basis functions and parameter optimisation in high order iterative learning control in this paper a new parameter optimal high order iterative learning control ilc algorithms is proposed to extend the work of owens and feng parameter optimisation in iterative learning control international journal of control 14 11 1059 1069 if the original plant is positive this new algorithm will result in convergent learning where the convergence is monotonic to zero tracking error if the original plant is not positive it can be shown that by adding a suitable set of basis functions into the algorithm the tracking error will again converge monotonically to zero this provides a considerable improvement to earlier work on parameter optimal ilc as it opens up the possibility of globally convergent algorithms for any linear plant g the number of parameters needed to ensure convergence could however become large the paper shows that the use of low order parameterisations is capable of achieving much of the benefit achieved in the ideal case

a procedure for obtaining general nonlinear fokker planck equations abstract a procedure for deriving general nonlinear fokker planck equations fpes directly from the master equation is presented the nonlinear effects are introduced in the transition probabilities which present a dependence on the probabilities for finding the system in a given state it is shown that the fpes obtained from master equations describing transitions among discrete and continuous sets of states are identical within such a procedure we construct nonlinear fpes that appear to be very general our general fpes recover as particular cases nonlinear fpes investigated previously by many authors introduced on a purely phenomenological basis and they lead to the possibility of more complete and complex diffusive equations

modelling of non minimum phase effects in discrete time norm optimal iterative learning control the subject of this article is the modelling of the influence of non minimum phase discrete time system dynamics on the performance of norm optimal iterative learning control noilc algorithms with the intent of explaining the observed phenomenon and predicting its primary characteristics it is established that performance in the presence of one or more non minimum phase plant zeros typically has two phases these consist of an initial fast monotonic reduction of the l 2 error norm mean square error followed by a very slow asymptotic convergence although the norm of the tracking error does eventually converge to zero the practical implications over a finite number of trials is apparent convergence to a non zero error the source of this slow convergence is identified using the singular value distribution of the system s all pass component a predictive model of the onset of slow convergence behaviour is developed as a set of linear constraints and shown to be valid when the iteration time interval i

matrix rank based conditions for reachability controllability of discrete linear repetitive processes abstract this paper uses both 2d and standard or 1d representations of the dynamics of discrete linear repetitive processes to characterise their reachability controllability properties the major new results are a 1d representation of constant dimensions and characterisations of reachability controllability in terms of matrix rank based conditions

multi diffusive nonlinear fokker planck equation nonlinear fokker planck equations characterized by more than one diffusion term have appeared recently in literature here it is shown that these equations may be derived either from approximations in a master equation or from a langevin type approach an h theorem is proven relating these fokker planck equations to an entropy composed by a sum of contributions each of them associated with a given diffusion term moreover the stationary state of the fokker planck equation is shown to coincide with the equilibrium state obtained by extremization of the entropy in the sense that both procedures yield precisely the same equation due to the nonlinear character of this equation the equilibrium probability may be obtained in most cases only by means of numerical approaches some examples are worked out where the equilibrium probability distribution is computed for nonlinear fokker planck equations presenting two diffusion terms corresponding to an entropy characterized by a sum of two contributions it is shown that the resulting equilibrium distribution in general presents a form that differs from a sum of the equilibrium distributions that maximizes each entropic contribution separately although in some cases one may construct such a linear combination as a good approximation for the equilibrium distribution

multivariable norm optimal and parameter optimal iterative learning control a unified formulation this article investigates the two paradigms of norm optimal iterative learning control noilc and parameter optimal iterative learning control poilc for multivariable mimo l input m output linear discrete time systems the main result is a proof that despite their algebraic and conceptual differences they can be unified using linear quadratic multi parameter optimisation techniques in particular whilst poilc has been naturally regarded as an approximation to noilc it is shown that the noilc control law can be generated from a suitable choice of control law parameterisation and objective function in a multi parameter mimo poilc problem the form of this equivalence is used to propose a new general approach to the construction of poilc problems for mimo systems that approximates the solution of a given noilc problem an infinite number of such approximations exist this great diversity is illustrated by the derivation of new convergent algorithms based on time interval and gradient partition that

