long time estimates in the mean field limit in this paper we prove a stability result for measure perturbations of some class of stationary distributions of a vlasov equation we use this result to prove that the n particles approximation of these stationary distributions is uniformly valid on a time scale of order n1 8 which is much longer than the usual log n scale we also prove similar results for the approximation of the two dimensional euler equation by the vortex blob method

h infty controller design for preview and delayed systems the h infty control problem of general preview delayed systems is solved using analytic solutions of the corresponding operator riccati equations the solution to the problem can be applied to a broad range of input output delayed systems and enables the handling of preview delayed control problems the solvability condition is characterized by the roots of the transcendental equations and the control law for the general problem is given based on a predictive compensation with an integro differential observer some interpretations of typical control problems are presented based on the solvability condition and the resulting control law

formulas on preview and delayed h infty control a generalized hinfin control problem which covers preview and delayed control strategies is discussed based on a state space approach by introducing a hamiltonian matrix which is associated with a delay free generalized plant the analytic solution to the corresponding operator riccati equation is newly established based on the result obtained here the hinfin control problem is solved and for typical control problems e g hinfin and linear quadratic lq control for multiple input delay systems hinfin preview control some interpretations are provided on the resulting control system

linear discrete time h sub spl infin optimal tracking with preview the problem of finite time h sub spl infin tracking for linear discrete time varying systems is considered no a prior knowledge of the dynamics of the reference signal is assumed a distinction between three cases is made depending on whether the reference signal is perfectly known in advance measured online or previewed in a fixed interval of time ahead the tracking problem is formulated as a game where the controller plays against nature which may choose the initial condition or the system and any energy bounded driving disturbance and measurement noise inputs necessary and sufficient conditions are derived for the existence of saddle point equilibrium solutions to the three different information structures of the reference and the corresponding tracking controllers are derived

robust controller design for delay systems in the gap metric a robust stabilization problem in the gap metric is discussed for a system with delays in control the authors derive a design procedure of robust controllers based on finite dimensional ricatti equations and it is shown that the resulting controller has a structure of observer based predictive action by employing completing the square argument a game theoretic interpretation is also provided on the trade off between the initial uncertainties and attenuating the disturbance caused by plant uncertainties

brief h performance of preview control systems performance of the preview control is investigated in terms of h criterion in the infinite horizon time setting the limitation of h performance in preview control action is characterized with the hamiltonian matrix by employing the property of hamiltonian matrix the solvability and analytic solution for the preview full information control problem are clarified based on an auxiliary introduced matrix riccati equation the property of resulting control law is illustrated with a numerical example

h sup spl infin control and estimation with preview part i matrix are solutions in continuous time preview control and fixed lag smoothing allow a noncausal component in the controller estimator time domain variational analysis is used in a reduction to an open loop differential game leading to a complete necessary and sufficient characterization of suboptimal values and an explicit state space design in terms of a parameterized nonstandard algebraic matrix riccati equation in a general continuous time linear system setting the solution offers insight into the appropriate structure of the associated hamiltonian where the state and co state are not the usual state of the original dynamic system and that of its adjoint rather the state and co state are selected to capture the respective lumped effects of initial data and future input selection in the allied game

brief paper inversion of sampled data system approximates the continuous time counterpart in a noncausal framework although correspondence between the poles of a continuous time and sampled data system with a piecewise constant input is simple and desirable from the stability viewpoint the relationship between zeros is intricate inversion of a sampled data system is mostly unstable irrespective of the stability of the continuous time counterpart this makes it difficult to apply inversion based control techniques such as perfect tracking transient response shaping or iterative learning control to sampled data systems although recently developed noncausal inversion techniques help us to circumvent unboundedness of the inversion caused by unstable zeros whether the inversion of sampled data systems approximates the continuous time counterpart or not as the sample period is shortened is still to be determined this article gives a positive conclusion to this problem

h2 optimal rejection with preview in the continuous time domain the synthesis of a feedforward unit for h 2 optimal rejection of previewed signals in continuous time invariant linear systems is considered the h 2 optimal compensator herein devised consists of a finite impulse response system working in connection with a standard dynamic unit the design strategy is based on a simple interpretation of the h 2 optimal rejection problem with preview as a compound optimal control problem i e as a problem consisting of a finite horizon lq control problem with constrained final state an infinite horizon lq control problem and the problem of minimizing the global cost functional an explicit description of the compensator is derived by exploiting some results on the parameterization of the solutions of the associated autonomous hamiltonian system

the linear quadratic optimal control approach to feedback control design for systems with delay abstract a generalized linear quadratic optimal control problem for systems with delay is formulated the optimal solution is given as a state feedback form which requires a solution of coupled infinite dimensional riccati equations it is shown that the closed loop system formed by the optimal state feedback control has some desirable sensitivity and robustness properties the generalization exists in the state quadratic form of the cost functional which makes it possible to discuss a pole location problem within the framework of the linear quadratic optimal control problem it is also shown that the generalized cost functional contains a special class of cost functionals for which the optimal control can be realized by solving only a finite dimensional riccati equation based on these results about the generalized linear quadratic optimal control a design method of feedback controls is proposed and an illustrative example is then presented

an innovation approach to h sub spl infin fixed lag smoothing for continuous time varying systems this note studies the finite horizon h sub spl infin fixed lag smoothing problem for linear continuous time varying systems a technique named as reorganized innovation analysis in krein space is developed to give a necessary and sufficient condition for the existence of an h sub spl infin fixed lag smoother the condition is given in terms of the boundedness of two matrix functions which are derived from the solutions of two riccati differential equations rdes one standard h sub spl infin filtering rde and one h sub 2 type of rde examples demonstrate the proposed h sub spl infin fixed lag smoother design and the fact that the existence of an h sub spl infin smoother does not depend on the solvability of h sub spl infin filtering

on the h 2 two sided model matching problem with preview the h2 optimization problem with preview and asymptotic behavior constraints is considered in a general two sided model matching setting the solution is obtained in terms of two constrained sylvester equations associated with asymptotic behavior and stabilizing solutions of two algebraic riccati equations the riccati equations do not depend on the preview length yet are affected by asymptotic behavior constraints and are thus different from the standard h2 riccati equations arising in problems with no steady state requirements or in one sided problems

a lagrangian finite element method for the 2 d euler equations a grid free lagrangian finite element method is introduced for the 2 d incompressible euler equations the method is derived based on the observation that the product of the biot savart kernel and a polynomial can be integrated analytically over any triangle this enables us to obtain a numerically stable lagrangian method without using numerical smoothing moreover we show that the method converges uniformly with second order accuracy actually we establish a l stability result which applies to kernels that are more singular than the biot savart kernel as long as the kernel is l integrable another useful result is that we prove convergence of our method when using local regridding which allows the method to run for longer time even with a fixed mesh the second order convergence is also illustrated by our numerical experiments

on the hydrodynamic limit of ginzburg landau wave vortices in this paper we study the hydrodynamic limit of the finite ginzburg landau wave vortices which was established in 16 unlike the classical vortex method for incompressible euler equations we prove here that the densities approximated by the vortex blob method associated with the ginzburg landau wave vortices tend to the solutions of the pressure less compressible euler poisson equations the convergence of such approximation is proved before the formation of singularities in the limit system as the blob sizes and the grid sizes tend to zero in appropriate rates 2002 john wiley sons inc

positive steady state solutions of a leslie gower predator prey model with holling type ii functional response and density dependent diffusion abstract in this paper we consider a leslie gower predator prey model with holling type ii functional response and density dependent diffusion under zero dirichlet boundary condition using degree theory bifurcation theory energy estimates and asymptotical behavior analysis the existence and multiplicity of positive steady state solutions were shown under certain conditions on the parameters

continuous time tracking problems in an h sub spl infin setting a game theory approach this paper investigates the problem of finite horizon h sub spl infin tracking for linear time varying systems three tracking problems are considered depending on whether the reference signal is perfectly known in advance measured on line or previewed in fixed interval of time ahead no a priori knowledge of a dynamic model for the reference signal is assumed a game theory approach to the latter tracking problems is presented where given a specific reference signal the controllers play against nature which can choose any initial state and any bounded energy disturbance input and measurement noise necessary and sufficient conditions for the existence of a saddle point equilibrium are determined and h sub spl infin tracking controllers for both the cases of state and output feedback are derived tracking problems for time invariant systems on infinite horizon are also analyzed and time invariant tracking controllers are obtained for zero initial conditions

a unified setting for decoupling with preview and fixed lag smoothing in the geometric context exact decoupling with preview perfect tracking of previewed references unknown input state observation with fixed lag and left inversion with fixed lag are considered from a unifying perspective where exact decoupling with preview is the basic problem necessary and sufficient constructive conditions for decoupling with finite preview are proved in the geometric framework structural and stabilizability conditions are considered separately and the use of self bounded controlled invariant subspaces allows the dynamic compensator with the minimal unassignable dynamics to be straightforwardly derived a steering along zeros technique is devised to guarantee decoupling with stability also in the presence of unstable unassignable dynamics of the minimal self bounded controlled invariant

when does the h sup spl infin fixed lag smoothing performance saturate for a finite smoothing lag a notable difference between the h sup 2 and h sup spl infin smoothing is that the achievable performance in the latter problem might saturate as the function of the smoothing lag in the sense that there might exist a finite smoothing lag for which the achievable performance level is the same as for the infinite smoothing lag in this note necessary and sufficient conditions under which such a saturation occurs are derived in particular it is shown that the h sup spl infin performance saturates only if the h sup spl infin norm of the optimal error system is achieved at the infinite frequency i e if the worst case disturbance for the infinite smoothing lag case can be arbitrarily fast and thus in a sense unpredictable

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

h sub spl infin filtering for multiple time delay measurements the aim of this paper is to study the h sub spl infin filtering problem for linear continuous time systems with both current and multiple time delay measurements the key technique applied for deriving the filter is the reorganized innovation analysis approach in krein space a necessary and sufficient condition for the existence of an h sub spl infin filter is derived and the solution to the h sub spl infin filter is given in terms of solutions of riccati and matrix differential equations an example is finally presented to show the effectiveness of the proposed approach

brief paper stochastic linear quadratic regulation for discrete time linear systems with input delay this paper considers the stochastic lqr problem for systems with input delay and stochastic parameter uncertainties in the state and input matrices the problem is known to be difficult due to the presence of interactions among the delayed input channels and the stochastic parameter uncertainties in the channels the key to our approach is to convert the lqr control problem into an optimization one in a hilbert space for an associated backward stochastic model and then obtain the optimal solution to the stochastic lqr problem by exploiting the dynamic programming approach our solution is given in terms of two generalized riccati difference equations rdes of the same dimension as that of the plant