality status

ensemble observability of bloch equations with unknown population density abstract we introduce in the paper a novel observability problem for a large population in the limit a continuum ensemble of nonholonomic control systems with unknown population density we address the problem by focussing on a prototype namely the ensemble of bloch equations which is known for its use of describing the evolution of the bulk magnetization of a collective of non interacting nuclear spins in a static field modulated by a radio frequency rf field the dynamics of the equations are structurally identical but show variations in larmor dispersion and rf inhomogeneity we assume that the initial state of any individual system i e individual bloch equation is unknown and moreover the population density of these individual systems is also unknown furthermore we assume that at any time there is only one scalar measurement output at our disposal the measurement output integrates a certain observation function common to all individual systems over the continuum ensemble the observability problem we pose in the paper is thus the following whether one is able to use the common control input i e the rf field and the single measurement output to estimate both the initial states of the individual systems and the population density amongst other things we establish a sufficient condition for the ensemble system to be observable we show that if the common observation function is any harmonic homogeneous polynomial of positive degree then the ensemble system is observable the proof of the result utilizes tools from representation theory of lie algebras although the results established in the paper are for the specific ensemble of bloch equations the approach developed along the analysis can be generalized to investigate observability of other ensemble systems with single integrated measurement outputs

solutions of a max type system of difference equations we show in an elegant way that the general solution to the following max type system of difference equations xn 1 maxaxn ynxn yn 1 maxayn xnyn n n0 for the case y0 x0 a 0 y0 x0 max a 1 a is given by xn afk n 1 n x0fk n y0fk n 1 n n n y1 x0 y0 and yn y0fk n 1 1afk n 1 n 1x0fk n 1 1 1 n n 2 where k n n for n even k n n 1 for n odd n n0 n n mod2 for n n0 and where the sequence fn n n is the fibonacci sequence correcting and giving a proof of a wrong result in the paper d simsek b demir c cinar on the solutions of the system of difference equations xn 1 max a xn yn xn yn 1 max a yn xn yn discrete dyn nat soc 2009 2009 11 pp article id 325296

on some periodic systems of max type difference equations we show that all positive solutions to the system of max type difference equations xn 1 max1 i m1f1ixn ki 1 1 1 xn ki 2 1 2 xn ki l 1 l n xn s 1 xn 2 max1 i m2f2ixn ki 1 2 1 xn ki 2 2 2 xn ki l 2 l n xn s 2 xn l max1 i mlflixn ki 1 l 1 xn ki 2 l 2 xn ki l l l n xn s l n n0 where s l mj ki t j n j t 1 l and for a fixed j i 1 mj and where the functions fji 0 l n0 0 j 1 l i 1 mj satisfy some conditions are eventually periodic with not necessarily prime period s a related result for the corresponding system of min type difference equations is also proved

on the system xn 1 ynx n k yn k 1 an bnynxn k yn 1 xnyn k xn k 1 cn dnxnyn k it is shown that the system of difference equationsx n 1 y nx n ky n k 1 a n b ny nx n k y n 1 x ny n kx n k 1 c n d nx ny n k email protected n 0 where email protected n the sequences a n b n c n d n email protected n 0 and the initial values x i y i i 0 email protected are real numbers can be solved in closed form asymptotic behavior of well defined solutions of the system for the case when all the sequences a n b n c n and d n are constant is studied in detail

control in the spaces of ensembles of points we study the controlled dynamics of the ensembles of points of a riemannian manifold m parameterized ensemble of points of m is the image of a continuous map gamma theta to m where the

on the system of difference equations xn cnyn 3 an bnyn 1xn 2y n 3 yn γnxn 3 αn βnxn 1yn 2 xn 3 we show that the system of difference equationsx n c ny n 3a n b ny n 1x n 2y n 3 y email protected nx n email protected email protected nx n 1y n 2x n 3 email protected n 0 where the sequences a n b n c n a n b n c n email protected n 0 and initial values x i y i email protected 1 2 3 are real numbers such that c n 0 c n 0 email protected n 0 can be solved in closed form and for the case when all the sequences a n b n c n a n b n and c n are constant we describe the asymptotic behavior of well defined solutions of the system