option pricing formulas based on a non gaussian stock price model options are financial instruments that depend on the underlying stock we explain their non gaussian fluctuations using the nonextensive thermodynamics parameter q a generalized form of the black scholes bs partial differential equation and some closed form solutions are obtained the standard bs equation q 1 which is used by economists to calculate option prices requires multiple values of the stock volatility known as the volatility smile using q 1 5 which well models the empirical distribution of returns we get a good description of option prices using a single volatility

power allocation for a mimo relay system with multiple antenna users a power allocation or scheduling problem is studied for a multiuser multiple input multiple output mimo wireless relay system where there is a non regenerative relay between one access point and multiple users each node in the system is equipped with multiple antennas the purpose of this study is to develop fast algorithms to compute the source covariance matrix or matrices and the relay transformation matrix to optimize a system performance we consider the minimization of power consumption subject to rate constraint and also the maximization of system throughput subject to power constraint these problems are nonconvex and apparently have no simple solutions in this paper a number of computational strategies are presented and their performances are investigated both uplink and downlink cases are considered the use of multiple carriers is also discussed moreover a generalized water filling gwf algorithm is developed to solve a special class of convex optimization problems the gwf algorithm is used for two of the strategies shown in this paper

an inverse model approach to multivariable norm optimal iterative learning control with auxiliary optimisation motivated by the commonly encountered problem in which tracking is only required at selected intermediate points within the time interval a general optimisation based iterative learning control ilc algorithm is derived that ensures convergence of tracking errors to zero whilst simultaneously minimising a specified quadratic objective function of the input signals and chosen auxiliary state variables in practice the proposed solutions enable a repeated tracking task to be accurately completed whilst simultaneously reducing undesirable effects such as payload spillage vibration tendencies and actuator wear the theory is developed using the well known norm optimal ilc noilc framework using general linear functional operators between real hilbert spaces solutions are derived using feedforward action convergence is proved and robustness bounds are presented using both norm bounds and positivity conditions algorithms are specified for both continuous and discrete time state space representations

accelerated norm optimal iterative learning control algorithms using successive projection this article proposes a novel technique for accelerating the convergence of the previously published norm optimal iterative learning control noilc methodology the basis of the results is a formal proof of an observation made by d h owens namely that the noilc algorithm is equivalent to a successive projection algorithm between linear varieties in a suitable product hilbert space this leads to two proposed accelerated algorithms together with well defined convergence properties the results show that the proposed accelerated algorithms are capable of ensuring monotonic error norm reductions and can outperform noilc by more rapid reductions in error norm from iteration to iteration in particular examples indicate that the approach can improve the performance of noilc for the problematic case of non minimum phase systems realisation of the algorithms is discussed and numerical simulations are provided for comparative purposes and to demonstrate the numerical performance and effectiveness of the proposed methods

duality and optimization for generalized multi hop mimo amplify and forward relay networks with linear constraints we consider a generalized multi hop mimo amplify and forward af relay network with multiple sources destinations and arbitrarily number of relays we establish two dualities and the corresponding dual transformations between such a network and its dual respectively under single network linear constraint and per hop linear constraint a unified optimization framework is proposed to find a stationary point for an important class of nonconvex optimization problems of af relay networks based on a local lagrange dual method where the primal algorithm only finds a stationary point for the inner loop problem of maximizing the lagrangian w r t the primal variables the input covariance matrices are shown to satisfy a polite water filling structure at a stationary point of the inner loop problem the duality and polite water filling are exploited to design fast primal algorithms compared with the existing algorithms the proposed optimization framework with duality based primal algorithms can be used to solve more general problems with lower computation cost

batch to batch finite horizon lq control for unknown discrete time linear systems via stochastic extremum seeking we employ our recent discrete time stochastic averaging theorems and stochastic extremum seeking to iteratively batch to batch optimize open loop control sequences for unknown but reachable discrete time linear systems with a scalar input and without known system dimension for a cost that is quadratic in the measurable output and the input first for a multivariable gradient based stochastic extremum seeking algorithm we prove local exponential convergence to the optimal open loop control sequence second to remove the convergence rate s dependence on the hessian matrix of the cost function which is unknown since the system s model the system matrices a b c is unknown we develop a multivariable discrete time newton based stochastic extremum seeking method design the newton based algorithm for the iteration of the input sequence and prove local exponential convergence to the optimal input sequence finally two simulation examples are given to illustrate the effectiveness of the two methods

