a bogolyubov type theorem with a nonconvex constraint in banach spaces we prove an analogue of the classical bogolyubov theorem with a nonconvex constraint in the case we consider the constraint is the solution set of a cauchy problem for a differential inclusion with a nonconvex right hand side satisfying a lipschitz condition our approach is based on a relaxation argument as in the filippov wazewski theorem

polyhedral sweeping processes with unbounded nonconvex valued perturbation abstract a polyhedral sweeping process with a multivalued perturbation whose values are nonconvex unbounded sets is studied in a separable hilbert space polyhedral sweeping processes do not satisfy the traditional assumptions used to prove existence theorems for convex sweeping processes we consider the polyhedral sweeping process as an evolution inclusion with subdifferential operators depending on time the widely used assumption of lipschitz continuity for the multivalued perturbation term is replaced by a weaker notion of h lipschitzness the existence of solutions is proved for this sweeping process

stability and euler approximation of one sided lipschitz differential inclusions ordinary differential and functional differential inclusions with compact right hand sides are considered stability theorems of filippov s type in the convex and nonconvex case are proved under a one sided lipschitz condition which extends the notions of lipschitz continuity dissipativity and the uniform one sided lipschitz condition for set valued mappings the accuracy of approximation of the solution sets by means of the euler discretization scheme for both types of inclusions is estimated

sampling design for gaussian detection problems we propose an approach for the design of sampling schemes for gaussian hypothesis testing problems our approach for this design is based on the class of ali silvey see j royal stat soc series b vol 28 p 131 43 1996 distance measures closed forms for the bhattacharyya distance the i divergence the j divergence and the chernoff distance between the class conditional densities are obtained for the sampling design problem in the strong signal case a new member of the class of ali silvey distance measures that is suitable for the detection problem in the weak signal case is also derived sampling schemes are determined to maximize those four distance measures as well as the new distance measure for the strong signal case and the weak signal case respectively the detection performance of our sampling schemes is compared with those of various other sampling schemes by means of numerical examples comparisons show that the sampling design based on ali silvey distance measures result in superior performance

numerical solution of a class of fractional order integro differential algebraic equations using muntz jacobi tau method abstract this paper presents a spectral tau method based on muntz jacobi basis functions for approximating the solutions of fractional order volterra integro differential algebraic equations we examine the solvability of the considered equation and we show that the exact solutions suffer from a singularity at the origin numerical solvability and convergence analysis of the proposed approximate approach are also studied and the error bounds are obtained in a weighted l 2 norm some illustrative examples are presented to validate the theoretical results

improved results on transmission power control for remote state estimation we consider a sensor transmission power control problem for remote state estimation in this problem a sensor sends its local estimate to a remote estimator over a wireless packet dropping communication channel the transmission power is determined by a recently proposed algorithm which uses the innovative information contained in the measurement in the current paper we focus on parameter optimization arising from the selection of design parameters for this power controller the existing work obtained a suboptimal solution to the parameter optimization problem while by using a vector rearrangement inequality argument and the vector majorization we now show that there exists an optimal solution within a subset of the whole feasible set by leveraging this property we obtain an optimal solution via solving a convex optimization problem

scheduling two gauss markov systems an optimal solution for remote state estimation under bandwidth constraint we consider scheduling two gauss markov systems two sensors each measuring the state of one of the two systems compute and report their local state estimates to a central remote estimator respectively due to the bandwidth constraint at each time only one of the sensors is allowed to communicate its estimate with the remote estimator upon receiving the data from the sensors the remote estimator computes the minimum mean squared error estimate of each system s state we provide an explicit construction of an optimal schedule which is periodic hence allows simple and efficient practical implementation and minimizes the sum of the average estimation error covariance of each system

discrete approximations and refined euler lagrange conditions fornonconvex differential inclusions this paper deals with the bolza problem p for differential inclusions subject to general endpoint constraints we pursue a twofold goal first we develop a finite difference method for studying p and construct a discrete approximation to p that ensures a strong convergence of optimal solutions second we use this direct method to obtain necessary optimality conditions in a refined euler lagrange form without standard convexity assumptions in general we prove necessary conditions for the so called intermediate relaxed local minimum that takes an intermediate place between the classical concepts of strong and weak minima in the case of a mayer cost functional or boundary solutions to differential inclusions this euler lagrange form holds without any relaxation the results obtained are expressed in terms of nonconvex valued generalized differentiation constructions for nonsmooth mappings and sets

