constrained receding horizon predictive control for systems with disturbances a receding horizon predictive control method for systems with input constraints and disturbances is proposed a polyhedral feasible set of states which is invariant with respect to a given state feedback control law is derived in the presence of bounded disturbances the proposed predicted control algorithm deploys a strategy in which the current state is steered into the polyhedral invariant feasible set within a finite number n of feasible control moves despite the presence of disturbances the future control moves over the horizon n are represented as the sum of the state feedback control and a perturbation the perturbation term provides the degrees of freedom with which to enlarge the stabilizable set of initial states the control algorithm is formulated in linear matrix inequalities so that it can be solved using semidefinite programming

brief paper convergence properties of constrained linear system under mpc control law using affine disturbance feedback this paper shows new convergence properties of constrained linear discrete time system with bounded disturbances under model predictive control mpc law the mpc control law is obtained using an affine disturbance feedback parametrization with an additional linear state feedback term this parametrization has the same representative ability as some recent disturbance feedback parametrization but its choice together with an appropriate cost function results in a different closed loop convergence property more exactly the state of the closed loop system converges to a minimal invariant set with probability one deterministic convergence to the same minimal invariant set is also possible if a less intuitive cost function is used numerical experiments are provided that validate the results

brief paper adaptive model predictive control for a class of constrained linear systems based on the comparison model this paper proposes an adaptive model predictive control mpc algorithm for a class of constrained linear systems which estimates system parameters on line and produces the control input satisfying input state constraints for possible parameter estimation errors the key idea is to combine the robust mpc method based on the comparison model with an adaptive parameter estimation method suitable for mpc to this end first a new parameter update method based on the moving horizon estimation is proposed which allows to predict an estimation error bound over the prediction horizon second an adaptive mpc algorithm is developed by combining the on line parameter estimation with an mpc method based on the comparison model suitably modified to cope with the time varying case this method guarantees feasibility and stability of the closed loop system in the presence of state input constraints a numerical example is given to demonstrate its effectiveness

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

causal state feedback parameterizations in robust model predictive control in this paper we investigate the problem of nonlinearity and non convexity typically associated with linear state feedback parameterizations in the robust model predictive control rmpc for uncertain systems in particular we propose two tractable approaches to compute an rmpc controller consisting of both a causal state feedback gain and a control perturbation component for linear discrete time systems involving bounded disturbances and norm bounded structured model uncertainties along with hard constraints on the input and state both the state feedback gain and the control perturbation are explicitly considered as decision variables in the online optimization while avoiding nonlinearity and non convexity in the formulation the proposed rmpc controller computed through lmi optimizations is responsible for steering the uncertain system state to a terminal invariant set numerical examples from the literature demonstrate the advantages of the proposed scheme

robust constrained predictive control using comparison model this paper proposes a quadratic programming qp approach to robust model predictive control mpc for constrained linear systems having both model uncertainties and bounded disturbances to this end we construct an additional comparison model for worst case analysis based on a robust control lyapunov function rclf for the unconstrained system not necessarily an rclf in the presence of constraints this comparison model enables us to transform the given robust mpc problem into a nominal one without uncertain terms based on a terminal constraint obtained from the comparison model we derive a condition for initial states under which the ultimate boundedness of the closed loop is guaranteed without violating state and control constraints since this terminal condition is described by linear constraints the control optimization can be reduced to a qp problem

input to state stability of robust receding horizon control with an expected value cost this paper is concerned with the stability of a class of receding horizon control rhc laws for constrained linear discrete time systems subject to bounded state disturbances and convex state and input constraints the paper considers the class of finite horizon feedback control policies parameterized as affine functions of the system state calculation of which can be shown to be tractable via a convex reparameterization when minimizing the expected value of a finite horizon quadratic cost we show that the value function is convex when solving this optimal control problem at each time step and implementing the result in a receding horizon fashion we provide sufficient conditions under which the closed loop system is input to state stable iss

parameterized tube model predictive control this paper develops a parameterized tube model predictive control mpc synthesis method the most relevant novel feature of our proposal is the online use of a single tractable linear program that optimizes parameterized minkowski decomposable state and control tubes and an associated fully separable nonlinear control policy the induced control policy enjoys a higher degree of nonlinearity than existing tube mpc and robust mpc using disturbance affine control policy our proposal offers greater generality than the state of the art robust mpc methods it is conjectured and also established in three cases that our proposal is equivalent feasibility wise to dynamic programming dp it is also shown that under natural assumptions our method is computationally efficient while it possesses rather strong system theoretic properties

model predictive control using segregated disturbance feedback this paper proposes a new control parametrization under the model predictive control mpc framework for constrained linear discrete time systems with bounded disturbances the proposed parametrization takes the form of a special piecewise affine disturbance feedback in an effort to reduce conservatism it is a generalization of linear disturbance feedback parametrization introduced in the recent literature numerical computations and stability properties of the resulting mpc problem using the proposed parametrization are discussed when the disturbance set and the problem data satisfy mild assumptions the associated finite horizon optimization can be computed efficiently and exactly the advantage of the proposed parametrization over linear disturbance feedback is illustrated via numerical examples

receding horizon output feedback control for constrained uncertain systems using periodic invariance in this article we consider a receding horizon output feedback control rhoc method for linear discrete time systems with polytopic model uncertainties and input constraints first we derive a set of estimator gains and then we obtain on the basis of the periodic invariance a series of state feedback gains stabilising the augmented output feedback system with these estimator gains these procedures are formulated as linear matrix inequalities an rhoc strategy is proposed based on these state feedback and state estimator gains in conjunction with their corresponding periodically invariant sets the proposed rhoc strategy enhances the performance in comparison with the case in which static periodic gains are used and increases the size of the stabilisable region by introducing a degree of freedom to steer the augmented state into periodically invariant sets

a linear programming approach to constrained robust predictive control a receding horizon predictive control algorithm for systems with model uncertainty and input constraints is developed the proposed algorithm adopts the receding horizon dual mode i e free control moves and invariant set paradigm the approach is novel in that it provides a convenient way of combining predictions of control moves which are optimal in the sense of worst case performance with large target invariant sets thus the proposed algorithm has a large stabilizable set of states corresponding to a cautious state feedback law while enjoying the good performance of a tightly tuned but robust control law unlike earlier approaches which are based on qp or semidefinite programming here computational complexity is reduced through the use of lp

infinite horizon performance bounds for uncertain constrained systems we present a new method to bound the performance of controllers for uncertain linear systems with mixed state and input constraints and bounded disturbances we take as a performance metric either an expected value or minimax discounted cost over an infinite horizon and provide a method for computing a lower bound on the achievable performance of any causal control policy in either case our lower bound is compared to an upper performance bound provided by restricting the choice of controller to one that is affine in the observed disturbances and we show that the two bounds are closely related in particular the lower bounds have a natural interpretation in terms of affine control policies that are optimal for a problem with a restricted disturbance set we show that our performance bounds can be computed via solution of a finite dimensional convex optimization problem and provide numerical examples to illustrate the efficacy of our method

striped parameterized tube model predictive control a modification of the parameterized tube model predictive control ptmpc strategy for linear systems with additive disturbances is proposed which reduces the dependence of the number of optimization variables on horizon length from quadratic to linear by using a triangular striped prediction structure unlike ptmpc which assumes a fixed linear terminal feedback law for predictions the proposed prediction scheme allows disturbance compensation to extend beyond the initial n step prediction horizon the resulting scheme can potentially outperform ptmpc in terms of the size of the domain of attraction and allows for a longer horizon n for the same computational demand

output feedback receding horizon control of constrained systems this paper considers output feedback control of linear discrete time systems with convex state and input constraints which are subject to bounded state disturbances and output measurement errors we show that the non convex problem of finding a constraint admissible affine output feedback policy over a finite horizon to be used in conjunction with a fixed linear state observer can be converted to an equivalent convex problem when used in the design of a time varying robust receding horizon control law we derive conditions under which the resulting closed loop system is guaranteed to satisfy the system constraints for all time given an initial state estimate and bound on the state estimation error when the state estimation error bound matches the minimal robust positively invariant mrpi set for the system error dynamics we show that this control law is time invariant but its calculation generally requires solution of an infinite dimensional optimization problem finally using an invariant outer

a simplified algorithm for approximate separable decomposition of morphological templates abstract decomposition of morphological templates is a useful technique for enhancing the computational efficiency of morphological image processing operations this paper presents a simplified algorithm for obtaining approximate separable decomposition of grayscale morphological templates this algorithm is computationally less intensive as compared to gader s 1 2 algorithm in yielding the separable parts of a given template further it overcomes the drawback of gader s algorithm by providing integer weight separable parts for integer weight morphological separable templates

optimization over state feedback policies for robust control with constraints this paper is concerned with the optimal control of linear discrete time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input it is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence this implies that a broad class of constrained finite horizon robust and optimal control problems where the optimization is over affine state feedback policies can be solved in a computationally efficient fashion using convex optimization methods this equivalence result is used to design a robust receding horizon control rhc state feedback policy such that the closed loop system is input to state stable iss and the constraints are satisfied for all time and all allowable disturbance sequences the cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance free state and input sequences the value of the receding horizon control law can be calculated at each sample instant using a single tractable and convex quadratic program qp if the disturbance set is polytopic or a tractable second order cone program socp if the disturbance set is given by a 2 norm bound

decomposition of convex polygonal morphological structuring elements into neighborhood subsets a discussion is presented of the decomposition of convex polygon shaped structuring elements into neighborhood subsets such decompositions will lead to efficient implementation of corresponding morphological operations on neighborhood processing based parallel image computers it is proved that all convex polygons are decomposable efficient decomposition algorithms are developed for different machine structures an o 1 time algorithm with respect to the image size is developed for the four neighbor connected mesh machines a linear time algorithm for determining the optimal decomposition is provided for the machines that can quickly perform 3 3 morphological operations

spectrographic measurement of instantaneous frequency and the time dependent weighted average instantaneous frequency instantaneous frequency if is an important signal characteristic arising in many fields it is a concept intimately linked to time frequency analysis where it can be obtained from a time frequency distribution tfd as the first conditional moment in frequency suggesting that the if is the average frequency at each time however this interpretation is questionable since it is well known that the if often ranges beyond the spectral support of the signal in addition to obtain the if from a spectrogram which is one possible tfd a very wideband and thus severely spectrally distorted spectrogram must be used more reasonable bandwidths are investigated and in particular give the conditions by which the first conditional moment of a spectrogram can indeed be interpreted as the average frequency at each time under these conditions namely when the spectrogram bandwidth is less than the frequency separation of the signal components in the time frequency plane the spectrogram yields not the usual if but a time dependent weighted average instantaneous frequency waif of the signal also while the if and waif are generally different sometimes they are the same in particular when there is symmetry in the time frequency spectrum of the signal in that case the first conditional spectral moments of both wideband and narrow band spectrograms are the same and interpretable as the average frequency at each time

decomposition of additively separable structuring elements with applications abstract the techniques of decomposing gray scale structuring elements with emphasis on the additively separable structuring elements are presented based on the concept of additively separable we proposed the square euclidean distance as the measure in the distance transformation since the structuring element corresponding to square euclidean distance is additively separable the developed techniques can be applied to decompose the structuring element into successive dilation of small structuring elements with window size 3 3

algorithms for the decomposition of gray scale morphological operations the choice and detailed design of structuring elements plays a pivotal role in the morphologic processing of images a broad class of morphological operations can be expressed as an equivalent supremum of erosions by a minimal set of basis filters diverse morphological operations can then be expressed in a single comparable framework the set of basis filters are data like structures each filter representing one type of local change possible under that operation the data level description of the basis set is a natural starting point for the design of morphological filters this paper promotes the use of the basis decomposition of gray scale morphological operations to design and apply morphological filters a constructive proof is given for the basis decomposition of general gray scale morphological operations as are practical algorithms to find all of the basis set members for these operations

on the behavior of the continuous time spectrogram for arbitrarily narrow windows the behavior of the continuous time ct spectrogram in particular of its first frequency moment ffm and instantaneous bandwidth ib in the limit of infinitely thin windows is revisited new insight is gained and novel quantitative results are presented power series in the width of the short time fourier transform stft window are derived for the ct spectrogram and its moments which are valid for any reasonably regular narrow window and which universally yield the instantaneous frequency if as the first term in the ffm expansion the well known result for ct signals according to which the spectrogram ffm tends to the if when the square of the stft window approaches a dirac delta delta function is thus extended indeed upon introduction of functional sequences depending on a small width parameter it is shown that the spectrogram ffm always tends to the if when the stft window becomes arbitrarily narrow with no actual need for the latter or any of its powers to converge to a delta function it is also checked within the framework here developed that the spectrogram ib behaves as expected going to infinity when the ffm approaches the if it is argued that when estimating the if of ct signals with the spectrogram it may be eventually more convenient to work with functions that become arbitrarily close to a delta function than to its square root whatever mathematical object this might be in addition the results of the analysis on the if and the ib are illustrated with a few examples of standard signal and window forms