stability analysis of mean field type nonlinear fokker planck equations associated with a generalized entropy and its application to the self gravitating system multidimensional nonlinear fokker planck equations of mean field type are proposed within the framework of generalized thermostatistics to develop a general formulation of stability analysis of their solutions two types of eigenvalue equations are studied the nonlinear fokker planck equations are shown to exhibit an h theorem with a liapunov functional that takes the form of a free energy involving generalized entropies of tsallis the second order variation of the liapunov functional is computed to conduct local stability analysis and the associated eigenvalue equation is derived for an arbitrary form of mean field coupling potential assuming quasiequilibrium for the velocity distribution the reduced eigenvalue equation with space coordinates alone is also obtained the alternative type of eigenvalue equation based on the linearization of the nonlinear fokker planck equations is presented taking the mean field coupling potential to be the gravitational one the nonlinear fokker planck equation in terms of three dimensional velocity and space coordinates together with the framework of stability analysis is shown to be applicable to a mean field model of self gravitating system by solving the eigenvalue equation for the eigenfunction with 0 eigenvalue the occurrence of stability change of the equilibrium probability density with spherical symmetry is discussed

multivariable norm optimal iterative learning control with auxiliary optimisation the paper describes a substantial extension of norm optimal iterative learning control noilc that permits tracking of a class of finite dimensional reference signals whilst simultaneously converging to the solution of a constrained quadratic optimisation problem the theory is presented in a general functional analytical framework using operators between chosen real hilbert spaces this is applied to solve problems in continuous time where tracking is only required at selected intermediate points of the time interval but simultaneously the solution is required to minimise a specified quadratic objective function of the input signals and chosen auxiliary state variables applications to the discrete time case including the case of multi rate sampling are also summarised the algorithms are motivated by practical need and provide a methodology for reducing undesirable effects such as payload spillage vibration tendencies and actuator wear whilst maintaining the desired tracking accuracy necessary f

adaptive iterative learning control for nonlinearly parameterised systems with unknown time varying delays and input saturations in this work an adaptive iterative learning control ailc scheme is proposed to address a class of nonlinearly parameterised systems with both unknown time varying delays and input saturations by incorporating a saturation function a novel iterative learning control mechanism is constructed with a feedback term in the time domain and a fully saturated adaptive learning term in the iteration domain which is used to estimate the unknown time varying system uncertainty a new time weighted lyapunov krasovskii like composite energy function lkl cef is designed for the convergence analysis where time weighted inputs states and estimates of system uncertainty are all considered despite the existence of time varying parametric uncertainties time varying delays input saturations and local lipschitz nonlinearities the learning convergence is guaranteed with rigorous mathematical analysis simulation results verify the correctness and effectiveness of the proposed method further

mimo b mac interference network optimization under rate constraints by polite water filling and duality we take two new approaches to design efficient algorithms for transmitter optimization under rate constraints in order to guarantee the quality of service for mimo b mac interference networks a b mac network is a generalized interference network that is a combination of multiple interfering broadcast channels bc and multiaccess channels mac two related optimization problems maximizing the minimum of weighted rates under a sum power constraint and minimizing the sum power under rate constraints are considered the first approach takes advantage of existing algorithms for sinr problems by building a bridge between rate and sinr through the design of optimal mappings between them the second approach exploits the polite water filling structure which is the network version of water filling satisfied by all the pareto optimal input of a large class of achievable regions of b mac networks it replaces most generic optimization algorithms currently used for such networks and reduces the complexity while demonstrating superior performance even in non convex cases both centralized and distributed algorithms are designed and the performance is analyzed in addition to numeric examples

iterative learning control in optimal tracking problems with specified data points in this paper we present two iterative learning control ilc frameworks for tracking problems with specified data points that are desired points at certain time instants to design ilc systems for such problems unlike traditional ilc approaches we first develop an algorithm in which not only the control signal but also the reference trajectory is updated at each trial we investigate the relationship between the reference trajectory and ilc tracking control as it relates to the rate of convergence second a new ilc scheme is proposed to produce output curves that pass close to the desired points here the control signals are generated by solving an optimal ilc problem with respect to the desired sampling points one of the key advantages of the proposed approaches is a significant reduction of the computational cost

