a new category of hermitian upwind schemes for computational acoustics ii two dimensional aeroacoustics this is the second paper of a series in which we build and study third order hermitian upwind schemes for numerically solving linear aeroacoustics in this paper we extend the method to non stationary flows for this purpose we employ a family of six wave models to discretize the space operator this family is parametrized by an acoustic propagation angle from this wave modelling specific boundary conditions are proposed to treat effectively subsonic supersonic boundary conditions a sequence of numerical simulations is then carried out and makes it possible to examine the effectiveness of the scheme

robust model predictive control of singular systems this note is concerned with model predictive control for linear singular systems with time varying uncertainties a piecewise constant control sequence is calculated by minimizing the worst case linear quadratic objective function at each sample time the sufficient conditions on the existence of the model predictive control are derived and expressed as linear matrix inequalities the robust stability of the closed loop systems is guaranteed by the proposed design method

receding horizon controls for input delayed systems this paper presents a receding horizon control rhc for an unconstrained input delayed system to begin with we derive a finite horizon optimal control for a quadratic cost function including two final weighting terms the rhc is easily obtained by changing the initial and final times of the finite horizon optimal control a linear matrix inequality lmi condition on two final weighting matrices is proposed to meet the cost monotonicity under which the optimal cost on the horizon is monotonically nonincreasing with time and hence the asymptotical stability is guaranteed only if an observability condition is met it is shown through simulation that the proposed rhc stabilizes the input delayed system effectively and its performance can be tuned by adjusting weighting matrices with respect to the state and the input

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

efficient region segmentation on compressed gray images using quadtree and shading representation abstract image segmentation which partitions the image into homogeneous regions is a fundamental operation in image processing suppose the input gray image with size n n has been compressed into the compressed image via quadtree and shading representation assume that the number of blocks in the representation is b commonly b n 2 due to the compression effect this paper first derives some closed forms for computing the mean variance of any block and for calculating the two statistical measures of any merged region in o 1 time it then presents an efficient o b b time algorithm for performing region segmentation on the compressed image directly where b is the inverse of the ackerman s function and is a very slowly growing function with the same time complexity our results extend the pioneering results by dillencourt and samet from the map image to the gray image in addition with four real images experimental results show that our proposed algorithm has about 55 4 execution time improvement ratio when compared to the previous fastest region segmentation algorithm by fiorio and gustedt whose o n 2 time algorithm is run on the original n n gray image

computing output feedback controllers to enlarge the domain of attraction in polynomial systems the problem of computing controllers to enlarge the domain of attraction da of equilibrium points of polynomial systems is considered in order to deal with such a problem a technique for computing static nonlinear output feedback controllers which maximize the largest estimate of the da leda induced by a given polynomial lyapunov function is proposed the main contribution of the note is to show that a lower bound of the maximum achievable leda and a corresponding controller can be obtained through linear matrix inequality optimizations moreover a necessary condition for tightness of this lower bound is presented which is also a sufficient condition to establish the tightness of the lower bound of the leda for a given controller

a new category of hermitian upwind schemes for computational acoustics a new high order upwind scheme is developed to solve linear acoustics in order to produce a compact scheme with a high level of precision a hermite interpolation is used an algorithm in three stages is built in order to optimize the procedure of discretization in the reconstruction stage a local spatial interpolator based on an upwind stencil is defined in the decomposition stage the calculation of a wave model adapted to the decomposition of the time derivatives in simple wave contributions is derived then the local spatial interpolator is used in order to calculate the wave strengths for each wave in the evolution stage we update by means of a procedure similar to that of cauchy kovaleskaya the discrete variable and its derivatives by using the information brought by each simple wave specific boundary conditions are finally established in this way a third order upwind hermitian scheme may be constructed d p3 scheme a one dimensional analysis in fourier series shows the principal properties of such a scheme the effectiveness and the exactitude of the new compact scheme are shown by their applications to several two dimensional problems and by comparisons to competing finite difference method for wave propagation

reachability analysis of discrete time systems with disturbances this paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps via state feedback control to a given target set the assumptions that are made in this paper are that the system is discrete time nonlinear and time invariant and subject to mixed constraints on the state and input a persistent disturbance dependent on the current state and input acts on the system existing results are not able to address state and input dependent disturbances and the results in this paper are therefore a generalization of previously published results one of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software provided the system is piecewise affine and the constraints are polygonal existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances whereas the results in this paper remove this limitation some simple examples are also given that show that even if all the relevant sets are convex and the system is linear convexity of the set of controllable states cannot be guaranteed

disturbance attenuation for systems with input saturation an lmi approach a new design technique is proposed to improve disturbance attenuation for systems with input saturation the main results rely on a multiobjective approach which combines the quadratic stabilization technique with constraints on inputs for the full state feedback problem the sufficient conditions for the feasibility of a high gain controller are expressed in terms of linear matrix inequalities lmi for output feedback design the controllers are assumed to have an observer based structure the sufficient conditions for the output feedback controller to recover the full state properties are also given in terms of lmi

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

on the gap between positive polynomials and sos of polynomials this note investigates the gap existing between positive polynomials and sum of squares sos of polynomials which affects several analysis and synthesis tools in control systems based on polynomial sos relaxations and about which almost nothing is known in particular a matrix characterization of the pns that is the positive homogeneous forms that are not sos is proposed which allows to show that any pns is the vertex of an unbounded cone of pns moreover a complete parametrization of the set of pns is introduced

an algorithm for encoding and decoding the 3 d hilbert order spatial ordering is a transformation relating an n dimensional voxel to a set of natural numbers interest in the hilbert order h order has been high because of its desirable performance when applied to image processing in this correspondence an encoding decoding algorithm for the three dimensional 3 d hilbert order is presented

brief an efficient off line formulation of robust model predictive control using linear matrix inequalities the practicality of model predictive control mpc is partially limited by its ability to solve optimization problems in real time moreover on line computational demand for synthesizing a robust mpc algorithm will likely grow significantly with the problem size in this paper we use the concept of an asymptotically stable invariant ellipsoid to develop a robust constrained mpc algorithm which gives a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids constructed off line one within another in state space this off line approach can address a broad class of model uncertainty descriptions with guaranteed robust stability of the closed loop system and substantial reduction of the on line mpc computation the controller design is illustrated with two examples

one dimensional b b polynomial and hilbert scan for graylevel image coding abstract effectiveness of one dimensional bezier bernstein polynomial has been studied for compression of graylevel images both raster and hilbert scan have been used for this purpose two different algorithms for one dimensional approximation and encoding of hilbert images provide evidence of better compression ratio compared to that for raster scanned images comparison with the result of an existing algorithm has also been performed to examine the effectiveness of our 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

robust explicit model predictive control via regular piecewise affine approximation this paper proposes an explicit model predictive control design approach for regulation of linear time invariant systems subject to both state and control constraints in the presence of additive disturbances the proposed control law is implemented as a piecewise affine function defined on a regular simplicial partition and has two main positive features first the regularity of the simplicial partition allows one to efficiently implement the control law on digital circuits thus achieving extremely fast computation times moreover the asymptotic stability or the convergence to a set including the origin of the closed loop system can be enforced a priori rather than checked a posteriori via lyapunov analysis

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

robust tube mpc for linear systems with multiplicative uncertainty recently a technical note 4 ensured recursive feasibility in robust model predictive control with multiplicative uncertainty by applying terminal constraints to the degrees of freedom available to the controller while constructing polytopic tube cross sections the current note extends this technique by bounding the tube parameters in norm and constructing a terminal set based on this bound this reduces the online computational load and so allows longer prediction horizons to be used

brief homogeneous lyapunov functions for systems with structured uncertainties the problem addressed in this paper is the construction of homogeneous polynomial lyapunov functions hplfs for linear systems with time varying structured uncertainties a sufficient condition for the existence of an hplf of given degree is formulated in terms of a linear matrix inequalities lmi feasibility problem this condition turns out to be also necessary in some cases depending on the dimension of the system and the degree of the lyapunov function the maximum norm of the parametric uncertainty for which there exists a homogeneous polynomial lyapunov function is computed by solving a generalized eigenvalue problem the construction of such lyapunov functions is efficiently performed by means of popular convex optimization tools for the solution of problems in lmi form comparisons with other classes of lyapunov functions through numerical examples taken from the literature show that hplfs are a powerful tool for robustness analysis

brief paper local stability analysis using simulations and sum of squares programming the problem of computing bounds on the region of attraction for systems with polynomial vector fields is considered invariant subsets of the region of attraction are characterized as sublevel sets of lyapunov functions finite dimensional polynomial parametrizations for lyapunov functions are used a methodology utilizing information from simulations to generate lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed the suitability of lyapunov function candidates is assessed solving linear sum of squares optimization problems qualified candidates are used to compute invariant subsets of the region of attraction and to initialize various bilinear search strategies for further optimization we illustrate the method on small examples from the literature and several control oriented systems

brief optimizing the end point state weighting matrix in model based predictive control in this paper a linear model based predictive control mpc algorithm is presented for which nominal closed loop stability is guaranteed the input is obtained by minimizing a quadratic performance index over a finite horizon plus an end point state eps penalty subject to input state and output constraints under certain conditions the weighting matrix in the eps penalty enables one to specify an invariant ellipsoid in which the input state and output constraints are satisfied in existing mpc algorithms this weighting matrix is calculated off line the main contribution of this paper is to incorporate the calculation of the eps weighting matrix into the on line optimization problem of the controller the main advantage of this approach is that a natural and automatic trade off between feasibility and optimality is obtained this is demonstrated in a simulation example

predictive control for sector bounded nonlinear model and its application to solid oxide fuel cell systems in this paper a nonlinear model predictive control method is presented for solid oxide fuel cell systems for realistic modeling a sector bounded nonlinear model with input constraint is considered as a performance index we consider one horizon cost function that is represented by the weighted sum of state control input and nonlinear function by minimizing the upper bound of the cost function the optimized control input sequences are obtained for cost monotonicity a terminal inequality condition is derived in terms of a finite number of linear matrix inequalities lmis by using augmented vector feedback law which consists of state and sector bounded nonlinear function in order to show the effectiveness of the proposed method the sector bounded nonlinear model is derived for the solid oxide fuel cell systems and the system performance is verified by applying the proposed mpc algorithm to the systems

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

manipulation and presentation of multidimensional image data using the peano scan a fractal curve first discussed by giuseppe peano has useful statistical properties in image processing the curve can act as a transform between a line and n dimensional space retaining some of the spatially associative properties of the space applications of the curve include multispectral image display compression in the color and spa tial domain classification and color display the technique enables the display of high quality color images on a frame store capable of displaying only 256 colors simultaneously a logically ordered and complete set of colors for false color work can be selected an im provement in compression by about 3x for color images can be ob tained by using this method in conjunction with an existing spatial compression technique a simple algorithm for constructing the curves is shown

stochastic control with uncertain parameters via chance constrained control chance constrained methods handle problem uncertainty by formulating the constraints probabilistically and only guaranteeing their satisfaction up to a given violation level this paper extends existing chance constrained methods to handle both uncertainty in the system state as well as in the constraint parameters due to the imperfect knowledge of the system state caused by motion sensor and environment uncertainty the system constraints cannot be guaranteed to be satisfied and consequently must be considered probabilistically prior work has primarily only dealt with uncertainty in the system state or constraint parameters but not both simultaneously however in many motivating applications both frequently occur to handle this case previous approaches either approximate the distribution leading to a nonconvex optimization program or use sampling alone to represent the uncertainty which requires a large number of samples to accurately represent the distribution to address these limitations a novel hybrid method is proposed that uses both analytical functions and sampling to represent the uncertainty it is shown that under certain conditions the resulting optimization program using this hybrid representation is convex to check the convexity an efficient a priori sufficient condition is developed furthermore by using this hybrid representation this method drastically reduces the computational complexity over previous methods which is demonstrated through two examples consequently this method has the ability to enable real time stochastic control for the motivating applications

quasi min max fuzzy model predictive control of direct methanol fuel cells abstract direct methanol fuel cells dmfcs are known as a promising power source in future in this paper we consider steering a dmfc plant to a desired operating point while optimizing the transient performance according to a quadratic cost function quasi min max fuzzy model predictive control fmpc with input constraints is proposed for the dmfc in order to reduce the computational burden for real time implementation a partial off line quasi min max fmpc is also proposed in this case a bank of invariant sets together with the corresponding feedback control laws are obtained by solving some linear matrix inequalities lmis off line leaving the online part a bisection search and a much simplified constrained optimization problem online computation complexity for both the quasi min max fmpc and the partial off line one is also analyzed simulation results are given to show the effectiveness of the proposed controllers

robust distributed model predictive control of linear systems with structured time varying uncertainties abstractin this work synthesis of robust distributed model predictive control mpc is presented for a class of linear systems subject to structured time varying uncertainties by decomposing a global system into smaller dimensional subsystems a set of distributed mpc controllers instead of a centralised controller are designed to ensure the robust stability of the closed loop system with respect to model uncertainties distributed state feedback laws are obtained by solving a min max optimisation problem the design of robust distributed mpc is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints an iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance the simulation results show the effectiveness of the proposed robust distributed mpc algorithm

four alternative patterns of the hilbert curve the second pattern of the hilbert curve was shown by moore in 1900 in this article we present four more patterns these patterns together with hilbert s original pattern and moore s pattern comprise a complete set of the hilbert curve

a linear programming oriented procedure for quadratic stabilization of uncertain systems abstract this paper gives a new necessary and sufficient condition for linear quadratic stabilization of linear uncertain systems when both the dynamic as well as the control matrix are subject to uncertainty a constructive numerical procedure is defined to check the condition and it furthermore provides a stabilizing linear feedback gain some experiments are presented

lyapunov methods for time invariant delay difference inclusions motivated by the fact that delay difference inclusions ddis form a rich modeling class that includes for example uncertain time delay systems and certain types of networked control systems this paper provides a comprehensive collection of lyapunov methods for ddis first the lyapunov krasovskii approach which is an extension of the classical lyapunov theory to time delay systems is considered it is shown that a ddi is mathcal kl stable if and only if it admits a lyapunov krasovskii function lkf second the lyapunov razumikhin method which is a type of small gain approach for time delay systems is studied it is proved that a ddi is mathcal kl stable if it admits a lyapunov razumikhin function lrf moreover an example of a linear delay difference equation which is globally exponentially stable but does not admit an lrf is provided thus it is established that the existence of an lrf is not a necessary condition for mathcal kl stability of a ddi then it is shown that the existence of an lrf is a sufficient condition for the existence of an lkf and that only under certain additional assumptions is the converse true furthermore it is shown that an lrf induces a family of sets with certain contraction properties that are particular to time delay systems on the other hand an lkf is shown to induce a type of contractive set similar to those induced by a classical lyapunov function the class of quadratic candidate functions is used to illustrate the results derived in this paper in terms of both lkfs and lrfs respectively both stability analysis and stabilizing controller synthesis methods for linear ddis are proposed

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

moving horizon control of linear systems with input saturation and plant uncertainty part 2 disturbance rejection and tracking 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 in part 1 we showed that the proposed moving horizon control system is robustly stable in this paper we show that it is capable of asymptotically suppressing a class of l bounded disturbances that are restricted to a subspace and of asymptotically following a class of reference inputs that are continuously differentiable bounded in magnitude and slope and restricted to a subspace

time optimal model predictive control for linear systems based on ellipsoidal and polytopic sets time optimal model predictive control mpc strategies are investigated in this paper we first derive a series of controllable sets described by ellipsoids or convex polytopes offline then obtain

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

a novel two phase hilbert scan based search algorithm for block motion estimation using ctf data structure motion estimation is one of the kernel issues in mpeg series in this correspondence a novel two phase hilbert scan based search algorithm for block motion estimation is presented first in the intra phase a segmentation of the hilbert curve is applied to the current block then a novel coarse to fine data structure is developed to eliminate the impossible reference blocks in the search window of the reference frame in the inter phase a new prediction scheme for estimating the initial motion vector of the current block is presented experimental results reveal that when compared to the gapd algorithm our proposed algorithm has better execution time and estimation accuracy performance under the same estimation accuracy our proposed algorithm has better execution time performance when compared to the fs algorithm in addition when comparing with the tss algorithm our proposed algorithm has better estimation accuracy performance but has worse execution time performance

robust triple mode mpc this paper reviews triple mode predictive control for linear time invariant systems and then proposes a new algorithm for robust triple mode predictive control for constrained linear systems described by polytopic uncertainty models the approach significantly enlarges the feasibility region compared to recently proposed robust dual mode approaches the efficacy of the approach is demonstrated with numerical examples

on the trade off between feasibility and performance in bilinear and state affine model based predictive control closed loop stabilizing model based predictive control mpc algorithms for discrete time bilinear and state affine models are presented stability of the closed loop is obtained through the use of an appropriate end point weighting and end point inequality constraint in this way the infinite horizon performance index is bounded from above by the objective function that is minimized in the mpc algorithm this paper presents an algorithm that aims at obtaining a large feasibility region by maximizing off line the region that is defined by the end point inequality constraint in order to improve the performance of the mpc algorithm the conservatism of the upper bound on the infinite horizon performance index is reduced in the on line computations

output feedback model predictive control for lpv systems based on quasi min max algorithm this paper proposes a robust output feedback model predictive control mpc scheme for linear parameter varying lpv systems based on a quasi min max algorithm this approach involves an off line design of a robust state observer for lpv systems using linear matrix inequality lmi and an on line robust output feedback mpc algorithm using the estimated state the proposed mpc method for lpv systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems a numerical example for an lpv system subject to input constraints is given to demonstrate its effectiveness

approximate robust dynamic programming and robustly stable mpc we present a technique for approximate robust dynamic programming that is suitable for linearly constrained polytopic systems with piecewise affine cost functions the approximation method uses polyhedral representations of the cost to go function and feasible set and can considerably reduce the computational burden compared to recently proposed methods for exact robust dynamic programming bemporad a borrelli f morari m 2003 min max control of constrained uncertain discrete time linear systems ieee transactions on automatic control 48 9 1600 1606 diehl m bjornberg j 2004 robust dynamic programming for min max model predictive control of constrained uncertain systems ieee transactions on automatic control 49 12 2253 2257 we show how to apply the method to robust mpc and give conditions that guarantee closed loop stability we finish by applying the method to a state constrained tutorial example a parking car with uncertain mass

a primal dual potential reduction method for problems involving matrix inequalities we describe a potential reduction method for convex optimization problems involving matrix inequalities the method is based on the theory developed by nesterov and nemirovsky and generalizes gonzaga and todd s method for linear programming a worst case analysis shows that the number of iterations grows as the square root of the problem size but in practice it appears to grow more slowly as in other interior point methods the overall computational effort is therefore dominated by the least squares system that taust be solved in each iteration a type of conjugate gradient algorithm can be used for this purpose which results in important savings for two reasons first it allows us to take advantage of the special structure the problems often have e g lyapunov or algebraic riccati inequalities second we show that the polynomial bound on the number ofiterations remains valid even if the conjugate gradient algorithm is not run until completion which in practice can greatly reduce the computational effort per iteration we describe in detail how the algorithm works for optimization problems with l lyapunov inequaliues each of size m we prove an overall worst case operation count of o mssll5 the average case complexity appears to be closer to o m4ll5 this estimate is justified by extensive numerical experimentation and is consistent with other researchers experience with the practical performance of interior point algorithms for linear programming this result means that the computational cost of extending current control theory based on the solution of lyapunov or riccati equations to a theory that is based on the solution of multiple coupled lyapunov or riccati inequalities is modest

space filling approach for fast window query on compressed images based on the space filling approach this paper presents a fast algorithm for window query on compressed images given a query window of size n sub 1 spl times n sub 2 the proposed algorithm takes o n sub 1 logt p time to perform the window query where n sub 1 max n sub 1 n sub 2 and t spl times t is the image size p is the number of outputted codes the proposed algorithm improves the naive algorithm which needs o n sub 1 n sub 2 log t p time significantly some experimentations are carried out to demonstrate the computational advantage of the proposed algorithm from the experimental results it is observed that the proposed algorithm has about 72 98 time improvement when compared to the naive algorithm

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

nonconvex optimization problem the infinite horizon linear quadratic control problem with quadratic constraints abstract we present a general method for the solution of the problem of minimization of a quadratic functional in a hilbert space over the intersection of some subspace and a set defined by special quadratic constraints many optimal control problems can be formulated in this abstract form as an example a stationary infinite horizon linear quadratic optimization problem with quadratic constraints is posed and solved

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

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

space filling curves and their use in the design of geometric data structures we are given a two dimensional square grid of size n n where n 2n and n 0 a space filling curve sfc is a numbering of the cells of this grid with numbers from c 1 to c n2 for some c 0 we call a sfc recursive rsfc if it can be recursively divided into four square rsfcs of equal size examples of well known rsfcs include the hilbert curve the z curve and the gray code

a nonlinear sum of squares model predictive control approach this note presents a novel model predictive control mpc strategy for input saturated nonlinear systems having a polynomial structure the results here proposed are a significant generalization w r t similar existing algorithms which are tailored only for linearized or multi model plant descriptions a first key aim is to present sum of squares sos conditions under which off line one step controllable sets for nonlinear polynomial systems can be derived a second relevant contribution is to describe an on line mpc strategy that leads to less conservative performance w r t most existing methods based on global linearization approaches an illustrative example is finally provided in order to show the effectiveness of the proposed sos based mpc algorithm

an ellipsoidal off line mpc scheme for uncertain polytopic discrete time systems an off line model predictive control mpc method based on ellipsoidal calculus and viability theory is described in order to address control problems in the presence of state and input constraints for uncertain polytopic linear plants subject to persistent disturbances in order to reduce the computational burdens and conservativeness of traditional polytopic mpc schemes the present approach carries out off line most of the computations and it makes use of closed loop predictions to improve the control performance this is done by recursively pre computing suitable ellipsoidal inner approximations of the exact controllable sets and solving on line a simple and numerically low demanding optimization problem subject to a set membership constraint comparisons with three other recent off line mpc approaches are also provided in the final example

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

efficient algorithms for coding hilbert curve of arbitrary sized image and application to window query previously several efficient hilbert scan based operations were presented but they all suffer from the constraint that the image size must be 2 rx2 r considering an image with arbitrary size i 1xi 2 this paper first presents an efficient snake scan based algorithm for coding the hilbert curve of the given image the proposed coding algorithm takes o k logu time to code the hilbert order of one pixel where k denotes the number of the quadrants and u min i 1 i 2 next a memory saving hilbert curve representation called hcgl is presented for representing the encoded hilbert curve and it can be constructed in o l 2logl time where l max i 1 i 2 based on the hcgl representation of arbitrary sized image an application to window query is presented and the proposed window query algorithm takes o mlogl p time where m denotes the number of generated maximal quadtree blocks and p denotes the number of output codes under the same psnr peak signal to noise ratio experimental results demonstrate that our proposed hcgl representation outperforms some existing related algorithms in terms of execution time and bpp bit per pixel in addition our proposed window query algorithm has been justified in the gis geographical information system application

technical communique who needs qp for linear mpc anyway conventional mpc uses quadratic programming qp to minimise on line a cost over n linearly constrained control moves however stability constraints often require the use of large n thereby increasing the on line computation rendering the approach impracticable in the case of fast sampling here we explore an alternative that requires a fraction of the computational cost which increases only linearly with n and propose an extension which in all but a small class of models matches to within a fraction of a percent point the performance of the optimal solution obtained through qp the provocative title of the paper is intended to point out that the proposed approach offers a very attractive alternative to qp based mpc

constrained infinite horizon model predictive control for fuzzy discrete time systems the problem of constrained infinite horizon model predictive control for fuzzy discrete systems is considered in this paper new sufficient conditions are proposed in terms of linear matrix inequalities based on the optimal solutions of these sufficient conditions at each sampling instant we design both parallel distributed compensation and nonparallel distributed compensation state feedback controllers which can guarantee that the resulting closed loop fuzzy discrete system is asymptotically stable in addition the fuzzy feedback controllers meet the specifications for the fuzzy discrete systems with both input and output constraints numerical examples are presented to demonstrate the effectiveness of the proposed techniques

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

ultra fast stabilizing model predictive control via canonical piecewise affine approximations this paper investigates the use of canonical piecewise affine pwa functions for approximation and fast implementation of linear mpc controllers the control law is approximated in an optimal way over a regular simplicial partition of a given set of states of interest the stability properties of the resulting closed loop system are analyzed by constructing a suitable pwa lyapunov function the main advantage of the proposed approach to the implementation of mpc controllers is that the resulting stabilizing approximate mpc controller can be implemented on chip with sampling times in the order of tens of nanoseconds

parametric optimization and optimal control using algebraic geometry methods we present two algebraic methods to solve the parametric optimization problem that arises in non linear model predictive control we consider constrained discrete time polynomial systems and the corresponding constrained finite time optimal control problem the first method is based on cylindrical algebraic decomposition the second uses grobner bases and the eigenvalue method for solving systems of polynomial equations both methods aim at moving most of the computational burden associated with the optimization problem off line by pre computing certain algebraic objects then an on line algorithm uses this pre computed information to obtain the solution of the original optimization problem in real time fast and efficiently introductory material is provided as appropriate and the algorithms are accompanied by illustrative examples

explicit solution of min max mpc with additive uncertainties and quadratic criterion abstract min max model predictive control mmmpc is one of the strategies proposed to control plants subject to bounded uncertainties this technique is very difficult to implement in real time because of the computation time required recently the piecewise affine nature of this control law has been proved for unconstrained linear systems with quadratic performance criterion however no algorithm to compute the explicit form of the control law was given this paper shows how to obtain this explicit form by means of a constructive algorithm an approximation to mmmpc in the presence of constraints is presented based on this algorithm

constrained robust feedback model predictive control for uncertain systems with polytopic description for the constrained uncertain systems with polytopic description a new design method of robust feedback model predictive control is proposed by using a sequence of feedback control laws and designing the parameter dependent lyapunov function for each model the design method provides more degrees of freedom and then can improve the control performance and enlarge the feasible region based on the characteristic property of the design method an offline design algorithm is developed to reduce the mpc controller s online computation burden the numerical examples verify the effectiveness of the results presented in this article

on efficient computation of low complexity controlled invariant sets for uncertain linear systems a method is presented for determining invariant low complexity polytopic sets and associated linear feedback laws for linear systems with polytopic uncertainty conditions based on the relationship between 2 and norms are used to define an initial invariant low complexity polytope as the solution of a semi definite program the problem of computing a maximal controlled invariant low complexity polytopic set is then formulated as a bilinearly constrained problem and a relaxation of this problem is derived as an iterative sequence of convex programs the proposed method scales linearly with the state dimension which allows the possibility of determining low complexity robust controlled invariant sets for high order systems

output feedback robust mpc for lpv system with polytopic model parametric uncertainty and bounded disturbance abstractthe output feedback robust model predictive control mpc for the linear parameter varying lpv system with norm bounded disturbance is addressed where the model parametric matrices are only known to be bounded within a polytope the previous techniques of norm bounding technique quadratic boundedness qb dynamic output feedback and ellipsoid true state bound tsb refreshment formula for guaranteeing recursive feasibility are fused into the newly proposed approaches in the notion of qb the full lyapunov matrix is applied for the first time in this context the single step dynamic output feedback robust mpc where the infinite horizon control moves are parameterised as a dynamic output feedback law is the main topic of this paper while the multi step method is also suggested in order to strictly guarantee the physical constraints the outer bound of the true state replaces the true state itself so tightness of this bound has a major effect on the control performance in order to ti

estimating the domain of attraction via union of continuous families of lyapunov estimates this paper proposes a new approach to estimate the domain of attraction of equilibrium points of polynomial systems the idea consists of estimating the domain of attraction via the union of a continuous family of lyapunov estimates rather than via one lyapunov estimate only as done in existing methods this family is obtained through a convex lmi optimization by deriving a stability condition which takes simultaneously into account all considered lyapunov functions moreover inner approximations of the union of this family via a set with simple shape are also derived

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

a framework for robustness analysis of constrained finite receding horizon control a framework for robustness analysis of input constrained finite receding horizon control is presented under the assumption of quadratic upper bounds on the finite horizon costs we derive sufficient conditions for robust stability of the standard discrete time linear quadratic receding horizon control formulation this is achieved by recasting conditions for nominal and robust stability as an implication between quadratic forms lending itself to s procedure tools which are used to convert robustness questions to tractable convex conditions robustness with respect to plant model mismatch as well as for state measurement error is shown to reduce to the feasibility of linear matrix inequalities simple examples demonstrate the approach

comments on constrained infinite horizon model predictive control for fuzzy discrete time systems this letter points out the errors in a previous paper by the authors ieee trans fuzzy syst vol 18 no 2 pp 429 436 apr 2010 an improved result is given

matrix sum of squares relaxations for robust semi definite programs we consider robust semi definite programs which depend polynomially or rationally on some uncertain parameter that is only known to be contained in a set with a polynomial matrix inequality description on the basis of matrix sum of squares decompositions we suggest a systematic procedure to construct a family of linear matrix inequality relaxations for computing upper bounds on the optimal value of the corresponding robust counterpart with a novel matrix version of putinar s sum of squares representation for positive polynomials on compact semi algebraic sets we prove asymptotic exactness of the relaxation family under a suitable constraint qualification if the uncertainty region is a compact polytope we provide a new duality proof for the validity of putinar s constraint qualification with an a priori degree bound on the polynomial certificates finally we point out the consequences of our results for constructing relaxations based on the so called full block s procedure which allows to apply recently developed tests in order to computationally verify the exactness of possibly small sized relaxations

a predictive control scheme for systems with variable time delay this article deals with the robust control design problem for linear time invariant systems affected by variable feedback delay constraints on the system state are considered in the system description the starting point is the construction of a predictive control law which guarantees the existence of a nonempty robust positive invariant rpi set with respect to the closed loop dynamics subsequently an iterative algorithm is proposed in order to obtain an approximation of the maximal rpi set the problem can be treated in the framework of piecewise affine systems due to the explicit formulations of the control law obtained via multiparametric programming

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

properties of generalized predictive control control design using long range prediction based on a dynamic model of the plant has become an important contender for high performance applications the model can be derived analytically but more typically it is provided by simple experiments or in the adaptive context by recursive estimation many methods have been proposed in the literature depending on the assumed model structure and the choice of cost function here the approach called generalized predictive control or gpc is reviewed of special interest is the derivation of prediction equations using an observer polynomial and a demonstration that the selection of particular horizons the costing horizons and the control horizon leads to well understood basic techniques such as dead beat pole placement and lq simulated examples show that gpc is suitable for controlling a complex plant such as unstable inverse unstable systems and how the observer polynomial independently tailors the response to the disturbances preprogrammed set points as with robot trajectory control and actuator nonlinearities can also be catered for a discussion of adaptive applications of gpc to several industrial process concludes that the method is easy to use and effective

a linear framework on the distributed model predictive control of positive systems abstract this paper investigates the distributed model predictive control dmpc for positive systems with interval and polytopic uncertainties respectively different from the traditional quadratic dmpc a new linear dmpc framework is established for positive systems first a linear cooperative cost function performance index function is introduced for the dmpc of positive systems accordingly some linear constraint conditions are imposed on the systems then a linear co positive lyapunov function is constructed using the linear lyapunov function the dmpc controllers are designed for interval positive systems and polytopic positive systems respectively the controller of each subsystem contains not only the state information of the subsystem but also the state information of other correlated subsystems linear programming based optimization algorithm is addressed to compute the controller parameters to guarantee the feasibility and stability of the systems a cone invariant set is proposed finally two case studies are provided to illustrate the effectiveness of the theoretical findings

generation of spatial orders and space filling curves space filling curves have been found useful for many applications in diverse fields a space filling curve is a path in a 2 r 2 r raster domain which visits each location exactly once in mathematical terms space filling curves linearize a 2d integer space bijectively mapping the space to the integer line an algorithm is presented which generates a large number of space filling curves spatial orders functions are derived such that the code of each location can be calculated from its coordinates and conversely a location code can be decoded to yield the coordinates the algorithm first generates generate 4 4 spatial orders they subsequently may be scaled up to any desired domain of size 2 r 2 r the underlying theory of the algorithm the processes for scaling up encoding and decoding are described in detail the curves are generated as a set of incongruent curves followed if required by the sets of associated congruent curves a number of space filling curves are illustrated

discontinuous galerkin methods with plane waves for time harmonic problems a general framework for discontinuous galerkin methods in the frequency domain with numerical flux is presented the main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element the method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two dimensional linearized euler equations it is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high order drp schemes in addition the conditioning of the method is found to be high but not critical in practice it is shown that the ultra weak variational formulation is in fact a subset of the present discontinuous galerkin method a special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles aeroacoustic problems with non uniform flows are also considered and results are presented for the sound radiated from a two dimensional jet

a new approach to vector median filtering based on space filling curves the availability of a wide set of multidimensional information sources in different application fields e g color cameras multispectral remote sensing imagery devices etc is the basis for the interest of image processing research on extensions of scalar nonlinear filtering approaches to multidimensional data filtering a new approach to multidimensional median filtering is presented the method is structured into two steps absolute sorting of the vectorial space based on peano space filling curves is proposed as a preliminary step in order to map vectorial data onto an appropriate one dimensional 1 d space then a scalar median filtering operation is applied the main advantage of the proposed approach is the computational efficiency of the absolute sorting step which makes the method globally faster than existing median filtering techniques this is particularly important when dealing with a large amount of data e g image sequences presented results also show that the filtering performances of the proposed approach are comparable with those of vector median filters presented in the literature

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

brief nonlinear model predictive control with polytopic invariant sets ellipsoidal invariant sets have been widely used as target sets in model predictive control mpc these sets can be computed by constructing appropriate linear difference inclusions together with additional constraints to ensure that the ellipsoid lies within a given inclusion polytope the choice of inclusion polytope has a significant effect on the size of the target ellipsoid but the optimal inclusion polytope cannot in general be computed systematically this paper shows that use of polytopic invariant sets overcomes this difficulty allowing larger stabilizable sets without loss of performance in the interests of online efficiency consideration is focused on interpolation based mpc

nonlinear control synthesis by convex optimization a stability criterion for nonlinear systems recently derived by the third author can be viewed as a dual to lyapunov s second theorem the criterion is stated in terms of a function which can be interpreted as the stationary density of a substance that is generated all over the state space and flows along the system trajectories toward the equilibrium the new criterion has a remarkable convexity property which in this note is used for controller synthesis via convex optimization recent numerical methods for verification of positivity of multivariate polynomials based on sum of squares decompositions are used

on robust stability and set invariance of switched linear parameter varying systems in this paper we address the problem of robust stability and set invariance of switched linear parameter varying lpv systems affected by bounded disturbances a switched lpv system is a collection of single lpv subsystems with a switching rule that decides which subsystem is active at each time this framework is useful for lpv systems with large parameter variation range for which it may be difficult to assess or guarantee stability over the whole parameter range our first contribution is to derive a result for a single lpv system that extends and generalises previous work for switched systems our second and main contribution is to apply this seed result in the derivation of dwell time type conditions on the switched lpv switching rule which ensure robust closed loop stability and set invariance of the trajectories of the switched lpv system across the whole parameter range as an application of the results we consider the problem of reference tracking for lpv systems using switched lpv state fe

on stability of constrained receding horizon control with finite terminal weighting matrix in this paper a new stabilizing receding horizon control based on a finite input and state horizon cost with a finite terminal weighting matrix is proposed for time varying discrete linear systems with constraints we propose matrix inequality conditions on the terminal weighting matrix under which closed loop stability is guaranteed for both cases of unconstrained and constrained systems with input and state constraints we show that such a terminal weighting matrix can be obtained by solving a linear matrix inequality lmi in the case of constrained time invariant systems an artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints using the invariant ellipsoid constraints a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control

technical communique improving off line approach to robust mpc based on nominal performance cost this paper gives two alternative off line synthesis approaches to robust model predictive control rmpc for systems with polytopic description in each approach a sequence of explicit control laws that correspond to a sequence of nested asymptotically invariant ellipsoids are constructed off line in order to accommodate a wider class of systems nominal performance cost is chosen to substitute the worst case one in an existing technique in the design of control law for a larger ellipsoid the second approach further incorporates the knowledge of control laws associated with all smaller ellipsoids so as to further improve feasibility and optimality the effectiveness of the alternative approaches is illustrated by a simulation example

stability region analysis using polynomial and composite polynomial lyapunov functions and sum of squares programming we propose using bilinear sum of squares programming for obtaining inner bounds of roas for dynamical systems with polynomial vector fields we search for polynomial as well as composite lyapunov functions comprised of pointwise maximums of polynomial functions results for several examples from the literature are presented using the proposed methods and the penbmi solver

robust stability in constrained predictive control through the youla parameterisations in this article we take advantage of the primary and dual youla parameterisations to set up a soft constrained model predictive control mpc scheme in this framework it is possible to guarantee stability in face of norm bounded uncertainties under special conditions guarantees are also given for hard input constraints in more detail we parameterise the mpc predictions in terms of the primary youla parameter and use this parameter as the on line optimisation variable the uncertainty is parameterised in terms of the dual youla parameter stability can then be guaranteed through small gain arguments on the loop consisting of the primary and dual youla parameter this is included in the mpc optimisation as a constraint on the induced gain of the optimisation variable we illustrate the method with a numerical simulation example

an interpolation strategy for discrete time bilinear mpc problems input output i o feedback linearization suffers from a number of restrictions which have limited its use in model based predictive control some of these restrictions do not apply to the case of bilinear systems but problems with input constraints and unstable zero dynamics persist this paper overcomes these difficulties by means of an interpolation strategy involved in this interpolation is a feasible and stabilizing trajectory which is computed through the use of invariant feasible sets and a more aggressive trajectory which can be chosen to be either the unconstrained optimal trajectory or any alternative one