operational tau method for singular system of volterra integro differential equations the legendre spectral tau matrix formulation is proposed to approximate solution of singular system of volterra integro differential equations the existence and uniqueness solution of this system are investigated by means of the smoothing property of a volterra integral operator and some projectors the l 2 convergence of the numerical method is analyzed it is proved theoretically and demonstrated numerically that the proposed method converges exponentially finally two numerical examples illustrate the theoretical results

optimal linear estimators for systems with random sensor delays multiple packet dropouts and uncertain observations this paper is concerned with the optimal linear estimation problem for linear discrete time stochastic systems with random sensor delays packet dropouts and uncertain observations we develop a unified model to describe the mixed uncertainties of random delays packet dropouts and uncertain observations by three bernoulli distributed random variables with known distributions based on the proposed model the optimal linear estimators that only depend on probabilities are developed via an innovation analysis approach their solutions are given in terms of a riccati equation and a lyapunov equation they can deal with the optimal linear filtering prediction and smoothing for systems with random sensor delays packet dropouts and uncertain observations in a unified framework simulation results show the effectiveness of the proposed optimal linear estimators

order of convergence of one step methods for volterra integral equations of the second kind nice proofs of convergence and asymptotic expansions are known for one step methods for ordinary differential equations it is shown that these proofs can be generalized in a natural way to extended one step methods for volterra integral equations of the second kind furthermore the convergence of mixed one step methods is investigated for both types general volterra runge kutta methods are considered as examples

the numerical solution of the semi explicit idaes by discontinuous piecewise polynomial approximation abstract in this paper we consider a semi explicit form of volterra integro differential algebraic equations idaes and investigate the existence and uniqueness of solution of these systems by using differentiability index numerical method based on discontinuous piecewise polynomial approximation is proposed for the solution of the semi explicit idaes and global convergence results are established the performance of the numerical scheme is illustrated by means of some test problems

existence stability and optimality for optimal control problems governed by maximal monotone operators abstract we study optimal control problems governed by maximal monotone differential inclusions with mixed control state constraints in infinite dimensional spaces we obtain some existence results for this kind of dynamics and construct the discrete approximations that allows us to strongly approximate optimal solutions of the continuous type optimal control problems by their discrete counterparts our approach allows us to apply our results for a wide class of mappings that are applicable in mechanics and material sciences

discrete approximations relaxation and optimization of one sided lipschitzian differential inclusions in hilbert spaces we study discrete approximations of nonconvex differential inclusions in hilbert spaces and dynamic optimization optimal control problems involving such differential inclusions and their discrete approximations the underlying feature of the problems under consideration is a modified one sided lipschitz condition imposed on the right hand side i e on the velocity sets of the differential inclusion which is a significant improvement of the conventional lipschitz continuity our main attention is paid to establishing efficient conditions that ensure the strong approximation in the w1 p norm as p 1 of feasible trajectories for the one sided lipschitzian differential inclusions under consideration by those for their discrete approximations and also the strong convergence of optimal solutions to the corresponding dynamic optimization problems under discrete approximations to proceed with the latter issue we derive a new extension of the bogolyubov type relaxation density theorem to the case of differential inclusions satisfying the modified one sided lipschitzian condition all the results obtained are new not only in the infinite dimensional hilbert space framework but also in finite dimensional spaces

on sinc discretization for systems of volterra integral algebraic equations abstract integral algebraic equations iaes are coupled systems of volterra integral equations of the first and second kind which naturally arise in many applications in mathematical physics in this paper we solve the iaes of index 1 by sinc collocation discretization and prove that the discrete solutions converge to the true solutions of the iaes exponentially the discrete solutions are determined by linear systems which can be effectively solved by suitable iteration methods numerical examples are given to illustrate the effective performance of our method

baire s category and the bang bang property for evolution differential inclusions of contractive type abstract the baire category method is employed in order to establish that the bang bang property holds for a class of evolution differential inclusions of contractive type in reflexive and separable real banach spaces

the numerical solution of integral algebraic equations of index 1 by polynomial spline collocation methods in this paper we study polynomial spline collocation methods applied to a particular class of integral algebraic equations of volterra type we analyse mixed systems of second and first kind integral equations global convergence and local superconvergence results are established