time evolution towards q gaussian stationary states through unified ito stratonovich stochastic equation we consider a class of single particle one dimensional stochastic equations which include external field additive and multiplicative noises we use a parameter 0 1 which enables the unification of the traditional ito and stratonovich approaches now recovered respectively as the 0 and 1 2 particular cases to derive the associated fokker planck equation fpe these fpe is a linear one and its stationary state is given by a q gaussian distribution with q 2m 2 2m 1 3 where 0 characterizes the strength of the confining external field and m 0 is the normalized amplitude of the multiplicative noise we also calculate the standard kurtosis and the q generalized kurtosis q i e the standard kurtosis but using the escort distribution instead of the direct one through these two quantities we numerically follow the time evolution of the distributions finally we exhibit how these quantities can be used as convenient calibrations for determining the index q from numerical data obtained through experiments observations or numerical computations

nonlinear inhomogeneous fokker planck equation within a generalized stratonovich prescription we deduce a nonlinear and inhomogeneous fokker planck equation within a generalized stratonovich or stochastic ensuremath alpha prescription ensuremath alpha 0 1 2 and 1 respectively correspond to the it o stratonovich and anti it o prescriptions we obtain its stationary state p st x for a class of constitutive relations between drift and diffusion and show that it has a q exponential form p st x n q 1 ensuremath 1 ensuremath q ensuremath beta v x 1 1 ensuremath q with an index q which does not depend on ensuremath alpha in the presence of any nonvanishing nonlinearity this is in contrast with the linear case for which the index q is ensuremath alpha dependent

parameter optimal iterative learning control using polynomial representations of the inverse plant based on the observation that iterative learning control ilc can be based on the inverse plant but that the approach can be degraded by modelling errors particularly at high frequencies this article investigates the construction and properties of a multi parameter parameter optimal ilc algorithm that uses an approximate polynomial representation of the inverse with natural high frequency attenuation in its simplest form the algorithm replicates the original work of owens and feng but more generally it is capable of producing significant improvements to the observed convergence rate as the number of parameters increases convergence rates approach that of the ideal plant inverse algorithm introducing compensation into the algorithm provides a formal link to previously published gradient and norm optimal ilc algorithms and indicates that the polynomial approach can be regarded as approximations to those control laws simulation examples verify the theoretical performance predictions

consistent thermodynamic framework for interacting particles by neglecting thermal noise an effective temperature ensuremath theta conjugated to a generalized entropy s q was introduced recently for a system of interacting particles since ensuremath theta presents values much higher than those of typical room temperatures t ensuremath ll ensuremath theta the thermal noise can be neglected t ensuremath theta ensuremath simeq 0 in these systems moreover the consistency of this definition as well as of a form analogous to the first law of thermodynamics du ensuremath theta d s q ensuremath delta w were verified lately by means of a carnot cycle whose efficiency was shown to present the usual form ensuremath eta 1 ensuremath ensuremath theta 2 ensuremath theta 1 herein we explore further the heat contribution ensuremath delta q ensuremath theta d s q by proposing a way for a heat exchange between two such systems as well as its associated thermal equilibrium as a consequence the zeroth principle is also established moreover we consolidate the first law proposal by following the usual procedure for obtaining different potentials i e applying legendre transformations for distinct pairs of independent variables from these potentials we derive the equation of state maxwell relations and define response functions all results presented are shown to be consistent with those of standard thermodynamics for tg0

robust iterative learning control for linear systems with multiple time invariant parametric uncertainties this article presents a novel robust iterative learning control algorithm ilc for linear systems in the presence of multiple time invariant parametric uncertainties the robust design problem is formulated as a min max problem with a quadratic performance criterion subject to constraints of the iterative control input update then we propose a new methodology to find a sub optimal solution of the min max problem by finding an upper bound of the worst case performance the min max problem is relaxed to be a minimisation problem applying lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities lmis an lmi based ilc algorithm is given afterward and the convergence of the control input as well as the system error are proved finally we apply the proposed ilc to a generic example and a distillation column the numerical results reveal the effectiveness of the lmi based algorithm

