the approximation for the boundary optimal control problem of burgers fisher equation with constraints this paper deals with the numerical approximation with meshless method for the boundary optimal control problem with some control and state constraints governed by the burgers fisher equation which is a nonlinear evolution equation and is the prototype model for the reaction convection and diffusion phenomena arising in many spatial temporal processes by making use of the element free galerkin efg method the original optimal control problem is discretized spatially to a semi discrete optimal control problem governed by a system of nonlinear ordinary differential equations then by using the control parameterization method the original problem can be reduced to an optimal parameter selection problem governed by a lumped parameter system which can be solved as a nonlinear optimization problems by using the sequential quadratic programming sqp algorithm the numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method

approximations of two dimensional mean field games with nonsymmetric controls abstract the numerical methods are presented for solving economic problems formulated in the mean field game mfg form the mean field equilibrium is a solution of the coupled system of two parabolic partial differential equations the fokker planck kolmogorov equation and the hamilton jacobi bellman one the description focuses on the discrete approximation of these equations and on the application of the mfg theory directly at discrete level this approach results in an efficient algorithm for finding the corresponding grid control functions contrary to other difference schemes here the semi lagrangian approximation is applied which improves properties of a discrete problem of this type this implies the fast convergence of an iterative algorithm for the minimization of the cost functional the constructed algorithms are implemented to the problem of carbon dioxide pollution

a new computational approach to solving a class of optimal control problems a class of optimal control problems in which the control signals are bounded and appear linearly in the hamiltonian function occur in many applications in the solutions to these problems the fact that optimal control trajectories may contain discontinuities and possibly singular arcs sub arcs makes the problems extremely difficult to solve if not impossible this paper presents a novel and efficient computational method for solving such problems the method consists of two steps in the first step the original optimal control problem with possible discontinuities and singular arcs in control is converted into one with continuous and non singular control trajectories by adding to the performance indexes a perturbed or weighted energy term the resultant boundary value problem can easily be solved for an appropriately large value of the perturbation parameter in the second step a continuation method imbedding method or homotopy method is developed to obtain the solution to the original problem by

a maximum principle for free endtime optimal control problems with data discontinuous in time recently a maximum principle has been proved for free endtime problems when the dynamics and the control constraint set are assumed to be merely measurable with respect to the time variable a new simple derivation of this optimality condition is given from standard fixed endtime results it involves a generalization of the customary boundary condition on the maximized hamiltonian function evaluated along the optimal state trajectory and costate function the hypotheses under which the maximum principle is proved permit unilateral state constraints data merely lipschitz continuous in the state variable and endpoint constraints expressed as general set inclusions the primary concern is with methodology and setting down a simple proof of the maximum principle for problems with data measurable in the time variable

shape recognition with spectral distances recent works have shown the use of diffusion geometry for various pattern recognition applications including nonrigid shape analysis in this paper we introduce spectral shape distance as a general framework for distribution based shape similarity and show that two recent methods for shape similarity due to rustamov and mahmoudi and sapiro are particular cases thereof

can one hear the shape of a drum revisited in a landmark paper mark kac in 1966 amer math monthly 73 pp 1 23 showed that geometric properties of regions in r 2 can be obtained by studying the asymptotic properties of the spectrum of the laplacian he also conjectured that the shape of a region might be completely determined by the spectrum we describe recent developments in this field and discuss the status of the kac conjecture as well as similar conjectures for operators other than the laplacian

a gromov hausdorff framework with diffusion geometry for topologically robust non rigid shape matching in this paper the problem of non rigid shape recognition is studied from the perspective of metric geometry in particular we explore the applicability of diffusion distances within the gromov hausdorff framework while the traditionally used geodesic distance exploits the shortest path between points on the surface the diffusion distance averages all paths connecting the points the diffusion distance constitutes an intrinsic metric which is robust in particular to topological changes such changes in the form of shortcuts holes and missing data may be a result of natural non rigid deformations as well as acquisition and representation noise due to inaccurate surface construction the presentation of the proposed framework is complemented with examples demonstrating that in addition to the relatively low complexity involved in the computation of the diffusion distances between surface points its recognition and matching performances favorably compare to the classical geodesic distances in the presence of topological changes between the non rigid shapes