power scheduling of universal decentralized estimation in sensor networks we consider the optimal power scheduling problem for the decentralized estimation of a noise corrupted deterministic signal in an inhomogeneous sensor network sensor observations are first quantized into discrete messages then transmitted to a fusion center where a final estimate is generated supposing that the sensors use a universal decentralized quantization estimation scheme and an uncoded quadrature amplitude modulated qam transmission strategy we determine the optimal quantization and transmit power levels at local sensors so as to minimize the total transmit power while ensuring a given mean squared error mse performance the proposed power scheduling scheme suggests that the sensors with bad channels or poor observation qualities should decrease their quantization resolutions or simply become inactive in order to save power for the remaining active sensors their optimal quantization and transmit power levels are determined jointly by individual channel path losses local observation noise variance and the targeted mse performance numerical examples show that in inhomogeneous sensing environment significant energy savings is possible when compared to the uniform quantization strategy

communication over fading channels with delay constraints we consider a user communicating over a fading channel with perfect channel state information data are assumed to arrive from some higher layer application and are stored in a buffer until transmitted we study adapting the user s transmission rate and power based on the channel state information as well as the buffer occupancy the objectives are to regulate both the long term average transmission power and the average buffer delay incurred by the traffic two models for this situation are discussed one corresponding to fixed length variable rate codewords and one corresponding to variable length codewords the tradeoff between the average delay and the average transmission power required for reliable communication is analyzed a dynamic programming formulation is given to find all pareto optimal power delay operating points we then quantify the behavior of this tradeoff in the regime of asymptotically large delay in this regime we characterize simple buffer control policies which exhibit optimal characteristics connections to the delay limited capacity and the expected capacity of fading channels are also discussed

optimal control of the sweeping process over polyhedral controlled sets abstract the paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given bolza type functional which depends on control and state variables as well as their velocities besides the highly non lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types all of this creates serious challenges for deriving necessary optimality conditions we develop here the method of discrete approximations and combine it with advanced tools of first order and second order variational analysis and generalized differentiation this approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions as a by product of the developed approach we prove the strong w 1 2 convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous time system and derive necessary optimality conditions for the discrete counterparts the established necessary optimality conditions for the sweeping process are illustrated by several examples

optimal full order and reduced order estimators for discrete time systems with multiple packet dropouts this paper is concerned with the estimation problem for discrete time stochastic linear systems with multiple packet dropouts based on a recently developed model for multiple packet dropouts the original system is transferred to a stochastic parameter system by augmentation of the state and measurement the optimal full order linear filter of the form of employing the received outputs at the current and last time instants is investigated the solution to the optimal linear filter is given in terms of a riccati difference equation governed by packet arrival rate the optimal filter is reduced to the standard kalman filter when there are no packet dropouts the steady state filter is also studied a sufficient condition for the existence of the steady state filter is given and the asymptotic stability of the optimal filter is analyzed at last a reduced order filter is investigated

topological theory of non autonomous parabolic evolution inclusions on a noncompact interval and applications in this paper we consider the topological structure of the solution set of non autonomous parabolic evolution inclusions with time delay defined on non compact intervals the result restricted to compact intervals is then extended to non autonomous parabolic control problems with time delay moreover as the applications of the information about the structure we establish the existence result of global integral solutions for non autonomous cauchy problems subject to nonlocal condition and prove the invariance of a reachability set for non autonomous control problems under single valued nonlinear perturbations finally some illustrating examples are supplied

optimal control of a nonconvex perturbed sweeping process abstract the paper concerns optimal control of discontinuous differential inclusions of the normal cone type governed by a generalized version of the moreau sweeping process with control functions acting in both nonconvex moving sets and additive perturbations this is a new class of optimal control problems in comparison with previously considered counterparts where the controlled sweeping sets are described by convex polyhedra besides a theoretical interest a major motivation for our study of such challenging optimal control problems with intrinsic state constraints comes from the application to the crowd motion model in a practically adequate planar setting with nonconvex but prox regular sweeping sets based on a constructive discrete approximation approach and advanced tools of first order and second order variational analysis and generalized differentiation we establish the strong convergence of discrete optimal solutions and derive a complete set of necessary optimality conditions for discrete time and continuous time sweeping control systems that are expressed entirely via the problem data

continuous collocation approximations to solutions of first kind volterra equations in this paper we give necessary and sufficient conditions for convergence of continuous collocation approximations of solutions of first kind volterra integral equations the results close some longstanding gaps in the theory of polynomial spline collocation methods for such equations the convergence analysis is based on a runge kutta or ode approach