robust optimal design and convergence properties analysis of iterative learning control approaches in this paper we address four major issues in the field of iterative learning control ilc theory and design the first issue is concerned with ilc design in the presence of system interval uncertainties targeting at time optimal fastest convergence and robustness properties concurrently we formulate the ilc design into a min max optimization problem and provide a systematic solution for linear type ilc consisting of the first order and higher order ilc schemes inherently relating to the first issue the second issue is concerned with the performance evaluation of various ilc schemes convergence speed is one of the most important factors in ilc a learning performance index q factor is introduced which provides a rigorous and quantified evaluation criterion for comparing the convergence speed of various ilc schemes we further explore a key issue how does the system dynamics affect the learning performance by associating the time weighted norm with the supreme norm we disclose the dynamics impact in ilc which can be assessed by global uniform bound and monotonicity in iteration domain finally we address a rather controversial issue in ilc can the higher order ilc outperform the lower order ilc in terms of convergence speed and robustness by applying the min max design which is robust and optimal and conducting rigorous analysis we reach the conclusion that the q factor of ilc sequences of lower order ilc is lower than that of higher order ilc in terms of the time weighted norm

iterative learning control for constrained linear systems this article considers iterative learning control ilc for linear systems with convex control input constraints first the constrained ilc problem is formulated in a novel successive projection framework then based on this projection method two algorithms are proposed to solve this constrained ilc problem the results show that when perfect tracking is possible both algorithms can achieve perfect tracking the two algorithms differ however in that one algorithm needs much less computation than the other when perfect tracking is not possible both algorithms can exhibit a form of practical convergence to a best approximation the effect of weighting matrices on the performance of the algorithms is also discussed and finally numerical simulations are given to demonstrate the effectiveness of the proposed methods

brief adaptive robust iterative learning control with dead zone scheme an adaptive robust iterative learning control method based on a new dead zone scheme is presented for the control of nonlinear uncertain systems the new dead zone scheme ceases both learning and adaptation whenever the previous iteration error enters a pre specified error bound in the sequel enhances the robustness of the control system and meanwhile achieves arbitrary tracking accuracy for guaranteed stability it is indicated that the system will converge to the error bound within finite iterations and stay inside it and that the boundedness of the system signals for any iteration is ensured no finite escape time iterative learning control ilc and adaptive robust control are synthesized to achieve a new control paradigm the iterative learning control strategy is applied directly to deal with structured system uncertainties unknown time functions which are invariant over iterations the adaptive robust control strategy is used to handle non periodic system uncertainties associated with partially known bounding functions where the unknown parameters in the upper bounding functions are estimated with adaptation by integrating learning adaptation robust control and the new dead zone scheme using lyapunov s direct method the proposed scheme is able to handle fairly broad classes of nonlinear uncertain systems

discrete time linear optimal multi periodic repetitive control a benchmark tracking solution the use of optimal control tracking methodologies for the development of feedback control schemes for arbitrary discrete time linear systems is considered for the special case when the demand signal is multi periodic i e can be expressed as a finite sum of periodic signals of different but known frequencies by embedding the reference signal into plant dynamics the problem is reduced to a classical linear quadratic control problem which yields an explicit formula for a globally stabilizing tracking controller asymptotic perfect tracking is guaranteed by the presence of the familiar internal model of the demand signal dynamics within the control structure transfer function analysis of the controller indicates that it consists of an inner state feedback loop plus an error actuated forward path control element containing the internal model

fast calculation of the ilc norm in iterative learning control in this paper we discuss and demonstrate a method for the exploitation of matrix structure in computations for iterative learning control ilc in barton bristow and alleyne international journal of control 83 2 1 8 2010 a special insight into the structure of the lifted convolution matrices involved in ilc is used along with a modified lanczos method to achieve very fast computational bounds on the learning convergence by calculating the ilc norm in computational complexity in this paper we show how their method is equivalent to a special instance of the sequentially semi separable sss matrix arithmetic and thus can be extended to many other computations in ilc and specialised in some cases to even faster methods our sss based methodology will be demonstrated on two examples a linear time varying example resulting in the same complexity as in barton et al and a linear time invariant example where our approach reduces the computational complexity to thus decreasing the computati

brief paper novel iterative learning controls for linear discrete time systems based on a performance index over iterations an optimal iterative learning control ilc is proposed to optimize an accumulative quadratic performance index in the iteration domain for the nominal dynamics of linear discrete time systems properties of stability convergence robustness and optimality are investigated and demonstrated in the case that the system under consideration contains uncertain dynamics the proposed ilc design can be applied to yield a guaranteed cost ilc whose solution can be found using the linear matrix inequality lmi technique simulation examples are included to demonstrate feasibility and effectiveness of the proposed learning controls

