noncanonical quantization of gravity i foundations of affine quantum gravity the nature of the classical canonical phase space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations prior to the introduction of constraints a primary kinematical representation is derived in the form of a reproducing kernel and its associated reproducing kernel hilbert space constraints are introduced following the projection operator method which involves no gauge fixing no complicated moduli space nor any auxiliary fields the result which is only qualitatively sketched in the present paper involves another reproducing kernel with which inner products are defined for the physical hilbert space and which is obtained through a reduction of the original reproducing kernel several of the steps involved in this general analysis are illustrated by means of analogous steps applied to one dimensional quantum mechanical models these toy models help in motivating and understanding the analysis in the case of gravity

almost output regulation of lft systems via gain scheduling control abstractoutput regulation of general uncertain systems is a meaningful yet challenging problem in spite of the rich literature in the field the problem has not yet been addressed adequately due to the lack of an effective design mechanism in this paper we propose a new design framework for almost output regulation of uncertain systems described in the general form of linear fractional transformation lft with time varying parametric uncertainties and unknown external perturbations a novel semi lft gain scheduling output regulator structure is proposed such that the associated control synthesis conditions guaranteeing both output regulation and l2 disturbance attenuation performance are formulated as a set of linear matrix inequalities lmis plus parameter dependent linear matrix equations which can be solved separately a numerical example has been used to demonstrate the effectiveness of the proposed approach

model reduction of nonstationary lpv systems this paper focuses on the model reduction of nonstationary linear parameter varying nslpv systems we provide a generalization of the balanced truncation procedure for the model reduction of stable nslpv systems along with a priori error bounds then for illustration purposes this method is applied to reduce the model of a two mass translational system furthermore we give an approach for the model reduction of stabilizable and detectable systems which requires the development and use of coprime factorizations for nslpv models for the general class of eventually periodic lpv systems which includes periodic and finite horizon systems as special cases our results can be explicitly computed using semidefinite programming

brief paper guaranteed cost control of stochastic uncertain systems with slope bounded nonlinearities via the use of dynamic multipliers this paper presents a new approach to constructive output feedback robust nonlinear guaranteed cost controller design the approach involves a class of controllers which include copies of the slope bounded nonlinearities occurring in the plant dynamic multipliers are introduced to exploit these repeated nonlinearities the linear part of the controller is synthesized using minimax lqg control theory

generalized l sub 2 synthesis introduces a general framework for control design which can be used to solve several open problems in robust and optimal control these include systems subject to independently norm bounded disturbances robust stability for systems subject to element by element bounded structured uncertainty certain classes of robust performance problems and systems subject to deterministic white noise disturbances this is achieved by combining concepts such as h infinity optimization linear matrix inequalities and integral quadratic constraints necessary and sufficient conditions for the general problem to have a solution are in terms of a computationally attractive finite dimensional linear matrix inequality

on switching h controllers for a class of linear parameter varying systems abstract we consider switching h controllers for a class of linear parameter varying lpv systems scheduled along a measurable parameter trajectory the candidate controllers are selected from a given controller set according to the switching rules based on the scheduling variable we provide sufficient conditions to guarantee the stability of the switching lpv systems in terms of the dwell time and the average dwell time our results are illustrated with an example where switching between two robust controllers is performed for an lpv system

class based feature matching across unrestricted transformations we develop a novel method for class based feature matching across large changes in viewing conditions the method is based on the property that when objects share a similar part the similarity is preserved across viewing conditions given a feature and a training set of object images we first identify the subset of objects that share this feature the transformation of the feature s appearance across viewing conditions is determined mainly by properties of the feature rather than of the object in which it is embedded therefore the transformed feature will be shared by approximately the same set of objects based on this consistency requirement corresponding features can be reliably identified from a set of candidate matches unlike previous approaches the proposed scheme compares feature appearances only in similar viewing conditions rather than across different viewing conditions as a result the scheme is not restricted to locally planar objects or affine transformations the approach also does not require examples of correct matches we show that by using the proposed method a dense set of accurate correspondences can be obtained experimental comparisons demonstrate that matching accuracy is significantly improved over previous schemes finally we show that the scheme can be successfully used for invariant object recognition

recognition using region correspondences recognition systems attempt to recover information about the identity of observed objects and their location in the environment a fundamental problem in recognition is pose estimation this is the problem of using a correspondence between some portions of an object model and some portions of an image to determine whether the image contains an instance of the object and in case it does to determine the transformation that relates the model to the image the current approaches to this problem are divided into methods that use global properties of the object e g centroid and moments of inertia and methods that use local properties of the object e g corners and line segments global properties are sensitive to occlusion and specifically to self occlusion local properties are difficult to locate reliably and their matching involves intensive computation we present a novel method for recognition that uses region information in our approach the model and the image are divided into regions given a match between subsets of regions without any explicit correspondence between different pieces of the regions the alignment transformation is computed the method applies to planar objects under similarity affine and projective transformations and to projections of 3 d objects undergoing affine and projective transformations the new approach combines many of the advantages of the previous two approaches while avoiding some of their pitfalls like the global methods our approach makes use of region information that reflects the true shape of the object but like local methods our approach can handle occlusion

robust control via concave minimization local and global algorithms this paper is concerned with the robust control problem of linear fractional representation lft uncertain systems depending on a time varying parameter uncertainty our main result exploits a linear matrix inequality lmi characterization involving scalings and lyapunov variables subject to an additional essentially nonconvex algebraic constraint the nonconvexity enters the problem in the form of a rank deficiency condition or matrix inverse relation on the scalings only it is shown that such problems but also more generally rank inequalities and bilinear constraints can be formulated as the minimization of a concave functional subject to lmi constraints first of all a local frank and wolfe 1956 feasible direction algorithm is introduced in this context to tackle this hard optimization problem exploiting the attractive concavity structure of the problem several efficient global concave programming methods are then introduced and combined with the local feasible direction method to secure and certify global optimality of the solutions computational experiments indicate the viability of our algorithms and in the worst case they require the solution of a few lmi programs

a partially augmented lagrangian method for low order rm h infinity controller synthesis using rational constraints this technical note proposes a method for low order h infinity synthesis where the constraint on the order of the controller is formulated as a rational equation the resulting nonconvex optimization problem is then solved by applying a partially augmented lagrangian method the proposed method is evaluated together with two well known methods from the literature the results indicate that the proposed method has comparable performance and speed

nonstationary lpv control for trajectory tracking a double pendulum example this article focusses on the implementation of recently developed nonstationary linear parameter varying nslpv control algorithms for the regulation of nonlinear systems about pre specified trajectories the trajectories of interest eventually settle into periodic orbits and hence are duly called eventually periodic trajectories parameterising the nonlinear system equations about such trajectories results in eventually periodic nslpv models and then nslpv controllers are designed for these models to ensure accurate trajectory tracking despite various disturbances and uncertainties these control algorithms will be applied to control a double pendulum where a vessel containing fluid is rigidly attached to the end of the second link of the pendulum the mass of the fluid varies in time and together with its rate of variation is available for measurement during plant operation

a direct characterization of l sub 2 gain controllers for lpv systems in this paper a class of linear parameter dependent output feedback controllers that satisfy quadratic stability and an induced l sub 2 norm bound for a given linear parameter varying lpv plant is considered by using a parameter independent common lyapunov function the solvability conditions are expressed in terms of finite dimensional linear matrix inequalities lmi evaluated at the extreme points of the admissible parameter set conditions under which strictly proper controllers can be used are obtained by restricting some of the controller matrices to be constant the input and output matrices can be parameter varying without destroying the problem s convexity cases where the controller matrices can be obtained without interpolation are also discussed thereby simplifying the implementation of the controller a numerical example is included which demonstrates the application of the results

set invariance analysis and gain scheduling control for lpv systems subject to actuator saturation in this paper a set invariance analysis and gain scheduling control design approach is proposed for the polytopic linear parameter varying systems subject to actuator saturation a set invariance condition is first established by utilizing this set invariance condition the design of a time invariant state feedback law is formulated and solved as an optimization problem with lmi constraints a gain scheduling controller is then designed to further improve the closed loop performance numerical examples are presented to demonstrate the effectiveness of the proposed analysis and design method

an algebraic approach to h output feedback control problems abstract we derive an output feedback controller which stabilizes a system and satisfies a prescribed h norm bound of the closed loop transfer function the proposed design method is available for any system i e there are no restrictions on d12 and d21 this approach utilizes only algebraic operations thus proofs are simple and clear

inequality based properties of detectability and stabilizability of linear time varying systems in discrete time well known properties of uniform detectability and uniform stabilizability are sharpened in terms of lyapunov and riccati inequalities for discrete time linear time varying systems in particular it is shown that the stabilizing output injection law can be taken to depend solely on a finite path of past and present system coefficients and the stabilizing state feedback law solely on a finite path of present and future coefficients these results are applied to time varying systems where the system coefficients vary among a finite set and lead to precise and computable convex conditions for the stability and dynamic output feedback stabilizability of such systems

brief rbust control of linear systems with real parametric uncertainty we discuss the problem of robust controller synthesis to provide quadratic stability and a desirable disturbance attenuation level through an appropriately small l 2 gain for systems with time varying real parametric uncertainty through the use of skewsymmetric matrices the conservatism of standard scaled h approach is reduced while the full state feedback problem is convex the output feedback problem is not a set of conditions under which the design of output feedback controllers can be broken into two sequential convex problems is presented the results are compared with recent results concerning the design of parameter varying controllers and a simple result regarding the mixed problem where some of the unknown parameters can be measured on line is discussed

extended coherent states and path integrals with auxiliary variables the usual construction of coherent states allows a wider interpretation in which the number of distinguishing state labels is no longer minimal the label measure determining the required resolution of unity is then no longer unique and may even be concentrated on manifolds with positive co dimension paying particular attention to the residual restrictions on the measure the authors choose to capitalize on this inherent freedom and in formally distinct ways systematically construct suitable sets of extended coherent states which in a minimal sense are characterized by auxiliary labels interestingly they find these states lead to path integral constructions containing auxiliary essentially unconstrained path space variables the impact of both standard and extended coherent state formulations on the content of classical theories is briefly examined the latter showing the existence of new and generally constrained classical variables some implications for the handling of constrained classical systems are given with a complete analysis awaiting further study

bounded amplitude performance of switched lpv systems with applications to hybrid systems this paper discusses recent results on multiple linear agent control for systems satisfying a bounded amplitude performance constraint the plant is assumed to be a linear parameter varying lpv system scheduled along a nominal parameter trajectory in this respect the control problem represents a plant operating between a prespecified set of operating conditions linear controllers are designed at setpoints along this scheduling trajectory to satisfy bounded amplitude performance constraints this paper discusses an approach to analyze the switched system behavior under practical assumptions on the structure of the switching rule the approach combines the scheduling parameter with lpv system properties to derive bounds on the switching behavior of the system these estimates are then used to construct a logical model of the switched system behavior in the form of a timed automaton in this respect this paper presents a way of extracting logical models of continuous time system behavior

lpv control of nonstationary systems a parameter dependent lyapunov approach the paper presents a parameter dependent lyapunov approach for the control of nonstationary linear parameter varying systems the work is motivated by the challenges encountered in controlling nonlinear systems about pre specified aggressive trajectories specifically ones which eventually settle into periodic orbits the control design method uses the l2 induced norm performance measure and the analysis and synthesis results are given in terms of parameterized linear matrix inequalities two fast and easy to implement algorithms for online controller construction are also provided

a new approach for analysis and synthesis of time varying systems in this paper new techniques are developed for the analysis of linear time varying ltv systems these lead to a formally simple treatment of robust control problems for ltv systems allowing methods more usually restricted to time invariant systems to be employed in the time varying case as an illustration of this methodology the so called h sub spl infin synthesis problem is solved for ltv systems

coprime factor based anti windup synthesis for parameter dependent systems abstract this paper presents a novel anti windup compensator synthesis for linear parameter varying lpv systems that have linear fractional transformation lft representations the lpv anti windup synthesis is based on a right coprime factor description of the lpv plant to be controlled it is shown that the anti windup compensator synthesis reduces to solving a robust l 2 gain state feedback control problem for the lpv lft system subject to input saturations the synthesis takes advantage of unstructured multipliers that is multipliers that do not commute with the parameter structure and exploits a detailed description of the parameter trajectory polytope the anti windup compensator is given in an explicit lpv lft form sharing with the plant the same order and same parameter structure

simultaneous parametric uncertainty modeling and robust control synthesis by lft scaling given a set of experimental data points in the plant parameter space the objective of this paper is to give a systematic method for designing a controller to achieve a prescribed level of robust performance for the closed loop system a standard procedure would be to model the data first and then to design a controller our focus here instead is to complete these two tasks simultaneously eliminating the conservatism caused by the fact that the data is modeled independently of the closed loop objective to this end integral quadratic constraints iqcs are used as a tool for uncertainty modeling we propose the lft scaling to integrate the iqc modeling with the control synthesis it is shown that the lft scaling provides a condition dual to the standard iqc for linear time invariant systems and this duality result is essential for solving the simultaneous modeling and synthesis problem a solution is given in terms of matrix inequalities and its computational aspects are discussed the proposed method is applied to the control design for an ac linear servo motor and experimental results demonstrate that our method achieves the performance superior to that achieved by existing methods

wavelets associated with representations of the affine weyl heisenberg group the affine weyl heisenberg group generated by time and frequency translations and time dilations is considered and some associated resolutions of the identity are derived as a result it will be shown that they can all be obtained from those associated with the affine group and the weyl heisenberg group by frequency translations of the analyzed function and the analyzing and reconstructing wavelets

design of controllers for linear parameter varying systems by the gain scheduling technique abstract design of controllers for linear multi input multi output systems whose dynamics depend on a time varying parameter is studied design algorithms for the state feedback control law based on the gain scheduling technique are proposed state feedback control laws are designed so that one of the following goals is achieved i the poles of the closed loop system for all fixed parameter values are placed in a small neighborhood of a set of desired closed loop poles ii the stability of the closed loop system for all fixed parameter values guarantees that the of the system with the time varying parameter independent of the rate of change of the parameter rigorously justified and computationally appealing design algorithms are developed

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

the behavioral approach to linear parameter varying systems linear parameter varying lpv systems are usually described in either state space or input output form when analyzing system equivalence between different representations it appears that the time shifted versions of the scheduling signal dynamic dependence need to be taken into account therefore representations used previously to define and specify lpv systems are not equal in terms of dynamics in order to construct a parametrization free description of lpv systems that overcomes these difficulties a behavioral approach is introduced that serves as a basis for specifying system theoretic properties lpv systems are defined as the collection of trajectories of system variables like inputs and outputs and scheduling variables lpv kernel input output and state space system representations are introduced with appropriate equivalence transformations

control of lpv systems with partly measured parameters the control of linear parameter varying lpv systems with time varying real uncertain parameters where only some of the parameters are measured and available for feedback is considered the control objectives are internal stability and disturbance attenuation in the sense of a bounded induced l sub 2 norm from the disturbance to the controlled output using parametric lyapunov functions the solvability conditions for dynamic output feedback controllers that depend on the measured parameters are expressed in terms of a set of linear matrix inequalities lmis and an additional coupling constraint which destroys the convexity of the overall problem by transforming the coupling constraint into a rank condition the problem is recast into a rank minimization problem with lmi constraints an example is included that demonstrates the application of the results

a unified approach to lmi based reduced order self scheduling control synthesis abstract we consider a reduced order controller synthesis for a general class of control specifications for linear parameter varying lpv systems when some of state variables are exactly available the class is defined in an abstract manner so that it uniformly deals with many significant specifications a necessary and sufficient condition for the existence of a reduced order controller is given in terms of linear matrix inequalities lmis we also show that the order of the controller can be reduced by the number of the state variables exactly available in the measurements moreover in the case of linear time invariant lti systems a parameterization of all desirable reduced order lti controllers is given by means of solutions of lmis the results in this paper generalize the class of control specifications in which a reduced order controller exists making it possible to synthesize a reduced order controller based on lmis for multi objective control specifications furthermore these results uniformly describe and generalize the existing results on synthesis of a constant state and a full order output feedback controller for lti and lpv systems such that the specification is given by the existence of a constant positive definite matrix

a necessary and sufficient minimality condition for uncertain systems a necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations lfts on structured operator sets this condition is based on the existence of a rank deficient solution to either of a pair of linear matrix inequalities which generalize lyapunov equations the notion of gramians is thus also generalized to uncertain systems as well as kalman like decomposition structures a related minimality condition the converse of the reducibility condition may then be inferred from these results and the equivalence class of all minimal lft realizations defined these results comprise the first stage of a complete generalization of realization theory concepts to uncertain systems subsequent results such as the definition of and rank tests on structured controllability and observability matrices are also given the minimality results described are applicable to multidimensional system realizations as well as to uncertain systems connections to formal powers series representations also exist

model reduction of multidimensional and uncertain systems model reduction methods are presented for systems represented by a linear fractional transformation on a repeated scalar uncertainty structure these methods involve a complete generalization of balanced realizations balanced gramians and balanced truncation model reduction with guaranteed error bounds based on solutions to a pair of linear matrix inequalities which generalize lyapunov equations the resulting reduction methods immediately apply to uncertainty simplification and state order reduction in the case of uncertain systems but also may be interpreted as state order reduction for multidimensional systems

lmi tools for eventually periodic systems abstract this paper is focused on the concept of an eventually periodic linear discrete time system we derive a necessary and sufficient analysis condition for checking open loop stability and performance of such systems and use this to derive exact controller synthesis conditions given eventually periodic plants all the conditions derived are provided in terms of semi definite programming problems the motivation for this work is controlling nonlinear systems along prespecified trajectories notably those which eventually settle down into periodic orbits and those with uncertain initial states

supervisory control and measurement scheduling for discrete time linear systems the problem of jointly synthesizing a supervisor a measurement scheduler and a feedback controller for discrete time linear systems is considered it is shown that open loop supervisory and scheduling laws are nonconservative for robust exponential stability and h2 and h type performance requirements and that they can be obtained separately from the feedback controller all the design conditions are formulated in terms of linear matrix inequalities

dynamic gain scheduled control and extended linearisation extensions explicit formulae and stability a controller designed for linearisations at various trim operating points of a nonlinear system using linear approaches is not necessarily performing well or stable once scheduled with a state under dynamic conditions the key idea of using this scheduled control law design is to retain states close to the current usually dynamically varying operating point dynamic gain scheduling dgs is a technique aimed to resolve this controller scheduling issue for rapidly changing dynamics and states it entails scheduling the control law gains with a fast varying state variable rather than with a slowly varying state it has been successfully applied to the aircraft system models allowing also for nested loops the aim of this paper is to extend dgs to a more general setting allowing for more complex multi input dynamics incorporating the more simple static scheduling within the same controller hence given a linear design suitable transformations are provided which allow fast scheduling of multi variable co

output feedback control of lpv sampled data systems in this paper we address the analysis and the output feedback synthesis problems for linear parameter varying lpv sampled data control systems with potentially variable sampling rates we assume that the state space matrices of the plant and the sampling interval depend on parameters that are measurable in real time and vary in a compact set with bounded variation rates we explore criteria such as the stability the energy to energy gain induced l 2 norm and the energy to peak gain induced l 2 to l x norm of such sampled data lpv systems using parameter dependent lyapunov functions based on these analysis results the corresponding sampled data output feedback control synthesis problems are examined both analysis and synthesis conditions are formulated in terms of linear matrix inequalities lmis that can be solved via efficient interior point algorithms

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

discrete markov image modeling and inference on the quadtree noncasual markov or energy based models are widely used in early vision applications for the representation of images in high dimensional inverse problems due to their noncausal nature these models generally lead to iterative inference algorithms that are computationally demanding in this paper we consider a special class of nonlinear markov models which allow one to circumvent this drawback these models are defined as discrete markov random fields mrf attached to the nodes of a quadtree the quadtree induces causality properties which enable the design of exact noniterative inference algorithms similar to those used in the context of markov chain models we first introduce an extension of the viterbi algorithm which enables exact maximum a posteriori map estimation on the quadtree two other algorithms related to the mpm criterion and to bouman and shapiro s 1994 sequential map smap estimator are derived on the same hierarchical structure the estimation of the model hyper parameters is also addressed two expectation maximization em type algorithms allowing unsupervised inference with these models are defined the practical relevance of the different models and inference algorithms is investigated in the context of image classification problem on both synthetic and natural images

optimal disturbance attenuation for discrete time switched and markovian jump linear systems an exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete time domain via the union of an increasing family of linear matrix inequality conditions associated with each markovian jump linear system is a switched linear system so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for markovian jump linear systems as well the results lead to semidefinite programming based controller synthesis techniques from which optimal finite path dependent linear dynamic output feedback controllers arise naturally in particular under the notion of path by path optimal disturbance attenuation finite path dependent controllers can outperform the usual mode dependent ones

robust output feedback guaranteed cost control of nonlinear stochastic uncertain systems via an iqc approach this technical note presents a new approach to constructive output feedback robust nonlinear controller design based on the use of iqcs and minimax lqg control the approach involves a class of controllers which include copies of the nonlinearities in the controller the linear part of the controller is synthesized using minimax lqg control theory which is closely related to h infin control theory

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

extension of parrott s theorem to nondefinite scalings in this paper the matrix version of parrott s theorem is extended to encompass nondefinite scalings this extension can be used to relax the causality requirements for many linear matrix inequality based synthesis problems

fixed structure lpv io controllers an implicit representation based approach abstract in this note novel linear matrix inequality lmi analysis conditions for the stability of linear parameter varying lpv systems in input output io representation form are proposed together with bilinear matrix inequality bmi conditions for fixed structure lpv io controller synthesis both the lpv io plant model and the controller are assumed to depend affinely and statically on the scheduling variables by using an implicit representation of the plant and the controller interaction an exact representation of the closed loop behavior with affine dependence on the scheduling variables is achieved this representation allows to apply finsler s lemma for deriving exact stability as well as exact quadratic performance conditions a dk iteration based solution is carried out to synthesize the controller the main results are illustrated by a numerical example

robust quasi lpv control based on neural state space models we derive a synthesis result for robust linear parameter varying lpv output feedback controllers for nonlinear systems modeled by neural state space models this result is achieved by writing the neural state space model on a linear fractional transformation lft form in a nonconservative way separating the system description into a linear part and a nonlinear part linear parameter varying control synthesis methods are then applied to design a nonlinear control law for this system since the model is assumed to have been identified from input output measurement data only it must be expected that there is some uncertainty on the identified nonlinearities the control law is therefore made robust to noise perturbations after formulating the controller synthesis as a set of linear matrix inequalities lmis with added constraints some implementation issues are addressed and a simulation example is presented

norm preserving dilations and their applications to optimal error bounds the problem is given a b c to find d such that left begin array 20 c a c b d end array right leqq mu here we deal with hilbert space operators a b and c ar

large scale optimization of eigenvalues optimization problems involving eigenvalues arise in many applications let x be a vector of real parameters and let a x be a continuously differentiable symmetric matrix function of x we consi

brief paper robust adaptive h control using integral quadratic constraints this paper introduces a new approach to robust adaptive h control the main idea of the paper is to extend an existing approach to robust h control to allow for constant or slowly varying unknown parameters in an adaptive way this is achieved by treating the presence of the unknown parameters as states resulting in a bilinear nonlinearity a copy of this nonlinearity is repeated in the controller and the presence of the repeated nonlinearity is exploited using a special integral quadratic constraint

brief stability preserving interpolation methods for the synthesis of gain scheduled controllers synthesis of gain scheduled controllers for nonlinear plants often requires that a parameter varying controller be generated from a finite set of linear time invariant controllers we propose interpolation methods for this task with the property that stability of the linearized closed loop system is preserved for all values of the scheduling parameter in addition slow variation arguments are presented that establish local stability of the nonlinear closed loop system with gain scheduled controller

control of rational systems using linear fractional representations and linear matrix inequalities abstract every system of the form x f x u y g x u where f and g are rational functions of the state x and linear functions of the input u possesses a linear fractional representation lfr in this lfr the system is viewed as an lti system connected with a diagonal feedback element linear in the state we devise an algorithm for computing lfrs based on this construction we give sufficient conditions for various properties to hold for the open loop system these include checking whether a given polytope is stable finding a lower bound on the decay rate of trajectories initiating in this polytope computing an upper bound on the l2 gain etc all these conditions are obtained by analyzing the properties of a differential inclusion related to the lfr and given as convex optimization problems over linear matrix inequalities lmis we show how to use this approach for static state feedback synthesis we then generalize the results to dynamic output feedback synthesis in the case when f and g are linear in every state coordinate that is not measured extensions towards a class of nonrational and uncertain nonliner systems are discussed

on the control of linear systems whose coefficients are functions of parameters the stabilization and regulation of linear discrete time systems whose coefficients depend on one or more parameters is studied for linear systems whose coefficients are continuous functions of real or complex parameters respectively analytic or rational functions of real parameters it is shown that reachability of the system for all values of the parameters implies that the system can be stabilized using gains that are also continuous analytic rational functions of the parameters closed form expressions for a collection of stabilizing gains are given in terms of the reachability gramian for systems which are stabilizable for all values of the parameters it is shown that continuous analytic rational stabilizing gains can be computed from a finite time solution to a riccati difference equation whose coefficients are functions of the parameters these results are then applied to the problem of tracking and disturbance rejection in the case when both the plant and the exogenous signals contain parameters

antiwindup for stable linear systems with input saturation an lmi based synthesis this paper considers closed loop quadratic stability and l sub 2 performance properties of linear control systems subject to input saturation more specifically these properties are examined within the context of the popular linear antiwindup augmentation paradigm linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification called the unconstrained closed loop behavior building on known results on h sub spl infin and lpv synthesis the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem which has an attractive system theoretic interpretation the lower bound on the achievable l sub 2 performance is the maximum of the open and unconstrained closed loop l sub 2 gains in the special cases of zero order static and plant order antiwindup compensation the feasibility conditions become convex linear matrix inequalities it is shown that if and only if the plant is asymptotically stable plant order linear antiwindup compensation is always feasible for large enough l sub 2 gain and that static antiwindup compensation is feasible provided a quasi common lyapunov function between the open loop and unconstrained closed loop exists using the solutions to the matrix feasibility problems the synthesis of the antiwindup augmentation achieving the desired level of l sub 2 performance is then accomplished by solving an additional lmi

smooth switching lpv controller design for lpv systems abstract this paper presents a method to design a smooth switching gain scheduled linear parameter varying lpv controller for lpv systems the moving region of the gain scheduling variables is divided into a specified number of local subregions as well as subregions for the smooth controller switching and one gain scheduled lpv controller is assigned to each of the local subregions for each switching subregion a function interpolating two local lpv controllers associated with its neighborhood subregions is designed to satisfy the constraint of smooth transition of controller system matrices the smooth switching controller design problem amounts to solving a feasibility problem which involves nonlinear matrix inequalities to find a solution to the feasibility problem an iterative descent algorithm which solves a series of convex optimization problems is proposed the usefulness of the proposed controller design method is demonstrated with a control example of a flexible ball screw drive system

optimal constant i o similarity scaling for full information and state feedback control problems abstract in robust control problems capturing all robustness and performance objectives in a single h norm cost function is impossible an alternative approach still untilizing the h norm involves diagonal similarity scaling of certain closed loop transfer functions the set of allowable diagonal scalings is problem dependent and reflects assumptions about the uncertainty and desired performance objectives the scaling set considered here is a prescribed convex set of positive definite matrices we consider the optimal constant scaling problem for the full information h control problem the solution is obtained by transforming the original problem into a convex feasibility problem specifically a structured linear matrix inequality in special cases solvability of the full information problem is equivalent to solvability of the state feedback problem

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

technical communique a stability and contractiveness analysis of discrete time markovian jump linear systems we propose performance criteria for discrete time linear systems with markov jumping parameters exact convex conditions for internal stability and contractiveness of such systems are expressed in terms of linear matrix inequalities these conditions are of the same form as that in the kalman yacubovich popov lemma

robust h control of a nonlinear uncertain system via a stable nonlinear output feedback controller a new approach to solving a nonlinear robust h control problem using a stable nonlinear output feedback controller is presented in this article the class of nonlinear uncertain systems being considered is characterised in terms of integral quadratic constraints and global lipschitz conditions describing the admissible uncertainties and nonlinearities respectively the nonlinear controller is able to exploit the plant nonlinearities through the inclusion of a copy of the known plant nonlinearities in the controller the h control objective is to obtain an absolutely stable closed loop system with a specified disturbance attenuation level the solution to this control problem involves stabilising solutions to parametrised algebraic riccati equations we apply a differential evolution algorithm to solve a non convex nonlinear optimisation problem arising in the controller synthesis