a characterization of von neumann rings in terms of linear systems abstract a new characterization of commutative von neumann regular rings is given in terms of linear control systems having locally a brunovsky canonical form the problem of enumerating reachable systems over certain von neumann regular ring is solved extending classical results over fields

optimal ensemble control of stochastic time varying linear systems abstract we consider the optimal guidance of an ensemble of independent structurally identical finite dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by applying a common control function without the use of feedback our exploration of such ensemble control systems is motivated by practical control design problems in which variation in system parameters and stochastic effects must be compensated for when state feedback is unavailable such as in pulse design for nuclear magnetic resonance spectroscopy and imaging in this paper we extend the notion of ensemble control to stochastic linear systems with additive noise and jumps which we model using white gaussian noise and poisson counters respectively and investigate the optimal steering problem in our main result we prove that the minimum norm solution to a fredholm integral equation of the first kind provides the optimal control that simultaneously minimizes the mean square error mse and the error in the mean of the terminal state the optimal controls are generated numerically for several example ensemble control problems and monte carlo simulations are used to illustrate their performance this work has immediate applications to the control of dynamical systems with parameter dispersion or uncertainty that are subject to additive noise which are of interest in quantum control neuroscience and sensorless robotic manipulation

asymptotic ensemble stabilizability of the bloch equation in this paper we are concerned with the stabilizability to an equilibrium point of an ensemble of non interacting half spins we assume that the spins are immersed in a static magnetic field with dispersion in the larmor frequency and are controlled by a time varying transverse field our goal is to steer the whole ensemble to the uniform down position two cases are addressed for a finite ensemble of spins we provide a control function in feedback form that asymptotically stabilizes the ensemble in the down position generically with respect to the initial condition for an ensemble containing a countable number of spins we construct a sequence of control functions such that the sequence of the corresponding solutions pointwise converges asymptotically in time to the target state generically with respect to the initial conditions the control functions proposed are uniformly bounded and continuous

on a nonlinear generalized max type difference equation abstract the boundedness character of positive solutions of the following max type difference equation x n max a x n 1 p x n k r n n 0 where k n 1 the parameters a and r are positive and p is a nonnegative real number is studied in this paper our main results considerably improve results appearing in the literature

on a system of difference equations abstract we show that the system of difference equations x n 1 ax n 1 by n x n 1 c y n 1 y n 1 x n y n 1 n n 0 where the parameters a b c and initial values x 1 x 0 y 1 y 0 are real numbers can be solved considerably improving the results in the literature

controllability for distributed bilinear systems this paper studies controllability of systems of the form dw dt mathcal a w p t mathcal b w where mathcal a is the infinitesimal generator of a c 0 semigroup of bounded linear operators e mathcal a t on a banach space x mathcal b x to x is a c 1 map and p in l 1 0 t mathbb r is a control the paper i gives conditions for elements of x to be accessible from a given initial state w 0 and ii shows that controllability to a full neighborhood in x of w 0 is impossible for dim x infty examples of hyperbolic partial differential equations are provided

on a third order system of difference equations abstract we show that the system of difference equations x n 1 a 1 x n 2 b 1 y n z n 1 x n 2 c 1 y n 1 a 2 y n 2 b 2 z n x n 1 y n 2 c 2 z n 1 a 3 z n 2 b 3 x n y n 1 z n 2 c 3 n n 0 where the parameters a i b i c i i 1 2 3 and initial values x j y j z j j 0 1 2 are real numbers can be solved developing further the results in the literature

global stability of a max type difference equation we show that every positive solution to the difference equationx n maxa 1x n p 1 a 1 a 2x n p 2 a 2 a kx n p k a k n n 0 where p i i 1 k are natural numbers such that 1 0 a i 1 1 i 1 k converges to max 1 i ka i 1 a i 1 this result improves and complements the main result in our recent note s stevic global stability of a difference equation with maximum appl math comput 210 2009 525 529 since it also considers the case when a i 1 0 i 1 k

on controllability of diagonal systems with one dimensional input space abstract this paper deals with diagonal systems on a hilbert state space with a one dimensional input space and a possibly unbounded control operator a priori it is not assumed that the input operator is admissible necessary and sufficient conditions for different notions of controllability such as null controllability exact controllability and approximate controllability are presented these conditions which are given in terms of the eigenvalues of the diagonal operator and in terms of the control operator are linked with the theory of interpolation in hardy spaces

on the controllability of quantum transport in an electronic nanostructure we investigate the controllability of quantum electrons trapped in a two dimensional device typically a metal oxide semiconductor mos field effect transistor the problem is modeled by the schrodinger equation in a bounded domain coupled to the poisson equation for the electrical potential the controller acts on the system through the boundary condition on the potential on a part of the boundary modeling the gate we prove that generically with respect to the shape of the domain and boundary conditions on the gate the device is controllable we also consider control properties of a more realistic nonlinear version of the device taking into account the self consistent electrostatic poisson potential

ensemble control of time invariant linear systems with linear parameter variation in this paper we study the control of a class of time invariant linear ensemble systems whose natural dynamics are linear in the system parameter this class of ensemble control systems arises from practical engineering and physical applications such as transport of quantum particles and control of uncertain harmonic systems we establish explicit algebraic criteria to examine controllability of such ensemble systems our derivation is based on the notion of polynomial approximation where the elements of the reachable set of the ensemble system are represented in polynomials of the system parameter and used to approximate the desired state of interest in addition we highlight the role of the spectra of the system matrices play in the determination of ensemble controllability finally illustrative examples and numerical simulations for optimal control of this class of linear ensemble systems are presented to demonstrate the theoretical results

cost driven parameter design parameter design methodology has focused primarily on the quadratic loss function which can often be solved by using a two step procedure involving the minimization of a dispersion measure and then adjusting the mean to target in some practical situations however the loss can be nonquadratic or highly skewed by building on a theory of leon and wu we develop a modeling and data analysis strategy for a general loss function in which the quality characteristic follows a location scale model the only difference from the two step procedure just mentioned is the adjustment step in which the mean is moved to that side of the target with lower cost the technique is illustrated on an experiment involving epitaxial layer growth in integrated circuit fabrication

on difference equations with powers as solutions and their connection with invariant curves abstract we look for nonlinear systems of difference equations which have power functions as solutions and we find a connection to the theory of invariant curves and to self reversed polynomials in particular we construct algebraic solutions of a special equation of invariant curves

periodicity of a class of nonautonomous max type difference equations abstract in this note we prove several general and easily applicable results regarding the periodicity of positive solutions of the following difference equations x n max f 1 x n k 1 n f m x n k m n x n s n n 0 and x n min f 1 x n k 1 n f m x n k m n x n s n n 0 where 1 k 1 k m m s n and where the functions f i 0 n 0 0 1 i m satisfy some additional conditions these results considerably extend and unify numerous results on max type difference equations existing in the literature

on the nonautonomous difference equation xn 1 an xn 1pxnq abstract in this paper we study the asymptotic behavior and the periodicity of the positive solutions of the nonautonomous difference equation x n 1 a n x n 1 p x n q n 0 1 where an is a positive bounded sequence p q 0 and x 1 x0 are positive numbers

local controllability and non controllability for a 1d wave equation with bilinear control abstract we consider a linear wave equation on the interval 0 1 with bilinear control and neumann boundary conditions we study the controllability of this nonlinear control system locally around a constant reference trajectory we prove that the following results hold generically for every t 2 this system is locally controllable in h 3 h 2 in time t with controls in l 2 0 t r for t 2 this system is locally controllable up to codimension one in h 3 h 2 in time t with controls in l 2 0 t r the reachable set is locally a non flat submanifold of h 3 h 2 with codimension one for every t 2 this system is not locally controllable more precisely the reachable set with controls in l 2 0 t r is contained in a non flat submanifold of h 3 h 2 with infinite codimension the proof of these results relies on the inverse mapping theorem and second order expansions

uniform ensemble controllability for one parameter families of time invariant linear systems abstract in this paper we derive necessary as well as sufficient conditions for approximate controllability of parameter dependent linear systems in the supremum norm using tools from complex approximation theory we prove the existence of parameter independent open loop controls that steer the zero initial state of an ensemble of linear systems uniformly to a prescribed family of terminal states new necessary conditions for uniform ensemble controllability of single input systems are derived our results extend earlier ones of li for ensemble controllability of linear systems