pareto optimal strategy for stochastic weakly coupled large scale systems with state dependent system noise this note is concerned with the decentralized infinite horizon stochastic pareto optimal static output feedback strategy for a class of weakly coupled systems with state dependent noise first pareto optimal control problems are formulated using a static output feedback strategy the necessary conditions are given by the cross coupled stochastic algebraic riccati type equations csares for proving the existence of the static output feedback strategy that minimizes the quadratic cost function after determining the asymptotic structure of the solutions of the csares a new sequential numerical algorithm and newton s method for solving the csares are described the resulting numerical solution is used to develop the pareto optimal strategy finally the efficiency of the proposed algorithm is demonstrated by solving a numerical example for a practical megawatt frequency control problem

most primitive groups are full automorphism groups of edge transitive hypergraphs abstract we prove that for a primitive permutation group g acting on a set x of size n other than the alternating group the probability that aut x y g g for a random subset y of x tends to 1 as n so the property of the title holds for all primitive groups except the alternating groups and finitely many others this answers a question of m h klin moreover we give an upper bound n 1 2 for the minimum size of the edges in such a hypergraph this is essentially best possible

robust stability and stabilization of discrete time non linear systems the lmi approach the purpose of this paper is to convert the problem of robust stability of a discrete time system under non linear perturbation to a constrained convex optimization problem involving linear matrix inequalities lmi the nominal system is linear and time invariant while the perturbation is an uncertain non linear time varying function which satisfies a quadratic constraint we show how the proposed lmi framework can be used to select a quadratic lyapunov function which allows for the least restrictive non linear constraints when the nominal system is unstable the framework can be used to design a linear state feedback which stabilizes the system with the same maximal results regarding the class of non linear perturbations of particular interest in this context is our ability to use the lmi formulation for stabilization of interconnected systems composed of linear subsystems with uncertain non linear and time varying coupling by assuming stabilizability of the subsystems we can produce local control la

robust l_ infty induced filtering and control of stochastic systems with state multiplicative noise linear continuous time systems with stochastic uncertainties in their state space model are considered the problems of induced l state feedback control and filtering are solved for the stationary case in both problems the cost function is defined to be the expected value of the standard induced l performance index with respect to the uncertain parameters an example that demonstrates the applicability of the theory is given

an iterative algorithm to solve state perturbed stochastic algebraic riccati equations in lq zero sum games an iterative algorithm to solve a kind of state perturbed stochastic algebraic riccati equation sare in lq zero sum game problems is proposed in our algorithm we replace the problem of solving a sare with an indefinite quadratic term by the problem of solving a sequence of sares with a negative semidefinite quadratic term which can be solved by existing methods under some appropriate conditions we prove that our algorithm is globally convergent we give a numerical example to show the effectiveness of our algorithm our algorithm also has a natural game theoretic interpretation

robustness of the exponential stability on a non linear controlled system under some state and control perturbations given a deterministic controlled system in continuous time or in discrete time we assume that we have computed a feedback control which stabilizes the system we show that the system remains exponentially stable under some stochastic perturbations of the applied control and of the system equation

state feedback control of systems with multiplicative noise via linear matrix inequalities we consider lti systems perturbed by parametric uncertainties modeled as white noise disturbances we show how to maximize via state feedback control the smallest norm of the noise intensity vector producing instability in the mean square sense using convex optimization over linear matrix inequalities we also show how to maximize performance robustness where performance is measured by expected output energy with either bounded initial conditions and zero inputs classical lqg cost or zero initial conditions and deterministic inputs of bounded energy a generalization of the h norm

rate distortion optimized graph based representation for multiview images with complex camera configurations graph based representation gbr has recently been proposed for describing color and geometry of multiview video content the graph vertices represent the color information while the edges represent the geometry information i e the disparity by connecting corresponding pixels in two camera views in this paper we generalize the gbr to multiview images with complex camera configurations compared with the existing gbr the proposed representation can handle not only horizontal displacements of the cameras but also forward backward translations rotations etc however contrary to the usual disparity that is a 2 d vector denoting horizontal and vertical displacements each edge in gbr is represented by a 1 d disparity this quantity can be seen as the disparity along an epipolar segment in order to have a sparse i e easy to code graph structure we propose a rate distortion model to select the most meaningful edges hence the graph is constructed with just enough information for rendering the given predicted view the experiments show that the proposed gbr allows high reconstruction quality with lower or equivalent coding rate than traditional depth based representations

some remarks on general nonlinear stochastic h_ infty control with state control and disturbance dependent noise this technical note studies the nonlinear stochastic h control of ito type differential systems with all the state control input and external disturbance dependent noise x u v dependent noise for short a sufficient condition is given for the finite infinite horizon h control of such a system by means of an hamilton jacobi inequality hji instead of three coupled hamilton jacobi equations hjes as in previous literature

the guaranteed cost control for uncertain nonlinear large scale stochastic systems via state and static output feedback abstract the guaranteed cost control gcc problem involved in decentralized robust control of a class of uncertain nonlinear large scale stochastic systems with high order interconnections is considered after determining the appropriate conditions for the stochastic gcc controller a class of decentralized local state feedback controllers is derived using the linear matrix inequality lmi the extension of the result of the study to the static output feedback control problem is discussed by considering the karush kuhn tucker kkt conditions the efficiency of the proposed design method is demonstrated on the basis of simulation results

low dimensional representations of special linear groups in cross characteristics the low dimensional projective irreducible representations in cross characteristics of the projective special linear group mbox psl n q are investigated if n geq 3 and n q neq 3 2 3 4 4 2 4 3 all such representations of the first degree which is q n q q 1 kappa with kappa 0 or 1 and the second degree which is q n 1 q 1 come from weil representations we show that the gap between the second and the third degree is roughly q 2n 4

robust fuzzy control for uncertain stochastic time delay takagi sugeno fuzzy models for achieving passivity this paper focuses on the robust passive stability and stabilization problems for uncertain nonlinear stochastic time delay systems via the fuzzy modeling approach the nonlinear stochastic system is described by takagi sugeno t s fuzzy model in which the consequent parts are presented by linear stochastic time delay differential equation with lyapunov krasovskii function and improved jensen s inequality the stability criteria are derived in addition the passivity theory is employed to discuss external disturbance effect on system for achieving attenuation performance according to the proposed design method the fuzzy controller is carried out by parallel distributed compensation pdc concept to guarantee the robust asymptotical stability and attenuation performance of system in the sense of mean square finally a synchronous generator power system is presented to manifest the application and effectiveness of the proposed fuzzy control method

robust h infinity control in the presence of stochastic uncertainty this paper considers a robust h infinity state feedback control problem for linear uncertain systems with stochastic uncertainty the uncertainty class considered in the paper involves uncertain multiplicative white noise perturbations which satisfy a certain variance constraint a state feedback controller is presented which guarantees a prescribed level of disturbance attenuation for all admissible stochastic uncertainties

on lmi formulations of some problems arising in nonlinear stochastic system analysis this work involves formulation of some problems arising in the analysis of a class of discrete time nonlinear stochastic systems in terms of linear matrix inequalities this allows one to utilize a wide variety of numerical techniques available for tackling both the feasibility problem and the actual numerical solution in an efficient manner

a control scheme for a class of discrete nonlinear stochastic systems a control scheme is presented for effective stabilization of discrete time nonlinear stochastic systems where the nonlinearity involves a zero mean independent random sequence the control is of a constant feedback type and makes use of finite time solutions of a riccati like matrix difference equation stability results are both in terms of mean square and almost sure stochastic stability moreover a matrix inequality is given to check the existence of weighting matrices which would result in a stable regulator problem

brief paper robust guaranteed cost control for uncertain stochastic systems with multiple decision makers the guaranteed cost control gcc problem for uncertain stochastic systems with n decision makers is investigated it is noteworthy that the necessary conditions which are determined from karush kuhn tucker kkt conditions for the existence of a guaranteed cost controller have been derived on the basis of the solutions of cross coupled stochastic algebraic riccati equations csares it is shown that if csares have an optimal solution then the closed loop system is exponentially mean square stable emss and has a cost bound in order to simplify computations and attain a global optimum the linear matrix inequality lmi technique is also considered finally a numerical example for a practical megawatt frequency control problem shows that the proposed methods can help in attaining an adequate cost bound furthermore the features of these methods are characterized

robust design of stochastic controllers for nonlinear systems the previous results are generalized on the stabilizing property of a control scheme designed for a class of discrete time nonlinear stochastic systems first the existing controller is made more robust with a prescribed degree of stability by proper modifications next the inherent robustness is illustrated by a design utilizing erroneous noise characteristics reconsideration of the stability analysis used allows one to treat a larger class of nonlinear stochastic systems with more general structures