a new parametrization of h suboptimal controllers elementary state space concepts are used to derive a transparent solution to the h control problem on an infinite horizon the main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric riccati equations with a coupling constraint unlike the classical parametrization in terms of linear fractional transformation this state space representation has a homogeneous riccati formulation which should help to make the most of the suboptimal controller diversity potential applications include the design of reduced order controllers and more generally the selection of suboptimal controllers to meet or optimize additional constraints

eigentracking robust matching and tracking of articulated objects using a view based representation this paper describes an approach for tracking rigid and articulated objects using a view based representation the approach builds on and extends work on eigenspace representations robust estimation techniques and parameterized optical flow estimation first we note that the least squares image reconstruction of standard eigenspace techniques has a number of problems and we reformulate the reconstruction problem as one of robust estimation second we define a subspace constancy assumption that allows us to exploit techniques for parameterized optical flow estimation to simultaneously solve for the view of an object and the affine transformation between the eigenspace and the image to account for large affine transformations between the eigenspace and the image we define a multi scale eigenspace representation and a coarse to fine matching strategy finally we use these techniques to track objects over long image sequences in which the objects simultaneously undergo both affine image motions and changes of view in particular we use this eigentracking technique to track and recognize the gestures of a moving hand

on the discretization of lmi synthesized linear parameter varying controllers reliable and efficient techniques are now available to synthesize gain scheduled controllers such techniques take advantage of linear matrix inequality lmi characterizations of gain scheduled controllers and provide a global and systematic treatment of the gain scheduling problem this paper examines how such controller structures designed in continuous time can be discretized and implemented in practical applications a special emphasis is placed on reducing the computational cost of discrete implementations the validity of the proposed concepts and schemes are illustrated through a two link flexible manipulator design example

dynamic output feedback control for continuous time t s fuzzy systems using fuzzy lyapunov functions a novel relaxation approach is proposed for the analysis and dynamic output feedback control of continuous time takagi sugeno t s fuzzy systems using fuzzy lyapunov functions previous relaxation methods for t s fuzzy systems have some drawbacks in relaxing quadratic functions depending on normalized fuzzy weighting functions they often introduce conservatism or lead to computational difficulty in analysis and control synthesis different from previous works the proposed approach employs linear fractional transformation mechanism and full block s procedure to reduce the conservatism in analysis furthermore the relaxation technique proposed in this paper can be used in solving the controller synthesis problem effectively as a result a design procedure of a nonparallel distributed compensation output feedback controller which ensures asymptotic stability and optimizes mathcal l 2 gain performance of the closed loop systems is provided several examples have been used to illustrate the advantages and efficiency of the proposed method extensively

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

brief paper control of nonstationary lpv systems this paper considers control of nonstationary linear parameter varying systems and is motivated by interest in the control of nonlinear systems along prespecified trajectories in the paper synthesis conditions are derived for such systems using an operator theoretical framework with the 2 induced norm as the performance measure these conditions are given in terms of structured operator inequalities in general evaluating the validity of these conditions is an infinite dimensional convex optimization problem however if the initial system is eventually periodic they reduce to a finite dimensional semi definite programming problem the paper concludes with an in depth example on the control of a two thruster hovercraft along an eventually periodic trajectory

brief lpv systems with parameter varying time delays analysis and control in this paper we address the analysis and state feedback synthesis problems for linear parameter varying lpv systems with parameter varying time delays it is assumed that the state space data and the time delays are dependent on parameters that are measurable in real time and vary in a compact set with bounded variation rates we explore the stability and the induced l 2 norm performance of these systems using parameter dependent lyapunov functionals in addition the design of parameter dependent state feedback controllers that guarantee desired l 2 gain performance is examined both analysis and synthesis conditions are formulated in terms of linear matrix inequalities lmis that can be solved via efficient interior point algorithms

simplified rapid switching gain scheduling for a class of lpv systems a limitation of the original gain scheduling approaches is that the closed loop stability can only be assured when the underlying parameters vary sufficiently slowly a remedy exists but requires for its implementation the possible solution of asymptotic riccati equations are for an infinite number of different parameter values and the on line solution of a riccati differential equation rde with time varying coefficient matrices our method avoids solving the rde online and instead uses an explicit transient formula that looks up the predetermined solutions of the associated ares at a finite set of given system operating points furthermore only a finite number of ares are solved to determine a finite set of controller gains

gain scheduled open loop system design for lpv systems using polynomially parameter dependent lyapunov functions abstract this paper addresses the design problem of full order gain scheduled gs open loop systems such as gs filters and gs inverse systems which are independent of unmeasurable parameters for linear parameter varying lpv systems in which the state space matrices are polynomially parameter dependent using structured polynomially parameter dependent lyapunov functions pdlfs in which some conservatism is admitted we propose design methods for our addressed problems via parametrically affine linear matrix inequality lmi conditions that are easily solved via semi definite programming for parametrically affine lpv systems including polytopic systems our design methods theoretically encompass existing methods which use structured quadratically pdlfs our proposed methods include robust open loop system design as a special case several numerical examples are introduced to demonstrate the effectiveness of our methods

h optimization without assumptions on finite or infinite zeros explicit algebraic conditions are presented for the suboptimality of some parameter in the h infty optimization problem by output measurement control apart from two strict properness conditions no artificial assumptions restrict the underlying system in particular the plant may have zeros on the imaginary axis or at infinity these suboptimality characterizations are applied to show how to compute the optimal value by quadratically convergent algorithms and to solve the almost disturbance decoupling problem with internal stability

bumpless transfer between observer based gain scheduled controllers this paper deals with bumpless transfer between a number of observer based controllers in a gain scheduling architecture linear observer based controllers are designed for a number of linear approximations of a non linear system in a set of operating points and gain scheduling control can subsequently be achieved by interpolating between each controller the youla jabr bongiorno kucera yjbk parameterization is used to achieve a smooth scheduling between the controllers this approach produces a scheduled controller as a linear fractional transformation between a fixed controller and a scheduling parameter the approach is tested on a simple but highly non linear model of a fossil fuel power plant

face recognition the problem of compensating for changes in illumination direction a face recognition system must recognize a face from a novel image despite the variations between images of the same face a common approach to overcoming image variations because of changes in the illumination conditions is to use image representations that are relatively insensitive to these variations examples of such representations are edge maps image intensity derivatives and images convolved with 2d gabor like filters here we present an empirical study that evaluates the sensitivity of these representations to changes in illumination as well as viewpoint and facial expression our findings indicated that none of the representations considered is sufficient by itself to overcome image variations because of a change in the direction of illumination similar results were obtained for changes due to viewpoint and expression image representations that emphasized the horizontal features were found to be less sensitive to changes in the direction of illumination however systems based only on such representations failed to recognize up to 20 percent of the faces in our database humans performed considerably better under the same conditions we discuss possible reasons for this superiority and alternative methods for overcoming illumination effects in recognition

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

generalized robust gain scheduled pid controller design for affine lpv systems with polytopic uncertainty in the paper a generalized guaranteed cost output feedback robust gain scheduled pid controller synthesis is presented for affine linear parameter varying systems under polytopic model uncertainty the controller synthesis is generalized in a sense that it covers robust robust gain scheduled and robust switched with arbitrary switching algorithm pid controller design the proposed centralized decentralized controller method is based on bellman lyapunov equation guaranteed cost and parameter dependent quadratic stability the proposed sufficient robust stability and performance conditions are derived in the form of bilinear matrix inequalities bmi which can efficiently be solved or further linearized as the main result the suggested performance and stability conditions without any restriction on the controller structure are convex functions of the scheduling and uncertainty parameters hence there is no need for applying multi convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method the viability of the novel design technique is demonstrated and evaluated through numerical examples

distributed control design for spatially interconnected systems this paper deals with analysis synthesis and implementation of distributed controllers designed for spatially interconnected systems we develop a state space framework for posing problems of this type and focus on systems whose model is spatially discrete in this paper analysis and synthesis results are developed for this class of systems using the l sub 2 induced norm as the performance criterion the results are stated in terms of linear matrix inequalities and are thus readily amenable to computation a special implementation of the resulting controllers is presented which is particularly attractive for distributed operation of the controller several examples are provided to further illustrate the application of the results

lpv control and full block multipliers a novel construction of linear parameter varying controllers is presented for arbitrarily fast parameter variations it is shown how full block multipliers allow to considerably reduce conservatism various auxiliary results of independent interest are included

robust and gain scheduling control of lft systems through duality and conjugate lyapunov functions in this paper we study stability and performance properties of linear fractional transformation lft parameter dependent systems using duality theory and tools from convex analysis a pair of conjugate functions the convex hull and the maximum of a family of quadratic functions are used for analysis and synthesis of lft systems sufficient synthesis conditions for both robust state feedback and gain scheduling output feedback control problems are formulated as a set of linear matrix inequalities lmis with linear search over scalar variables finally a numerical example is used to demonstrate the advantages of the proposed approaches

robust linear time varying control for trajectory tracking computation and an experimental application this paper provides computational and experimental verification of the use of recently developed linear time varying ltv robust control synthesis methods for controlling systems along prespecified trajectories the linearization of system dynamics along trajectories yield ltv systems and we compute and design robust controllers with respect to such linearizations the techniques employed require the computation of potentially large linear matrix inequalities and complexity reduction using new model reduction for ltv systems is also demonstrated