duality and rate optimization for multiple access and broadcast channels with amplify and forward relays in this paper we consider multihop multiple access mac and broadcast channels bc where communication takes place with the assistance of relays that amplify and forward af their received signals for a two hop parallel af relay mac assuming a sum power constraint across all relays we characterize optimal relay amplification factors and the resulting optimal rate regions we find the maximum sum rate and the maximum rate for each user in closed form and express the optimal rate pair r1 r2 that maximizes mu1r1 mu2r2 as the solution of a pair of simultaneous equations we find that the parallel af relay mac with total transmit power of the two users p1 p2 p and total relay power pr is the dual of the parallel af relay bc where the mac source nodes become the bc destination nodes the mac destination node becomes the bc source node the dual bc source transmit power is pr and the total transmit power of the af relays is p the duality means that the rate region of the af relay mac with a sum power constraint p on the transmitters is the same as that of the dual bc the duality relationship is found to be useful in characterizing the rate region of the af relay bc as the union of mac rate regions the duality is established for distributed multiple antenna af relay nodes and multiple more than 2 hops as well

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

entropy production and nonlinear fokker planck equations the entropy time rate of systems described by nonlinear fokker planck equations which are directly related to generalized entropic forms is analyzed both entropy production associated with irreversible processes and entropy flux from the system to its surroundings are studied some examples of known generalized entropic forms are considered and particularly the flux and production of the boltzmann gibbs entropy obtained from the linear fokker planck equation are recovered as particular cases since nonlinear fokker planck equations are appropriate for the dynamical behavior of several physical phenomena in nature like many within the realm of complex systems the present analysis should be applicable to irreversible processes in a large class of nonlinear systems such as those described by tsallis and kaniadakis entropies

multihop nonregenerative mimo relays qos considerations for nonregenerative multihop multiple input multiple output mimo relay communication systems the optimal source precoding matrix and the optimal relay amplifying matrices have been recently established for a broad class of objective functions subjecting to the transmission power constraint at each node however existing works do not consider any quality of service qos constraints which are important in practical communication systems in this paper we derive the optimal source and relay matrices of a multihop mimo relay system that guarantee the predetermined qos criteria be attained with the minimal total transmission power in particular we consider two types of receivers at the destination node the linear minimal mean squared error mmse receiver and the nonlinear decision feedback equalizer dfe based on the mmse criterion we show that for both types of receivers the solution to the original optimization problem can be upper bounded by using a successive geometric programming gp approach and lower bounded by utilizing a dual decomposition technique simulation results show that both bounds are tight and to obtain the same qos the mimo relay system using the nonlinear mmse dfe receiver requires substantially less total transmission power than the linear mmse receiver based system

iterative learning control using optimal feedback and feedforward actions an algorithm for iterative learning control is developed on the basis of an optimization principle which has been used previously to derive gradient type algorithms the new algorithm has numerous benefits which include realization in terms of riccati feedback and feedforward components this realization also has the advantage of implicitly ensuring automatic step size selection and hence guaranteeing convergence without the need for empirical choice of parameters the algorithm is expressed as a very general norm optimization problem in a hilbert space setting and hence in principle can be used for both continuous and discrete time systems a basic relationship with almost singular optimal control is outlined the theoretical results are illustrated by simulation studies which highlight the dependence of the speed of convergence on parameters chosen to represent the norm of the signals appearing in the optimization problem

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

singular optimal control a geometric approach linear quadratic singular optimal control problem is solved for nonminimum phase and noninvertible systems a state space decomposition is obtained and a reduced order nonsingular subproblem is solved the optimal stabilizing input of the singular problem has been found when there are no transmission zeros on the imaginary axis

consequences of the h theorem from nonlinear fokker planck equations a general type of nonlinear fokker planck equation is derived directly from a master equation by introducing generalized transition rates the h theorem is demonstrated for systems that follow those classes of nonlinear fokker planck equations in the presence of an external potential for that a relation involving terms of fokker planck equations and general entropic forms is proposed it is shown that at equilibrium this relation is equivalent to the maximum entropy principle families of fokker planck equations may be related to a single type of entropy and so the correspondence between well known entropic forms and their associated fokker planck equations is explored it is shown that the boltzmann gibbs entropy apart from its connection with the standard linear fokker planck equation may be also related to a family of nonlinear fokker planck equations

newton method based iterative learning control for discrete non linear systems significant progress has been achieved in terms of both theory and industrial applications of iterative learning control ilc in the past decade however the techniques of solving non linear ilc problems are still under development the main result of this paper is a novel non linear ilc algorithm that utilizes the capability of the newton method by setting up links between non linear ilc problems and non linear multivariable equations the newton method is introduced into the ilc framework the implementation of the new algorithm allows one to decompose a nonlinear ilc problem into a sequence of linear time varying ilc problems simulations on a discrete non linear system and a manipulator model display its advantages conditions for its semi local convergence are analysed links of ilc with existing non linear topics are pointed out as ways to construct new non linear ilc schemes potential improvements are discussed for future work

discrete time inverse model based iterative learning control stability monotonicity and robustness this paper considers the robustness of an inverse iterative learning control algorithm a simple learning gain results in robust convergence that is monotonic in the least squares sense provided that the multiplicative plant uncertainty satisfies a matrix positivity requirement the results are extended to the frequency domain using a simple graphical nyquist test the analysis extends naturally to a parameter optimal control setting non monotone convergence is considered by using a simple weighted norm based on exponential weighting of time series

derivation of nonlinear fokker planck equations by means of approximations to the master equation nonlinear fokker planck equations fpes are derived as approximations to the master equation in cases of transitions among both discrete and continuous sets of states the nonlinear effects introduced through the transition probabilities are argued to be relevant for many real phenomena within the class of anomalous diffusion problems the nonlinear fpes obtained appear to be more general than some previously proposed on a purely phenomenological basis ones in spite of this the same kind of solution applies i e it is shown that the time dependent tsallis s probability distribution is a solution of both equations obtained either from discrete or continuous sets of states and that the corresponding stationary solution is in the infinite time limit a stable solution

non linear kinetics underlying generalized statistics abstract the purpose of the present effort is threefold firstly it is shown that there exists a principle that we call kinetical interaction principle kip underlying the non linear kinetics in particle systems independently on the picture kramers boltzmann used to describe their time evolution secondly the kip imposes the form of the generalized entropy associated to the system and permits to obtain the particle statistical distribution both as stationary solution of the non linear evolution equation and as the state which maximizes the generalized entropy thirdly the kip allows on one hand to treat all the classical or quantum statistical distributions already known in the literature in a unifying scheme and on the other hand suggests how we can introduce naturally new distributions finally as a working example of the approach to the non linear kinetics here presented a new non extensive statistics is constructed and studied starting from a one parameter deformation of the exponential function holding the relation f x f x 1

parameter optimization in iterative learning control in this paper parameter optimization through a quadratic performance index is introduced as a method to establish a new iterative learning control law with this new algorithm monotonic convergence of the error to zero is guaranteed if the original system is a discrete time lti system and it satisfies a positivity condition if the original system is not positive two methods are derived to make the system positive the effect of the choice of weighting parameters in the performance index on convergence rate is analysed as a result adaptive weights are introduced as a method to improve the convergence properties of the algorithm a high order version of the algorithm is also derived and its convergence analysed the theoretical findings in this paper are highlighted with simulations

effective temperature concept a physical application for nonextensive statistical mechanics the h theorem df dt ensuremath le 0 for a free energy functional f u ensuremath ensuremath theta s with u and s representing respectively the internal energy and a generalized entropy of a given physical system has been proven previously by making use of a nonlinear fokker planck equation herein we focus on a nonlinear fokker planck equation derived by means of a coarse graining procedure on the equations of motion of a system of interacting vortices under overdamped motion in the absence of thermal noise t 0 in this case we show that the parameter ensuremath theta is directly related to the density as well as to the interactions among vortices generalized quantities such as entropy internal energy free energy and heat capacity are analyzed for varying ensuremath theta important relations and physical behavior analogous to those of standard thermodynamics are found showing that ensuremath theta plays the role of an effective temperature estimates of ensuremath theta in typical physical situations of different type ii superconductors are presented in addition to this possible experimental procedures for varying ensuremath theta are proposed