two dimensional integral algebraic systems analysis and computational methods abstract in this article we formulate sufficient conditions for the existence and uniqueness of solution to systems of two dimensional volterra integral equations in which the coefficient of the main term is a singular matrix a numerical method is introduced which can be applied to approximate the solution when the given conditions are satisfied the convergence of this method is proved and illustrated by numerical examples

differential algebraic equations indices and integral algebraic equations in a recent report hairer lubich and roche report ch 1211 dept de mathematiques universite de geneve geneve switzerland 1988 define the index of differential algebraic equations daes by considering the effect of perturbations of the equations on the solutions this index which will be called the perturbation index p i is one more than the number of derivatives of the perturbation that must appear in any estimate of the bound of the change in the solution an earlier form of index used by a number of authors including gear and petzold siam j numer anal 21 1984 pp 716 728 is determined by the number of differentiations of the daes that are required to generate an ordinary differential equation ode satisfied by the solution this will be called the differential index d i hairer lubich and roche give an example whose differential index is one and perturbation index is two and other examples where they are identical it will be shown that d i leqq p i leqq d i 1 and th

optimal convergence results of piecewise polynomial collocation solutions for integral algebraic equations of index 3 in this work we will consider piecewise polynomial collocation methods for a new class of integral algebraic equations of index 3 an analysis of the global convergence properties of the collocation methods is given and the optimal order of convergence results is established the performance of the proposed scheme is illustrated by means of two numerical examples and confirm that we can achieve the expected theoretical orders of convergence

optimal periodic transmission power schedules for remote estimation of arma processes we consider periodic sensor transmission power allocation with an average energy constraint the sensor sends its kalman filter based state estimate to the remote estimator through an unreliable link dropout probabilities depend on the power level used to encompass applications where the estimator needs to attend to multiple tasks we allow for irregular sampling following a periodic pattern using properties of an underlying markov chain model we derive an explicit expression for the estimation error covariance the results are then used to study optimal sensor power scheduling which minimizes the average error covariance

integral algebraic equations theory of collocation methods i our analysis of collocation solutions for general systems of linear integral algebraic equations iaes is based on the notions of the tractability index and the nu smoothing property of a volterra integral operator these are used to decouple the given iae system into the inherent system of regular second kind volterra integral equations vies and a system of first kind vies this decoupling is then used to derive the optimal convergence properties of piecewise polynomial collocation solutions numerical examples illustrate the theoretical results

variational analysis of evolution inclusions the paper is devoted to optimization problems of the bolza and mayer types for evolution systems governed by nonconvex lipschitzian differential inclusions in banach spaces under endpoint constraints described by finitely many equalities and inequalities with generally nonsmooth functions we develop a variational analysis of such problems mainly based on their discrete approximations and the usage of advanced tools of generalized differentiation satisfying comprehensive calculus rules in the framework of asplund and hence any reflexive banach spaces in this way we establish extended results on stability of discrete approximations with the strong w 1 2 convergence of optimal solutions under consistent perturbations of endpoint constraints and derive necessary optimality conditions for nonconvex discrete time and continuous time systems in the refined euler lagrange and weierstrass pontryagin forms accompanied by the appropriate transversality inclusions in contrast to the case of geometric endpoint constraints in infinite dimensions the necessary optimality conditions obtained in this paper do not impose any nonempty interiority finite codimension normal compactness assumptions the approach and results developed in the paper make a bridge between optimal control dynamic optimization and constrained mathematical programming problems in infinite dimensional spaces

difference methods for differential inclusions a survey the main objective of this survey is to study convergence properties of difference methods applied to differential inclusions it presents in a unified way a number of results scattered in the li

structural analysis of linear integral algebraic equations abstract the choice of a feasible numerical method for the solution of an integral algebraic equation iae requires knowledge about its index and solvability in this paper the method for structural analysis of differential algebraic equation systems daes is extended to analyze the structure of a linear iae its index and solvability are determined based on the sparsity pattern of the iae and the smoothing property of a volterra integral operator

numerical solution of volterra integral algebraic equations using block pulse functions this paper presents a method for computing numerical solutions for linear volterra integral algebraic equations using block pulse functions the problem is transformed to a linear lower triangular system of algebraic equations using the operational matrix associated with block pulse functions convergence result and numerical examples are presented to illustrate the efficiency and applicability of the method

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms