further results on infinity norms as lyapunov functions for linear systems this note continues on the results proposed in two previous papers for computing vector 1 or infin norm based lyapunov functions for linear discrete time systems by presenting a finitely terminating algorithm for the construction of lyapunov functions of that class the algorithm utilizes the solution of a finite sequence of feasibility linear programs lps with very few constraints or equivalently very simple algebraic tests in contrast to solving the original problem where a bilinear matrix equation with rank and norm constraint needs to be solved

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

model predictive control based on linear programming the explicit solution we study model predictive control mpc schemes for discrete time linear time invariant systems with constraints on inputs and states that can be formulated using a linear program lp in particular we focus our attention on performance criteria based on a mixed 1 norm namely 1 norm with respect to time and norm with respect to space first we provide a method to compute the terminal weight so that closed loop stability is achieved we then show that the optimal control profile is a piecewise affine and continuous function of the initial state and briefly describe the algorithm to compute it the piecewise affine form allows to eliminate online lp as the computation associated with mpc becomes a simple function evaluation besides practical advantages the availability of the explicit structure of the mpc controller provides an insight into the type of control action in different regions of the state space and highlights possible conditions of degeneracies of the lp such as multiple optima

efficient robust optimization for robust control with constraints this paper proposes an efficient computational technique for the optimal control of linear discrete time systems subject to bounded disturbances with mixed linear constraints on the states and inputs the problem of computing an optimal state feedback control policy given the current state is non convex a recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program while the reparameterized problem is theoretically tractable the number of variables is quadratic in the number of stages or horizon length n and has no apparent exploitable structure leading to computational time of mathcal o n 6 per iteration of an interior point method we focus on the case when the disturbance set is norm bounded or the linear map of a hypercube and the cost function involves the minimization of a quadratic cost here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem that is the policy optimization problem may be decomposed into a set of coupled finite horizon control problems this decomposition can then be formulated as a highly structured quadratic program solvable by primal dual interior point methods in which each iteration requires mathcal o n 3 time this cubic iteration time can be guaranteed using a riccati based block factorization technique which is standard in discrete time optimal control numerical results are presented using a standard sparse primal dual interior point solver that illustrate the efficiency of this approach

robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks this paper presents a neural network approach to robust model predictive control mpc for constrained discrete time nonlinear systems with unmodeled dynamics affected by bounded uncertainties the exact nonlinear model of underlying process is not precisely known but a partially known nominal model is available this partially known nonlinear model is first decomposed to an affine term plus an unknown high order term via jacobian linearization the linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning the minimax methodology is exploited to deal with bounded uncertainties the minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two layer recurrent neural network the proposed neurodynamic approach to nonlinear mpc improves the computational efficiency and sheds a light for real time implementability of mpc technology simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach

design of energy conserving algorithms for frictionless dynamic contact problems this paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum angular momentum and energy in finite element simulations it is seen that a lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties a related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized this penalty method sacrifices the energy conservation property but is dissipative under all conditions of changing contact so that the global algorithm remains stable notably it is also shown that augmented lagrangian iteration utilizing this penalty kernel reproduces the energy conserving i e lagrange multiplier solution to any desired degree of accuracy the result is a robust stable method even in the context of large deformations as is shown by some representative numerical examples in particular the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations 1997 by john wiley sons ltd

input to state stability of efficient robust h mpc scheme for nonlinear systems propose an efficient constrained h nmpc with guaranteed iss w r t bounded disturbances use piecewise affine h control and augmented pldi models to decrease conservatism of nmpc use pldi method to turn the non convex min max problem into a semi definite programming present a sufficient condition in form of lmis to ensure the iss of the proposed nmpc scheme apply the proposed nmpc to some fast systems such as mass carts and vehicular platoon in this work we present an efficient h model predictive control mpc scheme with guaranteed input to state stability iss for constrained nonlinear systems subject to unknown but bounded disturbances the nonlinear system is represented by using some given inclusion polytope the notion of iss is introduced to derive the sufficient condition in terms of linear matrix inequalities lmis which ensures the iss of the closed loop system in order to reduce the online computational demand of mpc the non convex min max optimization problem is converted to a minimization problem in form of lmis a suboptimal mpc algorithm is then addressed to further decrease the computational demand the applicability of the proposed results is illustrated by two numerical examples of a mass cart and a vehicular platoon

inexact alternating direction methods for image recovery in the image processing community there have recently been many restoration and reconstruction problems that can be reformulated into linearly constrained convex programming models whose objective functions have separable structures these favorable reformulations have promoted impressive applications of the alternating direction method adm in the field of image processing at each iteration the computation of adm is dominated by solving two subproblems exactly however in many restoration and reconstruction applications it is either impossible or extremely expensive to obtain exact solutions of these adm subproblems this fact urges the development on inexact versions of adm which allow the generated adm subproblems to be solved approximately subject to certain inexactness criteria in this paper we develop some truly implementable inexact adms whose inexactness criteria controlling the accuracy of the adm subproblems are easily implementable the convergence of the new inexact adms will be proved numerical results on several image processing problems will be given to illustrate the effectiveness of the proposed inexact adms

simultaneous nonlinear model predictive control and state estimation an output feedback approach to model predictive control that combines state estimation and control into a single minmax optimization is introduced for discrete time nonlinear systems specifically a criterion that involves finite forward and backward horizons is minimized with respect to control input variables and is maximized with respect to the unknown initial state as well as disturbance and measurement noise variables under appropriate assumptions that encode controllability and observability we show that the state of the closed loop remains bounded and that a bound on tracking error can be found for trajectory tracking problems we also introduce a primaldual interior point method that can be used to efficiently solve the minmax optimization problem and show in simulation examples that the method succeeds even for severely nonlinear and non convex problems

a variational approach to removing multiplicative noise this paper focuses on the problem of multiplicative noise removal we draw our inspiration from the modeling of speckle noise by using a map estimator we can derive a functional whose minimizer corresponds to the denoised image we want to recover although the functional is not convex we prove the existence of a minimizer and we show the capability of our model on some numerical examples we study the associated evolution problem for which we derive existence and uniqueness results for the solution we prove the convergence of an implicit scheme to compute the solution

design of near optimal decision rules in multistage adaptive mixed integer optimization in recent years decision rules have been established as the preferred solution method for addressing computationally demanding multistage adaptive optimization problems despite their success existing decision rules a are typically constrained by their a priori design and b do not incorporate in their modeling adaptive binary decisions to address these problems we first derive the structure for optimal decision rules involving continuous and binary variables as piecewise linear and piecewise constant functions respectively we then propose a methodology for the optimal design of such decision rules that have a finite number of pieces and solve the problem robustly using mixed integer optimization we demonstrate the effectiveness of the proposed methods in the context of two multistage inventory control problems we provide global lower bounds and show that our approach is i practically tractable and ii provides high quality solutions that outperform alternative methods

efficient schemes for total variation minimization under constraints in image processing this paper presents new fast algorithms to minimize total variation and more generally l 1 norms under a general convex constraint such problems are standards of image processing the algorithms are based on a recent advance in convex optimization proposed by yurii nesterov depending on the regularity of the data fidelity term we solve either a primal problem or a dual problem first we show that standard first order schemes allow one to get solutions of precision epsilon in o frac 1 epsilon 2 iterations at worst we propose a scheme that allows one to obtain a solution of precision epsilon in o frac 1 epsilon iterations for a general convex constraint for a strongly convex constraint we solve a dual problem with a scheme that requires o frac 1 sqrt epsilon iterations to get a solution of precision epsilon finally we perform some numerical experiments which confirm the theoretical results on various problems of image processing

optimal robust linear quadratic regulator for systems subject to uncertainties in this technical note a robust recursive regulator for linear discrete time systems which are subject to parametric uncertainties is proposed the main feature of the optimal regulator developed is the absence of tuning parameters in online applications to achieve this purpose a quadratic cost function based on the combination of penalty function and robust weighted least squares methods is formulated the convergence and stability proofs for the stationary system and a numerical comparative study among the standard linear quadratic regulator guaranteed cost and h controllers are provided

multiplicative noise removal via using nonconvex regularizers based on total variation and wavelet frame abstract total variation based regularization and wavelet frame based regularization are two different methods for image restoration moreover nonconvex regularization has advantages over convex regularization for preserving edges in images in this paper a variational model consisting of two nonconvex regularizers based respectively on total variation and wavelet frame is proposed for multiplicative noise removal the proposed model combines the advantages of the nonconvex regularization and the hybrid regularization so it can more effectively preserve edges and details in images than any single regularization can the alternating minimization method is proposed to solve the novel model although the corresponding minimization problem is nonconvex the convexity of all subproblems is guaranteed under some mild conditions therefore we study the convergence property of the algorithm numerical experiments have proved that the proposed model with the corresponding algorithm outperforms some state of the art models in terms of the peak signal to noise ratio and the relative error of the restored images

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

model predictive control for linear parameter varying constrained systems using ellipsoidal set prediction this paper proposes a new model predictive control mpc method for linear parameter varying systems with bounded parameter variation subject to input constraints the method adopts closed loop prediction and constructs ellipsoidal sets to predict the future states with reasonable computational effort then the information on the parameter variation rate is exploited to improve the accuracy of the prediction furthermore a relaxed terminal condition which guarantees the stability for infinite horizon is introduced to enlarge the stabilizable region it is shown that the feasibility of the mpc problem at the initial step ensures the stability of the closed loop system finally a simulation result illustrates the effectiveness of the proposed method

worst case formulations of model predictive control for systems with bounded parameters two different predictive control formulations are developed based on minimization of the worst case quadratic cost for systems with bounded parameters the two formulations differ on the assumptions made about the future inputs in optimizing the current input one assumes open loop control while the other considers closed loop control their closed loop properties such as asymptotic stability are examined we then focus on a moving average model with an integrator and derive computationally simpler suboptimal algorithms

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

multiplicative noise and blur removal by framelet decomposition and l_ 1 based l curve method this paper proposes a framelet based convex optimization model for multiplicative noise and blur removal problem the main idea is to employ framelet expansion to represent the original image and use the variable decomposition to solve the problem because of the nature of multiplicative noise we decompose the observed data into the original image variable and the noise variable to obtain the resulting model the original image variable is represented by framelet and it is determined by using l 1 norm in the selection and shrinkage of framelet coefficients the noise variable is measured by using the mean and the variance of the underlying probability distribution this framelet setting can be applied to analysis synthesis and balanced approaches and the resulting optimization models are convex such that they can be solved very efficiently by the alternating direction of a multiplier method an another contribution of this paper is to propose to select the regularization parameter by using the l 1 based l curve method for these framelet based models numerical examples are presented to illustrate the effectiveness of these models and show that the performance of the proposed method is better than that by the existing methods

consistency results on newmark methods for dynamical contact problems the paper considers the time integration of frictionless dynamical contact problems between viscoelastic bodies in the frame of the signorini condition among the numerical integrators interest focuses on the classical newmark method the improved energy dissipative version due to kane et al and the contact stabilized newmark method recently suggested by deuflhard et al in the absence of contact any such variant is equivalent to the stormer verlet scheme which is well known to have consistency order 2 in the presence of contact however the classical approach to discretization errors would not show consistency at all because of the discontinuity at the contact surprisingly the question of consistency in the constrained situation has not been solved yet the present paper fills this gap by means of a novel proof technique using specific norms based on earlier perturbation results due to the authors the corresponding estimation of the local discretization error requires the bounded total variation of the solution the results have consequences for the construction of an adaptive timestep control which will be worked out subsequently in a forthcoming paper

generalisation of euler lagrange equations to find min max optimal solution of uncertain systems a major problem in optimal control theory is existing uncertainty in initial state cost function or in state equations in this paper a generalised euler lagrange approach to find min max optimal solution of uncertain systems with uncertain or certain cost function using calculus of variation is considered the work is based on an admissible system path or a trajectory which minimises the maximum value of the functional over all uncertainty first of all a new form of euler lagrange conditions for uncertain systems is presented then several cases are indicated where final condition can be specified or free also necessary conditions are introduced to existence of min max optimal solution of the uncertain systems also the method is generalised when the uncertainties are bounded with using pontryagin s minimum principle finally efficiency of the proposed methods is verified through some examples

restoration of chopped and nodded images by framelets in infrared astronomy an observed image from a chop and nod process can be considered as the result of passing the original image through a high pass filter here we propose a restoration algorithm which builds up a tight framelet system that has the high pass filter as one of the framelet filters our approach reduces the solution of restoration problem to that of recovering the missing coefficients of the original image in the tight framelet decomposition the framelet approach provides a natural setting to apply various sophisticated framelet denoising schemes to remove the noise without reducing the intensity of major stars in the image a proof of the convergence of the algorithm based on convex analysis is also provided simulated and real images are tested to illustrate the efficiency of our method over the projected landweber method

technical communique evaluation of piecewise affine control via binary search tree we present an algorithm for generating a binary search tree that allows efficient computation of piecewise affine pwa functions defined on a polyhedral partition this is useful for pwa control approaches such as explicit model predictive control as it allows the controller to be implemented online with small computational effort the computation time is logarithmic in the number of regions in the pwa partition

multiplicative noise removal via a learned dictionary multiplicative noise removal is a challenging image processing problem and most existing methods are based on the maximum a posteriori formulation and the logarithmic transformation of multiplicative denoising problems into additive denoising problems sparse representations of images have shown to be efficient approaches for image recovery following this idea in this paper we propose to learn a dictionary from the logarithmic transformed image and then to use it in a variational model built for noise removal extensive experimental results suggest that in terms of visual quality peak signal to noise ratio and mean absolute deviation error the proposed algorithm outperforms state of the art methods

robust optimal feedback for terminal linear quadratic control problems under disturbances we consider a linear dynamic system in the presence of an unknown but bounded perturbation and study how to control the system in order to get into a prescribed neighborhood of a zero at a given final moment the quality of a control is estimated by the quadratic functional we define optimal guaranteed program controls as controls that are allowed to be corrected at one intermediate time moment we show that an infinite dimensional problem of constructing such controls is equivalent to a special bilevel problem of mathematical programming which can be solved explicitely an easy implementable algorithm for solving the bilevel optimization problem is derived based on this algorithm we propose an algorithm of constructing a guaranteed feedback control with one correction moment we describe the rules of computing feedback which can be implemented in real time mode the results of illustrative tests are given

min max control of constrained uncertain discrete time linear systems for discrete time uncertain linear systems with constraints on inputs and states we develop an approach to determine state feedback controllers based on a min max control formulation robustness is achieved against additive norm bounded input disturbances and or polyhedral parametric uncertainties in the state space matrices we show that the finite horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs when the optimal control law is implemented in a receding horizon scheme only a piecewise affine function needs to be evaluated on line at each time step the technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state space

min max feedback model predictive control for constrained linear systems min max feedback formulations of model predictive control are discussed both in the fixed and variable horizon contexts the control schemes the authors discuss introduce in the control optimization the notion that feedback is present in the receding horizon implementation of the control this leads to improved performance compared to standard model predictive control and resolves the feasibility difficulties that arise with the min max techniques that are documented in the literature the stabilizing properties of the methods are discussed as well as some practical implementation details

on linear programming and robust modelpredictive control using impulse responses abstract campo and morari have derived a linear programming problem with a potentially large number of constraints which is equivalent to a min max formulation for robust model predictive control of linear systems that formulation involves minimization with respect to the controls of the maximum with respect to the system s impulse response from a set of possible impulse responses of the infinity norm of the error between the predicted and required system output sequences here an alternative linear programming problem is derived which has a smaller number of constraints and is therefore potentially more convenient for on line control

inherent robustness properties of quasi infinite horizon nonlinear model predictive control we consider inherent robustness properties of model predictive control mpc for continuous time nonlinear systems with input constraints and terminal constraints we show that mpc with a nominal prediction model and persistent but bounded disturbances has some degree of inherent robustness when the terminal control law and the terminal penalty matrix are chosen as the linear quadratic control law and the related lyapunov matrix respectively we emphasize that the input constraint sets can be any compact set rather than convex sets and our results do not depend on the continuity of the optimal cost function or of the control law in the interior of the feasible region

finite element analysis of nonsmooth contact this work develops robust contact algorithms capable of dealing with complex contact situations involving several bodies with corners amongst the mathematical tools we bring to bear on the problem is nonsmooth analysis following clarke f h clarke optimization and nonsmooth analysis john wiley and sons new york 1983 we specifically address contact geometries for which both the use of normals and gap functions have difficulties and therefore precludes the application of most contact algorithms proposed to date such situations arise in applications such as fragmentation where angular fragments undergo complex collision sequences before they scatter we demonstrate the robustness and versatility of the nonsmooth contact algorithms developed in this paper with the aid of selected two and three dimensional applications

wavelet algorithms for high resolution image reconstruction high resolution image reconstruction refers to the reconstruction of high resolution images from multiple low resolution shifted degraded samples of a true image in this paper we analyze this problem from the wavelet point of view by expressing the true image as a function in cal l bbb r 2 we derive iterative algorithms which recover the function completely in the cal l sense from the given low resolution functions these algorithms decompose the function obtained from the previous iteration into different frequency components in the wavelet transform domain and add them into the new iterate to improve the approximation we apply wavelet packet thresholding methods to denoise the function obtained in the previous step before adding it into the new iterate our numerical results show that the reconstructed images from our wavelet algorithms are better than that from the tikhonov least squares approach extension to super resolution image reconstruction where some of the low resolution images are missing is also considered

monotone multigrid methods on nonmatching grids for nonlinear multibody contact problems nonconforming domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations we use a generalized mortar method based on dual lagrange multipliers for the discretization of a nonlinear contact problem between linear elastic bodies in the case of unilateral contact problems pointwise constraints occur and monotone multigrid methods yield efficient iterative solvers here we generalize these techniques to nonmatching triangulations where the constraints are realized in terms of weak integral conditions the basic new idea is the construction of a nested sequence of nonconforming constrained spaces we use suitable basis transformations and a multiplicative correction in contrast to other approaches no outer iteration scheme is required the resulting monotone method is of optimal complexity and can be implemented as a multigrid method numerical results illustrate the performance of our approach in two and three dimensions

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

affine systems in l2 rd the analysis of the analysis operator abstract discrete affine systems are obtained by applying dilations to a given shift invariant system the complicated structure of the affine system is due first and foremost to the fact that it is not invariant under shifts affine frames carry the additional difficulty that they are global in nature it is the entire interaction between the various dilation levels that determines whether the system is a frame and not the behaviour of the system within one dilation level we completely unravel the structure of the affine system with the aid of two new notions the affine product and a quasi affine system this leads to a characterization of affine frames the induced characterization of tight affine frames is in terms of exact orthogonality relations that the wavelets should satisfy on the fourier domain several results such as a general oversampling theorem follow from these characterizations most importantly the affine product can be factored during a multiresolution analysis construction and this leads to a complete characterization of all tight frames that can be constructed by such methods moreover this characterization suggests very simple sufficient conditions for constructing tight frames from multiresolution of particular importance are the facts that the underlying scaling function does not need to satisfy any a priori conditions and that the freedom offered by redundancy can be fully exploited in these constructions an

efficient robust predictive control predictive constrained control of time varying and or uncertain linear systems has been effected through the use of ellipsoidal invariant sets kothare et al 1996 linear matrix inequalities lmis have been used to design a state dependent state feedback law that maintains the state vector inside invariant feasible sets for the purposes of prediction however at each time instant the state feedback law is assumed constant in addition due to the large number of lmis involved online computation becomes intractable for anything other than small dimensional systems here we propose an approach that deploys a fixed state feedback law but introduces extra degrees of freedom through the use of perturbations on the fixed state feedback law the problem is so formulated that all demanding computations can be performed offline leaving only a simple optimization problem to be solved online over and above the very significant reduction in computational cost the extra degrees of freedom allow for better performance and wider applicability

on optimization of stochastic maxmin plus scaling systemsan approximation approach a large class of discrete event and hybrid systems can be described by a maxmin plus scaling mmps model i e a model in which the main operations are maximization minimization addition and scalar multiplication accordingly optimization of mmps systems appears in different problems defined for discrete event and hybrid systems for a stochastic mmps system this optimization problem is computationally highly demanding as often numerical integration has to be used to compute the objective function the aim of this paper is to decrease such computational complexity by applying an approximation method that is based on the moments of a random variable and that can be computed analytically

min max optimal control of linear systems with uncertainty and terminal state constraints in this paper a class of min max optimal control problems with continuous dynamical systems and quadratic terminal constraints is studied the main contribution is that the original terminal state constraint in which the disturbance is involved is transformed into an equivalent linear matrix inequality without disturbance under certain conditions then the original min max optimal control problem is solved via solving a sequence of semi definite programming problems an example is presented to illustrate the proposed method

the contact stabilized newmark method consistency error of a spatiotemporal discretization the paper considers a slightly improved variant of the contact stabilized newmark method by deuflhard et al which provides a spatio temporal numerical integration of dynamical contact problems between viscoelastic bodies in the frame of the signorini condition up to now the question of consistency in the case of contact constraints has been discussed for time integrators in function space under the assumption of bounded total variation of the solution here interest focuses on the consistency error of the newmark scheme in physical energy norm after discretization both in time and in space the resulting estimate for the local discretization error allows to prove global convergence of the newmark scheme under an additional assumption on the active contact boundaries

solving constrained total variation image restoration and reconstruction problems via alternating direction methods in this paper we study alternating direction methods for solving constrained total variation image restoration and reconstruction problems alternating direction methods can be implementable variants of the classical augmented lagrangian method for optimization problems with separable structures and linear constraints the proposed framework allows us to solve problems of image restoration impulse noise removal inpainting and image cartoon texture decomposition as the constrained model is employed we need only to input the noise level and the estimation of the regularization parameter is not required in these imaging problems experimental results for such imaging problems are presented to illustrate the effectiveness of the proposed method we show that the alternating direction method is very efficient for solving image restoration and reconstruction problems

robust mpc strategy with optimized polytopic dynamics for linear systems with additive and multiplicative uncertainty abstract polytopic dynamics have been introduced into the predictions in model predictive control mpc and have been optimized so as to maximize invariant ellipsoids for systems subject to multiplicative uncertainty this work was recently extended to the case of mixed additive and multiplicative uncertainty and sufficient conditions were provided to guarantee the invariance of an ellipsoid additionally under the assumption that the multiplicative uncertainty is known during a prediction horizon n this extension was used as the terminal control law of an overall robust mpc strategy that deployed an affine in the disturbance policy this assumption was needed to enable the handling of constraints in the overall mpc strategy the aims of this paper are to establish the necessity and sufficiency of the relevant invariance conditions of the polytopic dynamics and to propose a robust mpc strategy that uses polytopic sets to describe the evolution of predicted variables and therefore does not make an assumption that future multiplicative uncertainty is known the number of constraints and free variables of the resulting online optimization grows linearly with n the benefits of the strategy are illustrated by numerical simulations

robust optimal control of material flows in demand driven supply networks abstract we develop a model based on stochastic discrete time controlled dynamical systems in order to derive optimal policies for controlling the material flow in supply networks each node in the network is described as a transducer such that the dynamics of the material and information flows within the entire network can be expressed by a system of first order difference equations where some inputs to the system act as external disturbances we apply methods from constrained robust optimal control to compute the explicit control law as a function of the current state for the numerical examples considered these control laws correspond to certain classes of optimal ordering policies from inventory management while avoiding however any a priori assumptions about the general form of the policy

convex liftings based robust control design this paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties this method hinges on so called convex liftings which emulate control lyapunov function by providing a constructive framework for optimization based control implementation it will be shown that this method can guarantee the recursive feasibility and robust stability finally a numerical example will be presented to illustrate this method