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

on conjugacy classes of maximal subgroups of finite simple groups and a related zeta function we prove that the number of conjugacy classes of maximal subgroups of bounded order in a finite group of lie type of bounded rank is bounded for exceptional groups this solves a longstanding open problem the proof uses among other tools some methods from geometric invariant theory using this result we provide a sharp bound for the total number of conjugacy classes of maximal subgroups of lie type groups of fixed rank drawing conclusions regarding the behaviour of the corresponding zeta function g s m maxg g m s which appears in many probabilistic applications more specifically we are able to show that for simple groups g and for any fixed real number s 1 g s 0 as g this confirms a conjecture made in 27 we also apply these results to prove the conjecture made in 29 that the symmetric group sn has n o 1 conjugacy classes of primitive maximal subgroups 2000 mathematics classification numbers 20e28 20g15 20d06

generating minimally transitive permutation groups abstract we prove that each minimally transitive permutation group of degree n can be generated by n 1 elements where n max m there exists a prime p such that p m divides n

graph based representation for multiview image geometry in this paper we propose a new geometry representation method for multiview image sets our approach relies on graphs to describe the multiview geometry information in a compact and controllable way the links of the graph connect pixels in different images and describe the proximity between pixels in 3d space these connections are dependent on the geometry of the scene and provide the right amount of information that is necessary for coding and reconstructing multiple views our multiview image representation is very compact and adapts the transmitted geometry information as a function of the complexity of the prediction performed at the decoder side to achieve this our graph based representation gbr carefully selects the amount of geometry information needed before coding this is in contrast with depth coding which directly compresses with losses the original geometry signal thus making it difficult to quantify the impact of coding errors on geometry based interpolation we present the principles of this gbr and we build an efficient coding algorithm to represent it we compare our gbr approach to classical depth compression methods and compare their respective view synthesis qualities as a function of the compactness of the geometry description we show that gbr can achieve significant gains in geometry coding rate over depth based schemes operating at similar quality experimental results demonstrate the potential of this new representation

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

output tracking of high order stochastic nonlinear systems with application to benchmark mechanical system this note considers output tracking of high order stochastic nonlinear systems without imposing any restriction on the high order and the drift and diffusion terms by using the backstepping design technique a smooth state feedback controller is given to guarantee that the solution process is bounded in probability and the error signal between the output and the reference signal can be regulated into a small neighborhood of the origin in probability a practical example of stochastic benchmark mechanical system and simulation are provided to demonstrate the effectiveness of the control scheme

disturbance observer based elegant anti disturbance saturation control for a class of stochastic systems in this paper the elegant anti disturbance saturation control problem is discussed for a class of stochastic systems with multiple heterogeneous disturbances which include three kinds of disturba

new approach to general nonlinear discrete time stochastic h_ infty control in this paper a new approach based on convex analysis is introduced to solve the h infty problem for discrete time nonlinear stochastic systems first by using the disintegration property of the conditional expectation sufficient necessary conditions are given for the internal stability of the concerned systems second in order to separate the unknown exogenous disturbance from the state variables the properties of convex functions are applied to prove the stochastic version of bounded real lemma brl third the state feedback h infty control problem is studied and an h infty control is designed based on the brl finally two numerical examples and one real world regulation control example of synthetic genetic circuit are presented to show the effectiveness of our developed theory

low dimensional representations of special unitary groups abstract we prove gap results for the low dimensional representation of unitary groups in nondefining characteristics more precisely we give a lower bound for the third smallest degree of a nontrivial absolutely irreducible representation of the groups mentioned above which is almost in the order of magnitude of the square of the two smallest such representations as a corollary we obtain the uniqueness of weil representations in all cross characteristics for the unitary groups our approach uses some results on ordinary representations which can be proved using deligne lusztig theory and which might be of independent interest as well as information on decomposition matrices

on stabilizability and exact observability of stochastic systems with their applications this paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications with the aid of the operator spectrum a necessary and sufficient condition is given for the stabilizability of stochastic systems some new concepts such as unremovable spectrum and strong solution are introduced an unremovable spectral theorem and a stochastic popov belevith hautus criterion for exact observability are presented as applications a comparison theorem for stochastic algebraic riccati equations and a result on lyapunov type equations are obtained

state feedback h_ infty control for a class of nonlinear stochastic systems this paper discusses the h infty control problem for a class of nonlinear stochastic systems with both state and disturbance dependent noise by means of hamilton jacobi equations both infinite and finite horizon nonlinear stochastic h infty control designs are developed some results on nonlinear h infty control of deterministic systems are generalized to a stochastic setting we introduce some useful concepts such as zero state observability and zero state detectability which together with the stochastic lasalle invariance principle yield some valuable consequences in infinite horizon nonlinear stochastic h infty control

absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty this paper is concerned with existence and optimality properties of so called guaranteed cost controllers for an uncertain system subject to structured uncertainty the uncertainty in the system is assumed to have a stochastic character and to satisfy certain stochastic integral constraints it is shown that a minimax optimal guaranteed cost state feedback controller for a stochastic system can be synthesized as a state feedback controller absolutely stabilizing this system for each initial state of the system this controller can be found by parametric optimization of solutions of a parameter dependent generalized matrix riccati equation arising in stochastic h infty theory

bounds on the number and sizes of conjugacy classes in finite chevalley groups with applications to derangements we present explicit upper bounds for the number and size of conjugacy classes in finite chevalley groups and their variations these results have been used by many authors to study zeta functions associated to representations of finite simple groups random walks on chevalley groups the final solution to the ore conjecture about commutators in finite simple groups and other similar problems in this paper we solve a strong version of the boston shalev conjecture on derangements in simple groups for most of the families of primitive permutation group representations of finite simple groups the remaining cases are settled in two other papers of the authors and applications are given in a third

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

stochastic h sub spl infin tracking with preview for state multiplicative systems the problem of finite horizon h sub spl infin tracking for linear time varying systems with stochastic parameter uncertainties is investigated we consider three tracking patterns depending on the nature of the reference signal i e whether it is perfectly known in advance measured on line or previewed in a fixed time interval ahead the stochastic uncertainties appear in both the dynamic and measurement matrices of the system for each of the above three cases a game theory approach is applied for the state feedback case where given a specific reference signal the controller plays against nature which chooses the initial condition and the energy bounded disturbance the problems are solved using an expected value of the standard performance index over the stochastic parameters where necessary and sufficient conditions are found for the existence of a saddle point equilibrium the infinite horizon time invariant tracking problem is also solved the theory developed is demonstrated by a simple tracking example

arbitrarily shaped motion prediction for depth video compression using arithmetic edge coding depth image compression is important for compact representation of 3d visual data in texture plus depth format where texture and depth maps from one or more viewpoints are encoded and transmitted a decoder can then synthesize a freely chosen virtual view via depth image based rendering using nearby coded texture and depth maps as reference further depth information can be used in other image processing applications beyond view synthesis such as object identification segmentation and so on in this paper we leverage on the observation that neighboring pixels of similar depth have similar motion to efficiently encode depth video specifically we divide a depth block containing two zones of distinct values e g foreground and background into two arbitrarily shaped regions sub blocks along the dividing boundary before performing separate motion prediction mp while such arbitrarily shaped sub block mp can lead to very small prediction residuals resulting in few bits required for residual coding it incurs an overhead to transmit the dividing boundaries for sub block identification at decoder to minimize this overhead we first devise a scheme called arithmetic edge coding aec to efficiently code boundaries that divide blocks into sub blocks specifically we propose to incorporate the boundary geometrical correlation in an adaptive arithmetic coder in the form of a statistical model then we propose two optimization procedures to further improve the edge coding performance of aec for a given depth image the first procedure operates within a code block and allows lossy compression of the detected block boundary to lower the cost of aec with an option to augment boundary depth pixel values matching the new boundary given the augmented pixels do not adversely affect synthesized view distortion the second procedure operates across code blocks and systematically identifies blocks along an object contour that should be coded using sub block mp via a rate distortion optimized trellis experimental results show an average overall bitrate reduction of up to 33 over classical h 264 avc

on maximal subfactors from quantum groups abstract motivated by a conjecture about maximal intermediate subfactors in this paper we show that subfactors from representations of universal quantum enveloping algebras with deformation parameter greater than zero are maximal this gives continuous family of non amenable subfactors which verify our conjecture using the same idea we also give a group theoretical description of our conjecture for subfactors related to representations of finite group

robust stability and stabilization of a class of nonlinear discrete time stochastic systems an lmi approach abstract a problem of robust state feedback stability and stabilization of nonlinear discrete time stochastic processes is considered the linear rate vector of a discrete time system is perturbed by a nonlinear function that satisfies a quadratic constraint our objective is to show how linear constant feedback laws can be formulated to stabilize this type of nonlinear discrete time systems and at the same time maximize the bounds on this nonlinear perturbing function which the system can tolerate without becoming unstable the state dependent diffusion is modeled by a normal sequence of identically independently distributed random variables the new formulation provides a suitable setting for robust stabilization of nonlinear discrete time systems where the underlying deterministic systems satisfy the generalized matching conditions our method which is based on linear matrix inequalities lmis is distinctive from the existing robust control and absolute stability techniques examples are given to demonstrate the obtained results

