optimal estimation in udp like networked control systems with intermittent inputs stability analysis and suboptimal filter design we investigate the optimal estimation problem in lossy networked control systems where the control packets are randomly dropped without acknowledgment to the estimator most existing results for this setup are concerned with the design of controller while the optimal estimation and its performance evaluation have been rarely treated in this paper we show that unlike many other cases such as intermittent observations or tcp like systems the system state follows a gaussian mixture distribution with exponentially increasing terms which leads to a gaussian sum filter based optimal estimation we develop an auxiliary estimator method to establish necessary and sufficient conditions for the stability of the mean estimation error covariance matrices it is revealed that the stability is independent of the packet loss rate and is not affected by the lack of acknowledgment a suboptimal filtering algorithm with improved computational efficiency is then developed numerical examples and simulations are employed to illustrate the theoretical results

a comparison of two classifications of solvable lie algebras the literature contains two different classifications of solvable lie algebras of dimensions up to and including 4 this paper is devoted to comparing the two classifications and translating each into the other in particular we exhibit an isomorphism between each solvable lie algebra of one classification and the corresponding algebra of the second the first classification is provided by de graaf and the second classification is from a recent book by snobl and winternitz

optimal control over multiple erasure channels using a data dropout compensation scheme in this paper we focus on networked control systems subject to data dropouts we consider that the controller communicates with the plant through multiple independent erasure channels and that each actuator sends acknowledgement packages to the controller we restrict our attention to the optimal design of a class of controllers that embeds a data dropout compensator and where besides this compensation mechanism all processing is an affine function of the available data our first result shows that the optimal design consists in solving separately an estimation problem and a control problem the optimal controller is a linear function of the estimated state which is obtained exploiting the information given by the acknowledgement packages and the data dropout compensator since we focus on a specific class of controllers our proposal is suboptimal however unlike the optimal lqg controller found in the literature our proposal is easier to implement and its steady state behaviour can be simply determined we also show that under standard conditions the affine part of the optimal controller converges to an lti filter which can be used as a simple alternative to the time varying controller

low dimensional real lie algebras all real lie algebras of dimension up to 8 that admit a nontrivial levi decomposition are found

new singular gelfand tsetlin mathfrak gl n modules of index 2 singular gelfand tsetlin modules of index 2 are modules whose tableaux bases may have singular pairs but no singular triples of entries on each row in this paper we construct singular gelfand tsetlin modules for arbitrary singular character of index 2 explicit bases of derivative tableaux and the action of the generators of mathfrak gl n are given for these modules our construction leads to new families of irreducible gelfand tsetlin modules and also provides tableaux bases for some simple verma modules

combinatorial construction of gelfand tsetlin modules for gln abstract we propose a new effective method of constructing explicitly gelfand tsetlin modules for gl n we obtain a large family of simple modules that have a basis consisting of gelfand tsetlin tableaux the action of the lie algebra is given by the gelfand tsetlin formulas and with all gelfand tsetlin multiplicities equal 1 as an application of our construction we prove necessary and sufficient condition for the gelfand and graev s continuation construction to define a module which was conjectured by lemire and patera

the gelfand cetlin system and quantization of the complex flag manifolds the construction of angle action variables for collective completely integrable systems is described and the associated bohr sommerfeld sets are determined the quantization method of sniatycki applied to such systems gives formulas for multiplicities for the gelfand cetlin system on complex flag manifolds we show that these formulas give the correct answers for the multiplicities of the associated representations

solvable lie algebras of dimension six six dimensional solvable lie algebras over the field of real numbers that possess nilradicals of dimension four are classified into equivalence classes this completes mubarakzyanov s classification of the real six dimensional solvable lie algebras

optimal estimation and control for lossy network stability convergence and performance in this paper we study the problems of optimal estimation and control i e the linear quadratic gaussian lqg control for systems with packet losses but without acknowledgment such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses for such system which is usually called as a user datagram protocol udp like system the optimal estimation is nonlinear and its calculation is time consuming making its corresponding optimal lqg problem complicated we first propose two conditions 1 the sensor has some computation abilities and 2 the control command exerted to the plant is known to the sensor for a udp like system satisfying these two conditions we derive the optimal estimation by constructing the finite and infinite product probability measure spaces for the estimation error covariances eec we give the stability condition for the expected eec and show the existence of a measurable function to which the eec converges in distribution and propose some practical methods to evaluate the estimation performance finally the lqg controllers are derived and the conditions for the mean square stability of the closed loop system are established

linear quadratic optimal control of continuous time lti systems with random input gains this note studies the linear quadratic lq optimal control of continuous time linear time invariant systems with random gains imposed on the input channels we start from the indefinite lq problem in which the cost weighting matrix can be indefinite the definite lq problem is discussed as a special case the main novelty originates from the point of view that in networked control designing the channels and controller jointly often leads to an easier problem and achieves better performance than designing them separately specifically we formulate the lq problem as a channel controller co design problem assuming that the channel capacities can be allocated among the input channels subject to an overall capacity constraint necessary and sufficient conditions are obtained for the well posedness and the attainability of the indefinite lq problem under a given channel capacity allocation satisfying the stabilization requirement the optimal controller is given by a linear state feedback associated with the mean square stabilizing solution of a modified algebraic riccati equation

lqg control for mimo systems over multiple erasure channels with perfect acknowledgment this technical note concerns control applications over lossy data networks sensor data is transmitted to an estimation control unit over a network and control commands are issued to subsystems over the same network sensor and control packets may be randomly lost according to a bernoulli process in this context the discrete time linear quadratic gaussian lqg optimal control problem is considered in schenato a complete analysis was carried out for the case that sensor measurements and control inputs are delivered into a single packet to the estimator and to the actuators respectively here a nontrivial generalization for mimo systems is presented under the assumption that each sensor and each actuator exchange data with the control unit in an independent way by using their own data packet no aggregation in such a framework it is shown that the separation principle still holds in the case where packet arrivals are acknowledged by the receiver moreover the optimal lqg control is a linear function of the state that explicitly depends on the loss probabilities of the actuator channels such a dependence is not present in the single channel case considered in mean square in the infinite horizon case stability conditions on the packet arrival probabilities are provided in terms of linear matrix inequalities lmis

finite horizon cal h _ infty control for discrete time varying systems with randomly occurring nonlinearities and fading measurements this technical note deals with the cal h infty control problem for a class of discrete time varying nonlinear systems with both randomly occurring nonlinearities and fading measurements over a finite horizon the system measurements are transmitted through fading channels described by a modified stochastic rice fading model the purpose of the addressed problem is to design a set of time varying controllers such that in the presence of channel fading and randomly occurring nonlinearities the cal h infty performance is guaranteed over a given finite horizon the model transformation technique is first employed to simplify the addressed problem and then the stochastic analysis in combination with the completing squares method are carried out to obtain necessary and sufficient conditions of an auxiliary index which is closely related to the finite horizon cal h infty performance moreover the time varying controller parameters are characterized via solving coupled backward recursive riccati difference equations rdes a simulation example is utilized to illustrate the usefulness of the proposed controller design scheme

bounds of gelfand tsetlin multiplicities and tableaux realizations of verma modules abstract we introduce the notion of essential support of a simple gelfand tsetlin gl n module as an attempt to understand the character formula of such module this support detects the weights having maximal possible gelfand tsetlin multiplicities using combinatorial tools we describe the essential supports of the simple socles of the universal tableaux modules we also prove that every simple verma module appears as the socle of a universal tableaux module as a consequence we prove the strong futorny ovsienko conjecture on the sharpness of the upper bounds of the gelfand tsetlin multiplicities we also give a very explicit description of the support and essential support of the simple singular verma module m

lie algebra modules with finite dimensional weight spaces i let g denote a reductive lie algebra over an algebraically closed field of characteristic zero and let 4 denote a cartan subalgebra of g in this paper we study finitely generated g modules that decompose into direct sums of finite dimensional 4 weight spaces we show that the classification of irreducible modules in this category can be reduced to the classification of a certain class of irreducible modules those we call torsion free modules we also show that if g is a simple lie algebra that admits a torsion free module then g is of type a or c

singular gelfand tsetlin modules of gl n abstract the classical gelfand tsetlin formulas provide a basis in terms of tableaux and an explicit action of the generators of gl n for every irreducible finite dimensional gl n module these formulas can be used to define a gl n module structure on some infinite dimensional modules the so called generic gelfand tsetlin modules the generic gelfand tsetlin modules are convenient to work with since for every generic tableau there exists a unique irreducible generic gelfand tsetlin module containing this tableau as a basis element in this paper we initiate the systematic study of a large class of non generic gelfand tsetlin modules the class of 1 singular gelfand tsetlin modules an explicit tableaux realization and the action of gl n on these modules is provided using a new construction which we call derivative tableaux our construction of 1 singular modules provides a large family of new irreducible gelfand tsetlin modules of gl n and is a part of the classification of all such irreducible modules for n 3

nonfragile h_ infty fuzzy filtering with randomly occurring gain variations and channel fadings this paper is concerned with the nonfragile h infty filtering problem for a class of discrete time takagi sugeno t s fuzzy systems with both randomly occurring gain variations rogvs and channel fadings the phenomenon of the rogvs is introduced into the system model so as to account for the parameter fluctuations occurring during the filter implementation two sequences of random variables obeying the bernoulli distribution are employed to describe the phenomenon of the rogvs bounded by prescribed norms in addition the rice fading model is utilized to describe the phenomena of channel fadings where the occurrence probabilities of the random channel coefficients are allowed to time varying through stochastic analysis and lyapunov functional approach sufficient conditions are established under which the filtering error dynamics is exponentially mean square stable with a prespecified h infty performance the set of the desired nonfragile h infty filters is characterized by solving a convex optimization problem via the semidefinite programming method an illustrative example is given to show the usefulness and effectiveness of the proposed design method in this paper

h_ infty fuzzy control with randomly occurring infinite distributed delays and channel fadings in this paper the h output feedback control problem is investigated for a class of discrete time fuzzy systems with randomly occurring infinite distributed delays and channel fadings a random variable obeying the bernoulli distribution is introduced to account for the probabilistic infinite distributed delays the stochastic rice fading model is employed to simultaneously describe the phenomena of random time delays and channel fadings via setting different values of the channel coefficients the aim of this paper is to design an h output feedback fuzzy controller such that the closed loop takagi sugeno t s fuzzy control system is exponentially mean square stable and the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of desired output feedback controllers ensuring both the exponential mean square stability and the prescribed h performance the cone complementarity linearization algorithm is utilized to cast the controller design problem into a sequential minimization one that is solvable by the semi definite programming method a simulation result is exploited to illustrate the usefulness and effectiveness of the proposed design technique

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance