receding horizon control of nonlinear systems without differentiability of the optimal value function abstract in this paper we show that receding horizon control when applied to a class of nonlinear systems has stabilizing properties our assumptions are necessarily fairly strong because they guarantee implicity that a smooth stabilizing feedback can be constructed this is an extension of our previous results which require the finite horizon value function to be continuously differentiable and therefore applies to a more restricted class of system continuous differentiability of the value function is replaced by local lipschitz continuity dini derivatives and a generalization of the invariance principle are employed to establish stability

on the stability of receding horizon lq control with zero state terminal constraint receding horizon control with zero state terminal constraint for linear time varying discrete systems is considered it is shown that uniform controllability suffices to ensure closed loop exponential stability thus relaxing the reversibility and or detectability requirements made in the existing literature the result has interesting implications in the design of predictive controllers with guaranteed closed loop stability

contraction based nonlinear model predictive control formulation without stability related terminal constraints contraction based nonlinear model predictive control nmpc formulations are attractive because they generally require short prediction horizons and there is no need for the terminal set computation and reinforcement that are common requirements to guarantee stability however the inclusion of the contraction constraint in the definition of the underlying optimization problem often leads to non standard features such as a need for the multi step open loop application of control sequences or the use of multi step memorization of the contraction level which may cause unfeasibility in the presence of unexpected disturbances in this study we propose a new contraction based nmpc formulation where no contraction constraint is explicitly involved the convergence of the resulting closed loop behavior is proved under mild assumptions an illustrative example is provided in order to demonstrate the relevance of the proposed formulation

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

generalized terminal state constraint for model predictive control a terminal state equality constraint for model predictive control mpc laws is investigated where the terminal state input pair is not fixed a priori but it is a free variable in the optimization the approach named generalized terminal state constraint can be used for both tracking mpc i e when the objective is to track a given steady state and economic mpc i e when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state it is shown that the proposed technique provides in general a larger feasibility set with respect to the existing approaches given the same prediction horizon moreover a new receding horizon strategy is introduced exploiting the generalized terminal state constraint under mild assumptions the new strategy is guaranteed to converge in finite time with arbitrarily good accuracy to an mpc law with an optimally chosen terminal state constraint while still enjoying a larger feasibility set the features of the new technique are illustrated by an inverted pendulum example in both the tracking and the economic contexts

moving horizon control of linear systems with input saturation and plant uncertainty part 1 robustness we present a moving horizon feedback system based on constrained optimal control algorithms for linear plants with input saturation the system is a non conventional sampled data system its sampling periods vary from sampling instant to sampling instant and the control during the sampling time is not constant but determined by the solution of an open loop optimal control problem this is a two part paper in this part we show that the proposed moving horizon control system is robustly stable whether the state of the plant is measurable or not in the second part we show that the proposed moving horizon control system is capable of following a class of reference inputs and suppressing a class of disturbances experimental results show that the behaviour of the moving horizon control system is superior to that resulting from some alternative control laws

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

robust receding horizon control of constrained nonlinear systems we present a method for the construction of a robust dual mode receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error the controller is dual mode in a neighborhood of the origin the control action is generated by a linear feedback controller designed for the linearized system outside this neighborhood receding horizon control is employed existing receding horizon controllers for nonlinear continuous time systems which are guaranteed to stabilize the nonlinear system to which they are applied require the exact solution at every instant of an optimal control problem with terminal equality constraints these requirements are considerably relaxed in the dual mode receding horizon controller presented in this paper stability is achieved by imposing a terminal inequality rather than an equality constraint only approximate minimization is required a variable time horizon is permitted robustness is achieved by employing conservative state and stability constraint sets thereby permitting a margin of error the resultant dual mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear constrained systems

contractive model predictive control for constrained nonlinear systems this paper addresses the development of stabilizing state and output feedback model predictive control mpc algorithms for constrained continuous time nonlinear systems with discrete observations moreover we propose a nonlinear observer structure for this class of systems and derive sufficient conditions under which this observer provides asymptotically convergent estimates the mpc scheme proposed consists of a basic finite horizon nonlinear mpc technique with the introduction of an additional state constraint which has been called a contractive constraint the resulting mpc scheme has been denoted contractive mpc this is a lyapunov based approach in which a lyapunov function chosen a priori is decreased not continuously but discretely it is allowed to increase at other times we show in this work that the implementation of this additional constraint into the online optimization makes it possible to prove strong nominal stability properties of the closed loop system

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

latent visual context learning for web image applications recently image representation based on bag of visual words bow model has been popularly applied in image and vision domains in bow a visual codebook of visual words is defined usually by clustering local features to represent any novel image with the occurrence of its contained visual words given a set of images we argue that the significance of each image is determined by the significance of its contained visual words traditionally the significances of visual words are defined by term frequency inverse document frequency tf idf which cannot necessarily capture the intrinsic visual context in this paper we propose a new scheme of latent visual context learning lvcl the visual context among images and visual words is formulated from latent semantic context and visual link graph analysis with lvcl the importance of visual words and images will be distinguished from each other which will facilitate image level applications such as image re ranking and canonical image selection we validate our approach on text query based search results returned by google image experimental results demonstrate the effectiveness and potentials of our lvcl in applications of image re ranking and canonical image selection over the state of the art approaches

image re ranking and rank aggregation based on similarity of ranked lists in content based image retrieval cbir systems ranking accurately collection images is of great relevance users are interested in the returned images placed at the first positions which usually are the most relevant ones collection images are ranked in increasing order of their distance to the query pattern e g query image defined by users therefore the effectiveness of these systems is very dependent on the accuracy of the distance function adopted in this paper we present a novel context based approach for redefining distances and later re ranking images aiming to improve the effectiveness of cbir systems in our approach distances among images are redefined based on the similarity of their ranked lists conducted experiments involving shape color and texture descriptors demonstrate the effectiveness of our method

ultimate boundedness control for uncertain discrete time systems via set induced lyapunov functions in this note linear discrete time systems affected by both parameter and input uncertainties are considered the problem of the synthesis of a feedback control assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence is investigated it is shown that the problem has a solution if and only if there exists a certain lyapunov function which does not belong to a preassigned class of functions e g the quadratic ones but it is determined by the target set in which ultimate boundedness is desired one of the advantages of this approach is that we may handle systems with control constraints no matching assumptions are made for systems with linearly constrained uncertainties it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets the resulting compensator may be implemented as a linear variable structure control

a new characterization of sobolev spaces on mathbb r n in this paper we present a new characterization of sobolev spaces on mathbb r n our characterizing condition is obtained via a quadratic multiscale expression which exploits the particular symmetry properties of euclidean space an interesting feature of our condition is that depends only on the metric of mathbb r n and the lebesgue measure so that one can define sobolev spaces of any order of smoothness on any metric measure space

explicit design of time varying stabilizing control laws for a class of controllable systems without drift abstract this paper gives a systematic way to design time variant feedback control laws for a class of controllable nonlinear systems this class contains a lot of systems which cannot be stabilized via a time invariant feedback control law the interest of this work lies in the design method since a general existence results is already available the techniques employed here are basic they mainly involve classical lyapunov analysis

moving horizon control of nonlinear systems with input saturation disturbances and plant uncertainty we present a moving horizon feedback system based on constrained optimal control algorithms for nonlinear plants with input saturation disturbances and plant uncertainty the system is a non conventional sampled data system its sampling periods vary from sampling instant to sampling instant and the control during the sampling time is not constant but determined by the solution of an open loop optimal control problem we show that the proposed moving horizon control system is robustly stable and is capable of attenuating l bounded disturbances

receding horizon control and discontinuous state feedback stabilization this paper addresses three aspects of receding horizon control in discrete time 1 feedback stabilization of general nonlinear systems with receding horizon control 2 the generation of stabili

a contraction property for state feedback design of linear discrete time systems abstract the contraction property is proposed as a tool for design of linear discrete time control systems explicit formulae are given for all linear time invariant state feedback controllers that imply the contraction property the obtained controllers are tuned with only two user parameters the two parameters are closely connected to the settling time and the damping of the closed loop system respectively the approach is illustrated by means of simulations

technical communique stabilizing decentralized model predictive control of nonlinear systems this note presents a stabilizing decentralized model predictive control mpc algorithm for nonlinear discrete time systems no information is assumed to be exchanged between local control laws the stability proof relies on the inclusion of a contractive constraint in the formulation of the mpc problem

moving horizon observers and observer based control in this paper two topics are explored a new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed the moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing or approximately minimizing a cost function over the preceding interval horizon t t t as t advances so does the horizon convergence of the estimator is established under the assumption that the corresponding global optimization problem can be approximately solved and a uniform reconstructability condition is satisfied the latter condition is automatically satisfied for linear observable systems the utility of the estimator for receding horizon control is explored in particular stability of a composite moving horizon system comprising a moving horizon regulator and a moving horizon observer is established

brief paper on receding horizon feedback control receding horizon feedback control rhfc was originally introduced as an easy method for designing stable state feedback controllers for linear systems here those results are generalized to the control of nonlinear autonomous systems and we develop a performance index which is minimized by the rhfc inverse optimal control problem previous results for linear systems have shown that desirable nonlinear controllers can be developed by making the rhfc horizon distance a function of the state that functional dependence was implicit and difficult to implement on line here we develop similar controllers for which the horizon distance is an easily computed explicit function of the state

dynamic observers as asymptotic limits of recursive filters special cases a method for constructing observers for dynamical systems as asymptotic limits of filters is described the program is carried out in detail for linear systems and in addition an observer is obtai

characterizations of sobolev spaces via averages on balls abstract in this paper the authors prove several equivalent characterizations of sobolev spaces of even integer orders on r n using the average b t f x 1 b x t b x t f y d y of a function f over the ball b x t y r n y x t with x r n and t 0 these characterizations rely only on the metric and the lebesgue measure on r n and are simpler than those obtained recently by alabern et al 2012 moreover these results may shed new light on the theory of high order sobolev spaces on spaces of homogeneous type

littlewood paley functions and sobolev spaces abstract we establish littlewood paley characterizations of the sobolev spaces w p in euclidean spaces using several square functions defined via the spherical average the ball average the bochner riesz means and some other well known operators we provide a simple proof so that we are able to extend and improve many results published in recent papers

cross indexing of binary sift codes for large scale image search in recent years there has been growing interest in mapping visual features into compact binary codes for applications on large scale image collections encoding high dimensional data as compact binary codes reduces the memory cost for storage besides it benefits the computational efficiency since the computation of similarity can be efficiently measured by hamming distance in this paper we propose a novel flexible scale invariant feature transform sift binarization fsb algorithm for large scale image search the fsb algorithm explores the magnitude patterns of sift descriptor it is unsupervised and the generated binary codes are demonstrated to be dispreserving besides we propose a new searching strategy to find target features based on the cross indexing in the binary sift space and original sift space we evaluate our approach on two publicly released data sets the experiments on large scale partial duplicate image retrieval system demonstrate the effectiveness and efficiency of the proposed algorithm

discontinuous control of nonholonomic systems the problem of asymptotic convergence for a class of nonholonomic control systems via discontinuous control is addressed and solved from a new point of view it is shown that control laws which ensures asymptotic exponential convergence of the closed loop system can be easily designed if the system is described in proper coordinates in such coordinates the system is discontinuous hence the problem of local asymptotic stabilization for a class of discontinuous nonholonomic control systems is dealt with and a general procedure to transform a continuous system into a discontinuous one is presented moreover a general strategy to design discontinuous control laws yielding asymptotic convergence for a class of nonholonomic control systems is proposed the enclosed simulation results show the effectiveness of the method

optimal state feedback control with a prescribed contraction property abstract in this paper we consider time varying state feedback control of single input linear time invariant discrete time systems the approach that we propose is based on a contraction property that was introduced in a previous paper all time varying controllers that yield the contraction property are derived it is seen that the state feedback vector becomes m periodic where the integer m is a user parameter related to the obtained contraction property from the class of control laws that yield the contraction property we determine the controller which minimizes a linear quadratic criterion results that are useful for tuning one of the user parameters are presented numerical examples which compare the methods are also included

littlewood paley characterizations of triebel lizorkin morrey spaces via ball averages abstract let 1 p u and q 1 in this article the authors establish equivalent characterizations of the triebel lizorkin morrey space e u q p r n with smoothness order 0 2 in terms of the lusin area function and the g function generated by the difference between f x and its ball average b 2 j f x 1 b x 2 j b x 2 j f y d y j 1 2 x r n where for any j 1 2 and x r n b x 2 j y r n y x 2 j as applications the authors obtain several characterizations of e u p r n via pointwise inequalities involving ball averages

characterizations of besov and triebel lizorkin spaces via averages on balls abstract let l n and p 1 in this article the authors prove that the sequence f b l 2 k f k z consisting of the differences between f and the ball average b l 2 k f characterizes the besov space b p q r n with q 0 and the triebel lizorkin space f p q r n with q 1 when the smoothness order 0 2 l more precisely it is proved that f b l 2 k f plays the same role as the approximation to the identity 2 k f appearing in the definitions of b p q r n and f p q r n the corresponding results for inhomogeneous besov and triebel lizorkin spaces are also obtained these results for the first time give a way to introduce besov and triebel lizorkin spaces with any smoothness order in 0 2 l on spaces of homogeneous type where l n

stability of a truncated infinite constrained receding horizon scheme the general discrete nonlinear case some results concerning the constrained receding horizon formulation with infinite and truncated prediction horizon are presented in this formulation a distinction is made between prediction and control horizons the main result is a generalization of a known fact for linear systems namely that under certain technical requirements the asymptotic stability of the above formulation holds for a sufficiently large finite prediction horizon existence results are also provided under stabilizability assumptions

bsift toward data independent codebook for large scale image search bag of words bows model based on scale invariant feature transform sift has been widely used in large scale image retrieval applications feature quantization by vector quantization plays a crucial role in bow model which generates visual words from the high dimensional sift features so as to adapt to the inverted file structure for the scalable retrieval traditional feature quantization approaches suffer several issues such as necessity of visual codebook training limited reliability and update inefficiency to avoid the above problems in this paper a novel feature quantization scheme is proposed to efficiently quantize each sift descriptor to a descriptive and discriminative bit vector which is called binary sift bsift our quantizer is independent of image collections in addition by taking the first 32 bits out from bsift as code word the generated bsift naturally lends itself to adapt to the classic inverted file structure for image indexing moreover the quantization error is reduced by feature filtering code word expansion and query sensitive mask shielding without any explicit codebook for quantization our approach can be readily applied in image search in some resource limited scenarios we evaluate the proposed algorithm for large scale image search on two public image data sets experimental results demonstrate the index efficiency and retrieval accuracy of our approach

stability constrained model predictive control this paper presents a new approach to guaranteeing stability of model predictive control mpc a stability constraint is computed and propagated forward at each stage as a constraint on the magnitude of the predicted state vector for a state space controllable form realization it is shown that asymptotic stability is guaranteed for the case of constrained multi input linear time invariant systems under full state measurement or with state estimation for any prediction horizon and any optimization objective function