feedback stabilizability of non linear stochastic systems with state dependent noise this paper deals with non linear stochastic systems with state dependent noise based on the solution of the stochastic algebraic riccati equation sufficient conditions are derived which assure the existence of state feedback control laws such that the closed loop system is locally and globally stable in probability

upper bounds for the number of conjugacy classes of a finite group abstract for a finite group g let k g denote the number of conjugacy classes of g we prove that a simple group of lie type of untwisted rank l over the field of q elements has at most 6 q l conjugacy classes using this estimate we show that for completely reducible subgroups g of gl n q we have k g q 10 n confirming a conjecture of kovacs and robinson for finite groups g with f g a p group we prove that k g cp a where p a is the order of a sylow p subgroup of g and c is a constant for groups with o p g 1 we obtain that k g g p this latter result confirms a conjecture of iranzo navarro and monasor we also improve various earlier results concerning conjugacy classes of permutation groups and linear groups as a by product we show that any finite group g has a soluble subgroup s and a nilpotent subgroup n such that k g s and k g n 3

exponential stability of large scale stochastic differential equations abstract given a large scale stochastic system described by a number of subsystems we introduce the corresponding isolated subsystems it is shown that the exponential stability of the isolated systems implies the exponential stability of the large scale system under some hypotheses added on the interconnected terms we also study a slightly special case where the large scale system is described in a hierarchical form i e the system consists of several subsystems and each subsystem interacts only with lower subsystems but not with higher subsystems

quadratic games and h type problems for time varying systems abstract h type control problems with state feedback are considered for time varying systems first general quadratic differential games are studied and then the relationship between h problems and differential games is clarified a necessary and sufficient condition for the existence of a stabilizing controller such that the norm of the operator from the disturbance to the output is less than a prescribed number is given in terms of a riccati equation earlier results on time invariant systems are found to be special cases of our main results the finite horizon problem is also studied

on a conjecture of g e wall abstract we prove that if g is a finite almost simple group having socle of lie type of rank r then the number of maximal subgroups of g is at most c r 2 3 g where c is an absolute constant this verifies a conjecture of wall for groups of sufficiently large rank using this we prove that any finite group g has at most 2 c g 3 2 maximal subgroups

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

numerical solution of stochastic nash games with state dependent noise for weakly coupled large scale systems abstract this paper discusses the infinite horizon stochastic nash games with state dependent noise after establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the cross coupled stochastic algebraic riccati equations csares a new algorithm that combines newton s method with two fixed point algorithms for solving the csares is derived as a result it is shown that the proposed algorithm attains quadratic convergence and the reduced order computations for sufficiently small parameter e as another important feature the high order approximate strategy that is based on the iterative solutions is proposed using such strategy the degradation of the cost functional is investigated finally in order to demonstrate the efficiency of the proposed algorithms computational examples are provided

adaptive stabilization of stochastic nonholonomic systems with nonlinear parameterization this paper investigates the problem of adaptive stabilization by state feedback for a class of stochastic nonholonomic systems in chained form with nonlinear parameterization a parameter separation technique is introduced to transform the nonlinear parameterized nonholonomic system into a linear like parameterized one then using input state scaling and backstepping techniques an adaptive state feedback controller is obtained based on switching strategy to eliminate the phenomenon of uncontrollability global asymptotic regulation in probability of the closed loop system states are guaranteed finally a simulation example is provided to illustrate the effectiveness of the proposed method

on a subfactor generalization of wallʼs conjecture abstract in this paper we discuss a conjecture on intermediate subfactors which is a generalization of wall s conjecture from the theory of finite groups we explore special cases of this conjecture and present supporting evidence in particular we prove special cases of this conjecture related to some finite dimensional kac algebras of izumi kosaki type which include relative version of wall s conjecture for solvable groups

invariable generation and the chebotarev invariant of a finite group a subset s of a finite group g invariably generates g if g sg s s s for each choice of g s g s s we give a tight upper bound on the minimal size of an invariable generating set for an arbitrary finite group g in response to a question in kowalski and zywina 2010 kz we also bound the size of a randomly chosen set of elements of g that is likely to generate g invariably along the way we prove that every finite simple group is invariably generated by two elements