on joining non singular and singular optimal control subarcs necessary conditions for junctions between non singular and singular optimal control subarcs are proved for the case where the singular problem order is greater than one the generalized legendre clebsch condition glc vanishes at the junction and the derivative of the glc expression is non zero at the junction the proof requires the derivation of two identities which are system properties of higher order singular problems

brief paper optimal control problems with a continuous inequality constraint on the state and the control we consider an optimal control problem with a nonlinear continuous inequality constraint both the state and the control are allowed to appear explicitly in this constraint by discretizing the control space and applying a novel transformation a corresponding class of semi infinite programming problems is derived a solution of each problem in this class furnishes a suboptimal control for the original problem furthermore we show that such a solution can be computed efficiently using a penalty function method on the basis of these two ideas an algorithm that computes a sequence of suboptimal controls for the original problem is proposed our main result shows that the cost of these suboptimal controls converges to the minimum cost for illustration an example problem is solved

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

monotonic parareal control for quantum systems following encouraging experimental results in quantum control numerical simulations have known significant improvements through the introduction of efficient optimization algorithms yet the computational cost still prevents using these procedures for high dimensional systems often present in quantum chemistry using parareal framework we present here a time parallelization of these schemes which allows us to reduce significantly their computational cost while still finding convenient controls

optimal control computation for nonlinear systems with state dependent stopping criteria in this paper we consider a challenging optimal control problem in which the terminal time is determined by a stopping criterion this stopping criterion is defined by a smooth surface in the state space when the state trajectory hits this surface the governing dynamic system stops by restricting the controls to piecewise constant functions we derive a finite dimensional approximation of the optimal control problem we then develop an efficient computational method based on nonlinear programming for solving the approximate problem we conclude the paper with four numerical examples

a chebyshev technique for solving nonlinear optimal control problems a numerical technique for solving nonlinear optimal control problems is introduced the state and control variables are expanded in the chebyshev series and an algorithm is provided for approximating the system dynamics boundary conditions and performance index application of this method results in the transformation of differential and integral expressions into systems of algebraic or transcendental expressions in the chebyshev coefficients the optimum condition is obtained by applying the method of constrained extremum for linear quadratic optimal control problems the state and control variables are determined by solving a set of linear equations in the chebyshev coefficients applicability is illustrated with the minimum time and maximum radius orbit transfer problems

optimal control of switched systems and its parallel optimization algorithm in this paper a class of optimal switching control problems is considered in which the mode sequence of active subsystems and the number of mode switchings are not pre specified and both the switching sequence and the control inputs are to be chosen such that the cost functional is minimized for solving this problem we discuss the necessary conditions for optimality and the construction method for suboptimal solutions and develop a few sufficient conditions of judgment on the optimal or suboptimal solutions of the switched system according to the sufficient conditions a parallel computational algorithm is constructed to find optimal or suboptimal solutions for illustration two examples are solved using the proposed algorithm

spectral log demons diffeomorphic image registration with very large deformations this paper presents a new framework for capturing large and complex deformations in image registration and atlas construction this challenging and recurrent problem in computer vision and medical imaging currently relies on iterative and local approaches which are prone to local minima and therefore limit present methods to relatively small deformations our general framework introduces to this effect a new direct feature matching technique that finds global correspondences between images via simple nearest neighbor searches more specifically very large image deformations are captured in spectral forces which are derived from an improved graph spectral representation we illustrate the benefits of our framework through a new enhanced version of the popular log demons algorithm named the spectral log demons as well as through a groupwise extension named the groupwise spectral log demons which is relevant for atlas construction the evaluations of these extended versions demonstrate substantial improvements in accuracy and robustness to large deformations over the conventional demons approaches

existence and structure of minimum time control for multiple robot arms handling a common object the problem of the existence and structure of minimum time control for multiple robot arms cooperatively handling a common object is addressed the dynamical system is modeled by considering the arms as closed kinematic chains the conditions of the existence of the time optimal solution are verified by applying a lyapunov approach and the concept of the feedback equivalence to linear systems furthermore it is shown that the structure of the minimum time control law for individual joint actuators requires that at least one of the actuators is always saturated on any finite time subinterval while the rest of them are either saturated or singular depending upon the motion configurations and robot parameters thus it is suggested that totally singular optimal control does not exist in this problem but that partially singular control may occur this theoretical result should be able to provide insight into the dynamic characteristics of the multiple robot system which can be valuable in the path planni

runge kutta methods in optimal control and the transformed adjoint system the convergence rate is determined for runge kutta discretizations of nonlinear control problems the analysis utilizes a connection between the kuhn tucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle this connection can also be exploited in numerical solution techniques that require the gradient of the discrete cost function

on the problem of the time optimal manipulator arm turning two kinds of manipulators making spatial movements are discussed the problem of control which provides manipulator turning in the minimum possible time is considered a control satisfying the maximum principle of pontryagin has been designed for some set of boundary configurations with this control a manipulator link in the process of turning oscillates around a position corresponding to a minimum moment of inertia of a system with respect to an axis of rotation movement satisfying the maximum principle is compared to that for which the moment of inertia is minimal within the entire interval of time the simplified equations as well as the complete ones are investigated

symmetric alpha stable filter theory symmetric spl alpha stable s spl alpha s processes are used to model infinite variance impulsive noise in general wiener filter theory is not meaningful in s spl alpha s environments because the expectations may be unbounded to develop a theory for linear finite impulse response systems with independent identically distributed s spl alpha s inputs we propose median orthogonality as a linear filter criterion derive a generalized wiener hopf solution equation and show a sufficient condition for a filter to achieve the criterion for non gaussian s spl alpha s densities zero forcing least mean squares is the only well known filter that satisfies the criterion but others can be designed we present a second algorithm and simulations showing that both converge to the generalized wiener hopf solution

brief paper initial condition of costate in linear optimal control using convex analysis the pontryagin maximum principle is one of the most important results in optimal control and provides necessary conditions for optimality in the form of a mixed initial terminal boundary condition on a pair of differential equations for the system state and its conjugate costate unfortunately this mixed boundary value problem is usually difficult to solve since the pontryagin maximum principle does not give any information on the initial value of the costate in this paper we explore an optimal control problem with linear and convex structure and derive the associated dual optimization problem using convex duality which is often much easier to solve than the original optimal control problem we present that the solution to the dual optimization problem supplements the necessary conditions of the pontryagin maximum principle and elaborate the procedure of constructing the optimal control and its corresponding state trajectory in terms of the solution to the dual problem

distributed optimal control for multi agent trajectory optimization this paper presents a novel optimal control problem referred to as distributed optimal control that is applicable to multiscale dynamical systems comprised of numerous interacting agents the system performance is represented by an integral cost function of the macroscopic state that is optimized subject to a hyperbolic partial differential equation known as the advection equation the microscopic control laws are derived from the optimal macroscopic description using a potential function approach the optimality conditions of the distributed optimal control problem are first derived analytically and then demonstrated numerically through a multi agent trajectory optimization problem

applications of optimal multiprocesses in a previous paper a theory of necessary conditions for optimal multiprocess problems was supplied that is problems in dynamic optimization involving a collection of control systems coupled through constraints on the endpoints of the trajectories and the cost functions here the scope of the new theory is illustrated by application to optimization problems in investment planning impulse control optics robotics and renewable resources

time optimal zermelo s navigation problem with moving and fixed obstacles in this paper we consider a time optimal zermelo s navigation problem znp with moving and fixed obstacles this problem can be formulated as an optimal control problem with continuous inequality constraints and terminal state constraints by using the control parametrization technique together with the time scaling transform the problem is transformed into a sequence of optimal parameters selection problems with continuous inequality constraints and terminal state constraints for each problem an exact penalty function method is used to append all the constraints to the objective function yielding a new unconstrained optimal parameters selection problem it is solved as a nonlinear optimization problem different scenarios are considered in the simulation and the results obtained show that the proposed method is effective

brief paper multi modal control using adaptive motion description languages abstract in this paper we address the problem of adaptively enriching motion description languages for multi modal control by systematically enlarging the set of available modes this problem is formulated as an optimal control problem where new modes are designed by combining recurring mode string fragments into smooth new meta modes and variational arguments are employed to derive optimality conditions for this construction

brief paper optimal control problems with multiple characteristic time points in the objective and constraints in this paper we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points these time points can be either fixed or variable using the control parametrization technique and a time scaling transformation this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems each of these approximate problems can be viewed as a finite dimensional optimization problem new gradient formulae for the cost and constraint functions are derived with these gradient formulae standard gradient based optimization methods can be applied to solve each approximate optimal parameter selection problem for illustration two numerical examples are solved

wesd weighted spectral distance for measuring shape dissimilarity this paper presents a new distance for measuring shape dissimilarity between objects recent publications introduced the use of eigenvalues of the laplace operator as compact shape descriptors here we revisit the eigenvalues to define a proper distance called weighted spectral distance wesd for quantifying shape dissimilarity the definition of wesd is derived through analyzing the heat trace this analysis provides the proposed distance with an intuitive meaning and mathematically links it to the intrinsic geometry of objects we analyze the resulting distance definition present and prove its important theoretical properties some of these properties include 1 wesd is defined over the entire sequence of eigenvalues yet it is guaranteed to converge 2 it is a pseudometric 3 it is accurately approximated with a finite number of eigenvalues and 4 it can be mapped to the 0 1 interval last experiments conducted on synthetic and real objects are presented these experiments highlight the practical benefits of wesd for applications in vision and medical image analysis

a monotonic method for nonlinear optimal control problems with concave dependence on the state initially introduced in the framework of quantum control the so called monotonic algorithms have demonstrated very good numerical performance when dealing with bilinear optimal control problems this article presents a unified formulation that can be applied to more general nonlinear settings compatible with the hypothesis detailed below in this framework we show that the well posedness of the general algorithm is related to a nonlinear evolution equation we prove the existence of the solution to the evolution equation and give important properties of the optimal control functional finally we show how the algorithm works for selected models from the literature we also compare the algorithm with the gradient algorithm

method of evolving junctions a new approach to optimal control with constraints abstract we propose a new strategy called method of evolving junctions mej to compute the solutions for a class of optimal control problems with constraints on both state and control variables our main idea is that by leveraging the geometric structures of the optimal solutions we recast the infinite dimensional optimal control problem into an optimization problem depending on a finite number of points called junctions then using a modified gradient flow method whose dimension can change dynamically we find local solutions for the optimal control problem we also employ intermittent diffusion a global optimization method based on stochastic differential equations to obtain the global optimal solution we demonstrate via a numerical example that mej can effectively solve path planning problems in dynamical environments

brief paper a unified framework for the numerical solution of optimal control problems using pseudospectral methods a unified framework is presented for the numerical solution of optimal control problems using collocation at legendre gauss lg legendre gauss radau lgr and legendre gauss lobatto lgl points it is shown that the lg and lgr differentiation matrices are rectangular and full rank whereas the lgl differentiation matrix is square and singular consequently the lg and lgr schemes can be expressed equivalently in either differential or integral form while the lgl differential and integral forms are not equivalent transformations are developed that relate the lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem the lg and lgr discrete costate systems are full rank while the lgl discrete costate system is rank deficient the lgl costate approximation is found to have an error that oscillates about the true solution and this error is shown by example to be due to the null space in the lgl discrete costate system an example is considered to assess the accuracy and features of each collocation scheme

optimal boundary control for water hammer suppression in fluid transmission pipelines when fluid flow in a pipeline is suddenly halted a pressure surge or wave is created within the pipeline this phenomenon called water hammer can cause major damage to pipelines including pipeline ruptures in this paper we model the problem of mitigating water hammer during valve closure by an optimal boundary control problem involving a nonlinear hyperbolic pde system that describes the fluid flow along the pipeline the control variable in this system represents the valve boundary actuation implemented at the pipeline terminus to solve the boundary control problem we first use the method of lines to obtain a finite dimensional ode model based on the original pde system then for the boundary control design we apply the control parameterization method to obtain an approximate optimal parameter selection problem that can be solved using nonlinear optimization techniques such as sequential quadratic programming sqp we conclude the paper with simulation results demonstrating the capability of optimal boundary control to significantly reduce flow fluctuation

performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha stable process impulsive noise bursts in communication systems are traditionally handled by incorporating in the receiver a limiter which clips the received signal before integration an empirical justification for this procedure is that it generally causes the signal to noise ratio to increase recently very accurate models of impulsive noise were presented based on the theory of symmetric spl alpha stable probability density functions we examine the performance of optimum receivers designed to detect signals embedded in impulsive noise which is modeled as an infinite variance symmetric spl alpha stable process and compare it against the performance of several suboptimum receivers as a measure of receiver performance we compute an asymptotic expression for the probability of error for each receiver and compare it to the probability of error calculated by extensive monte carlo simulation

optimal control of systems with hard control bounds the numerical solution of the optimal control and trajectory of systems with hard control bounds is considered a new algorithm which extends the gradient method 1 to systems with hard control bounds is presented the algorithm is based on the use of an adjustable control variation weight acw matrix to enforce the bounds the application of the algorithm to the minimum time control of a two link robot arm is presented as an example

resolving isospectral drums by counting nodal domains several types of systems have been put forward during the past few decades to show that there exist isospectral systems which are metrically different one important class consists of laplace beltrami operators for pairs of flat tori in r n with n 4 we propose that the spectral ambiguity can be resolved by comparing the nodal sequences the numbers of nodal domains of eigenfunctions arranged by increasing eigenvalues in the case of isospectral flat tori in four dimensions where a four parameter family of isospectral pairs is known we provide heuristic arguments supported by numerical simulations to support the conjecture that the isospectrality is resolved by the nodal count thus one can count the shape of a drum if it is designed as a flat torus in four dimensions less

pseudospectral legendre based optimal computation of nonlinear constrained variational problems it is well known that spectrally accurate solution can be maintained if the grids on which a nonlinear physical problem is to be solved must be obtained by spectrally accurate techniques in this paper the pseudospectral legendre method for general nonlinear smooth and nonsmooth constrained problems of the calculus of variations is studied the technique is based on spectral collocation methods in which the trajectory x t is approximated by the nth degree interpolating polynomial using legendre gauss lobatto points as the collocation points and lagrange polynomials as trial functions the integral involved in the formulation of the problem is approximated based on legendre gauss lobatto integration rule thereby reducing the problem to a nonlinear programming one to which existing well developed algorithms may be applied the method is easy to implement and yields very accurate results illustrative examples are included to confirm the convergence of the pseudospectral legendre method moreover a numerical experiment on a nonsmooth problem indicates that by applying a smoothing filter procedure to the pseudospectral legendre approximation one can recover the nonsmooth solution within spectral accuracy

analysis of two dimensional non rigid shapes analysis of deformable two dimensional shapes is an important problem encountered in numerous pattern recognition computer vision and computer graphics applications in this paper we address three major problems in the analysis of non rigid shapes similarity partial similarity and correspondence we present an axiomatic construction of similarity criteria for deformation invariant shape comparison based on intrinsic geometric properties of the shapes and show that such criteria are related to the gromov hausdorff distance next we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole and present a construction of set valued distances based on the notion of pareto optimality finally we show that the correspondence between non rigid shapes can be obtained as a byproduct of the non rigid similarity problem as a numerical framework we use the generalized multidimensional scaling gmds method which is the numerical core of the three problems addressed in this paper

on the schrodinger equation and the eigenvalue problem if k is thekth eigenvalue for the dirichlet boundary problem on a bounded domain in n h weyl s asymptotic formula asserts that lambda k sim c n left frac k v d right 2 n hence sum limits i 1 k lambda i sim frac nc n n 2 k frac n 2 n v d 2 n we prove that for any domain and for all sum limits i 1 k lambda i geqq frac nc n n 2 k frac n 2 n v d 2 n a simple proof for the upper bound of the number of eigenvalues less than or equal to for the operator v x defined on n n 3 in terms of int limits mathbb r n v alpha n 2 is also provided

discriminative segmentation based evaluation through shape dissimilarity segmentation based scores play an important role in the evaluation of computational tools in medical image analysis these scores evaluate the quality of various tasks such as image registration and segmentation by measuring the similarity between two binary label maps commonly these measurements blend two aspects of the similarity pose misalignments and shape discrepancies not being able to distinguish between these two aspects these scores often yield similar results to a widely varying range of different segmentation pairs consequently the comparisons and analysis achieved by interpreting these scores become questionable in this paper we address this problem by exploring a new segmentation based score called normalized weighted spectral distance nwsd that measures only shape discrepancies using the spectrum of the laplace operator through experiments on synthetic and real data we demonstrate that nwsd provides additional information for evaluating differences between segmentations which is not captured by other commonly used scores our results demonstrate that when jointly used with other scores such as dice s similarity coefficient the additional information provided by nwsd allows richer more discriminative evaluations we show for the task of registration that through this addition we can distinguish different types of registration errors this allows us to identify the source of errors and discriminate registration results which so far had to be treated as being of similar quality in previous evaluation studies

on the linear quadratic minimum time problem a nontraditional minimum time problem that includes quadratic state and control weighting terms in the performance index is investigated this formulation provides a convenient solution to the problem that uses the solution of the riccati equation to compute the optimal feedback gain and the optimal time in some cases the latter is simply found using the derivative of the riccati equation solution

gradient method using pseudospectral collocation scheme for two stage optimal control with an unspecified switching time a two stage gradient method tgm based on traditional backward integration is firstly proposed for solving two stage nonlinear optimal control problem with arbitrary performance index and unspecif

finding interpolating curves minimizing l infty acceleration in the euclidean space via optimal control theory we study the problem of finding an interpolating curve passing through prescribed points in the euclidean space the interpolating curve minimizes the pointwise maximum length i e l infty norm of its acceleration we reformulate the problem as an optimal control problem and employ simple but effective tools of optimal control theory we characterize solutions associated with singular and nonsingular controls some of the results we obtain are new even for the scalar interpolating function case we reduce the infinite dimensional interpolation problem to an ensuing finite dimensional one and derive closed form expressions for interpolating curves consequently we devise efficient numerical techniques and illustrate them with examples

metric optimization for surface analysis in the laplace beltrami embedding space in this paper we present a novel approach for the intrinsic mapping of anatomical surfaces and its application in brain mapping research using the laplace beltrami eigen system we represent each surface with an isometry invariant embedding in a high dimensional space the key idea in our system is that we realize surface deformation in the embedding space via the iterative optimization of a conformal metric without explicitly perturbing the surface or its embedding by minimizing a distance measure in the embedding space with metric optimization our method generates a conformal map directly between surfaces with highly uniform metric distortion and the ability of aligning salient geometric features besides pairwise surface maps we also extend the metric optimization approach for group wise atlas construction and multi atlas cortical label fusion in experimental results we demonstrate the robustness and generality of our method by applying it to map both cortical and hippocampal surfaces in population studies for cortical labeling our method achieves excellent performance in a cross validation experiment with 40 manually labeled surfaces and successfully models localized brain development in a pediatric study of 80 subjects for hippocampal mapping our method produces much more significant results than two popular tools on a multiple sclerosis study of 109 subjects

robust suboptimal control of nonlinear systems in this paper we consider a nonlinear dynamic system with uncertain parameters our goal is to choose a control function for this system that balances two competing objectives i the system should operate efficiently and ii the system s performance should be robust with respect to changes in the uncertain parameters with this in mind we introduce an optimal control problem with a cost function penalizing both the system cost a function of the final state reached by the system and the system sensitivity the derivative of the system cost with respect to the uncertain parameters we then show that the system sensitivity can be computed by solving an auxiliary initial value problem this result allows one to convert the optimal control problem into a standard mayer problem which can be solved directly using conventional techniques we illustrate this approach by solving two example problems using the software miser3

brief paper pseudospectral methods for solving infinite horizon optimal control problems an important aspect of numerically approximating the solution of an infinite horizon optimal control problem is the manner in which the horizon is treated generally an infinite horizon optimal control problem is approximated with a finite horizon problem in such cases regardless of the finite duration of the approximation the final time lies an infinite duration from the actual horizon at t in this paper we describe two new direct pseudospectral methods using legendre gauss lg and legendre gauss radau lgr collocation for solving infinite horizon optimal control problems numerically a smooth strictly monotonic transformation is used to map the infinite time domain t 0 onto a half open interval t 1 1 the resulting problem on the finite interval is transcribed to a nonlinear programming problem using collocation the proposed methods yield approximations to the state and the costate on the entire horizon including approximations at t these pseudospectral methods can be written equivalently in either a differential or an implicit integral form in numerical experiments the discrete solution exhibits exponential convergence as a function of the number of collocation points it is shown that the map f 1 1 0 can be tuned to improve the quality of the discrete approximation

monotonic time discretized schemes in quantum control most of the numerical simulations in quantum bilinear control have used monotonically convergent algorithms of krotov introduced by tannor et al 15 of zhu rabitz 16 or their unified formulation in 17 however the properties of the discrete version of these procedures have not been yet tackled with we present in this paper a stable time and space discretization which preserves the monotonic properties of the monotonic algorithms numerical results show that the newly derived algorithms are stable and enable various experimentations

an effective pseudospectral method for constraint dynamic optimisation problems with characteristic times dynamic optimisation problem with characteristic times widely existing in many areas is one of the frontiers and hotspots of dynamic optimisation researches this paper considers a class of dynam

optimal bilinear control of an abstract schro dinger equation well posedness of abstract quantum mechanical systems is considered and the existence of optimal control of such systems is proved first order optimality systems are derived convergence of the monotone scheme for the solution of the optimality system is proved

on the hybrid optimal control problem theory and algorithms a class of hybrid optimal control problems hocp for systems with controlled and autonomous location transitions is formulated and a set of necessary conditions for hybrid system trajectory optimality is presented which together constitute generalizations of the standard maximum principle these are given for the cases of open bounded control value sets and compact control value sets the derivations in the paper employ i classical variational and needle variation techniques and ii a local controllability condition which is used to establish the adjoint and hamiltonian jump conditions in the autonomous switching case employing the hybrid minimum principle hmp necessary conditions a class of general hmp based algorithms for hybrid systems optimization are presented and analyzed for the autonomous switchings case and the controlled switchings case using results from the theory of penalty function methods and ekeland s variational principle the convergence of these algorithms is established under reasonable assumptions the efficacy of the proposed algorithms is illustrated via computational examples

an optimization approach to state delay identification we consider a nonlinear delay differential system with unknown state delays our goal is to identify these state delays using experimental data to this end we formulate a dynamic optimization problem in which the state delays are decision variables and the cost function measures the discrepancy between predicted and observed system output we then show that the gradient of this problem s cost function can be computed by solving an auxiliary delay differential system by exploiting this result the state delay identification problem can be solved efficiently using a gradient based optimization method

recursive local orthogonality filtering recursive local orthogonality rlo is a stochastic newton algorithm to achieve a condition we term local orthogonality which only requires unimodal symmetric densities with continuous nonzero second derivatives near the origin for gaussian systems rlo reduces to recursive least squares local orthogonality is both a subset of median orthogonality and a form of constrained maximum likelihood optimization fast multichannel time and multichannel frequency domain implementations are given simulations show the utility for system identification and inverse modeling