interpolation operators in orlicz sobolev spaces we study classical interpolation operators for finite elements like the scott zhang operator in the context of orlicz sobolev spaces furthermore we show estimates for these operators with respect to quasi norms which appear in the study of systems of p laplace type

exact ltp representation of the generalized periodic reference fxlms algorithm the analysis of the filtered x least mean square fxlms algorithm can be based either on a stochastic or deterministic approach one of the drawbacks of the stochastic analysis is that it relies on several assumptions which are not justified if the reference signal is time periodic to overcome these limitations several deterministic methods have been suggested however useful results have been reported only for setups with certain filter length secondary path model or reference signal in this paper an exact linear time periodic ltp representation is proposed assuming only that the reference is synchronously sampled the representation is derived for a general fxlms system which also covers the multichannel topology of several parallel filters and its common narrowband modification the representation is found to have a linear time invariant lti form if the filter length is suitably chosen the usability of the method is demonstrated in a numerically computed example by comparing it to an approximate lti model

a new active noise control algorithm that requires no secondary path identification based on the spr property active noise control anc has been widely applied in industry to reduce environmental noise and equipment vibrations most available control algorithms require the identification of the secondary path which increases the control system complexity contributes to an increased residual noise power and can even cause the control system to fail if the identified secondary path is not sufficiently close to the actual path in this paper based on the geometric analysis and the strict positive real spr property of the filtered x lms algorithm we introduce a new anc algorithm suitable for single tone noises as well as some specific narrowband noises that does not require the identification of the secondary path though its convergence can be very slow in some special cases we are able to extend the developed anc algorithm to the case of active control of broadband noises through our use of a subband implementation of the anc algorithm compared to other available control algorithms that do not require secondary path identification our developed method is simple to implement yields good performance and converges quickly simulation results confirm the effectiveness of our proposed algorithm

a confluence matrix condition for exponential error convergence in overparametrized adaptive systems many practical adaptive feedforward systems are overparametrized and for this reason will not satisfy persistent excitation pe conditions for these systems a weaker pe condition is proposed under which it is shown that the while parameters may not converge the cancellation error the error between the desired and estimated outputs still converges exponentially bounds are given on the exponential rate of convergence useful for understanding the various tradeoffs and for systematic optimization and design purposes the convergence rate is determined by properties of the confluence matrix defined herein that plays a role similar to that played by the autocorrelation matrix for fully pe systems as a case study the structure of the confluence matrix is examined in detail for adaptive systems with a tap delay line tdl regressor and sinusoid excitation

cancellation of harmonic interference by baseline shifting of wavelet packet decomposition coefficients presented in this paper is a distortion free filtering approach for cancellation of sinusoidal harmonic interference using wavelet packet decomposition wpd under a special sampling condition the transform coefficients of the harmonic interference in each subband become a constant exhibiting as a shift of the baseline of the wpd coefficients in that subband the harmonic interference is thus removed by shifting the baselines back to zero unlike the use of a notch or a comb filter the new approach does not cause any distortion to the original signal in principle this advantage makes this approach especially suitable for the removal of harmonic interference that is located within the spectrum of the original signal evaluation of the new approach has been conducted using a simulated piecewise smooth signal and a real irregularly pulsating signal results obtained from the studies have demonstrated the effectiveness of the new approach

optimal regularization parameter of the multichannel filtered x affine projection algorithm we discuss the optimal regularization parameter of the filtered affine projection fx ap algorithm suitable for feedforward active noise control while the original fx ap algorithm always provides a biased estimate of the minimum mean square solution we show that the optimal regularized fx ap algorithm is capable to eliminate the bias of the asymptotic solution and thus that the regularization parameter can optimize both the convergence speed and the residual mse of the algorithm we derive some expressions for the optimal regularization parameter and we discuss some heuristic estimations of the optimal regularization parameter in practical conditions

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

affine orlicz polya szego principle for log concave functions abstract the affine l p polya szego principle significantly strengthens the classical polya szego principle it is an open problem whether there exists an affine orlicz polya szego principle which includes the affine l p polya szego principle as special case in this paper an affine orlicz polya szego principle for log concave functions is established by using functional steiner symmetrizations

transient and steady state analysis of filtered x affine projection algorithms this paper provides an analysis of transient and steady state behavior of different filtered x affine projection algorithms algorithms suitable for single channel and for multichannel active noise controllers are treated within a unified framework very mild assumptions are posed on the active noise control system model which is only required to have a linear dependence of the output from the filter coefficients therefore the analysis applies not only to the linear finite impulse response models but also to nonlinear volterra filters i e polynomial filters and other nonlinear filter structures the convergence analysis presented in this paper relies on energy conservation arguments and does not apply the independence theory nor does it impose any restriction to the signal distributions it is shown in the paper that filtered x affine projection algorithms always provide a biased estimate of the minimum mean square solution nevertheless in many cases the bias is small and therefore these algorithms can be profitably applied to active noise control

unconstrained and constrained stabilisation of bilinear discrete time systems using polyhedral lyapunov functions the constrained and unconstrained stabilisation problem of discrete time bilinear systems is investigated using polyhedral lyapunov functions conditions for a polyhedral set to be both positively invariant and domain of attraction for systems with second order polynomial nonlinearities are first established then systematic methods for the determination of stabilising linear feedback for both constrained and unconstrained bilinear systems are presented attention is drawn to the case where no linear control law rendering the pre specified desired domain of attraction positively invariant exists for this case an approach guaranteeing the existence of a possibly suboptimal solution is established

eigenvalue equalization filtered x algorithm for the multichannel active noise control of stationary and nonstationary signals the fxlms algorithm which is extensively used in active noise control exhibits frequency dependent convergence behavior this leads to degraded performance for time varying and multiple frequency signals a new algorithm called the eigenvalue equalization filtered x least mean squares ee fxlms has been developed to overcome this limitation without increasing the computational burden of the controller the algorithm is easily implemented for either single or multichannel control the magnitude coefficients of the secondary path transfer function estimate are altered while preserving the phase for a reference signal that has the same magnitude at all frequencies the secondary path estimate is given a flat response over frequency for a reference signal that contains tonal components of unequal magnitudes the magnitude coefficients of the secondary path are adjusted to be the inverse magnitude of the reference tones both modifications reduce the variation in the eigenvalues of the filtered x autocorr

steady state mse convergence of lms adaptive filters with deterministic reference inputs with applications to biomedical signals we analyze the steady state mean square error mse convergence of the lms algorithm when deterministic functions are used as reference inputs a particular adaptive linear combiner is presented where the reference inputs are any set of orthogonal basis functions the adaptive orthogonal linear combiner aolc several authors have applied this structure always considering in the analysis a time average behavior over one signal occurrence we make a more precise analysis using the deterministic nature of the reference inputs and their time variant correlation matrix two different situations are considered in the analysis orthogonal complete expansions and incomplete expansions the steady state misadjustment is calculated using two different procedures with equivalent results the classical one analyzing the transient behavior of the mse and as the residual noise at the output of the equivalent time variant transfer function of the system the latter procedure allows a very simple formalism being valid for colored noise as well the derived expressions for steady state misadjustment are contrasted with experimental results in electrocardiographic ecg signals giving exact concordance for any value of the step size

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

adaptive cancellation of periodic synchronously sampled interference a special case of the adaptive noise canceller is considered in which the interference is harmonic and synchronously sampled the implementation of the lms algorithm in this case can be made very efficient and its behavior can be represented exactly by that of a linear time invariant comb filter

sinusoidal interference rejection analysis of an lms adaptive feedforward controller with a noisy periodic reference this paper applies a new vector subspace model to determine the non wiener solutions of the lms algorithm when the reference input is an arbitrary noisy periodic signal the lms weights are modeled as a deterministic time varying mean plus a zero mean fluctuating part for the mean weight each harmonic component of the periodic reference is shown to excite only a two dimensional 2 d subspace of the n dimensional tap weight space the fluctuating part of the weight is due to the reference noise that excites the full n dimensional space the power spectrum of the error is computed using the correlation function of the weight fluctuations the error is shown to be primarily the sum of a white noise and the canceled periodic residual for an independent noise vector model when the effects of the tapped delay line are incorporated in the model the noise becomes colored with a spectrum centered about the canceled sinusoidal frequency this weight model significantly simplifies the understanding of the non wiener behavior and can be applied to active noise cancellation problems when filters appear in the cancellation loop

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

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 direct approach to orlicz sobolev capacity abstract this paper is motivated by federer and ziemer s potential free approach to sobolev capacity we extend their results to orlicz sobolev spaces and analyze the resulting notion of orlicz sobolev capacity in particular we explore the relationship between the orlicz sobolev capacity of a set and its hausdorff dimension and then establish the quasicontinuity of orlicz sobolev functions

sobolev s inequalities and vanishing integrability for riesz potentials of functions in the generalized lebesgue space lp logl q abstract our aim in this paper is to deal with sobolev s inequalities for riesz potentials of functions belonging to l p log l q to do so we study the boundedness of hardy littlewood maximal functions and apply the hedberg s trick as an application we treat vanishing integrability for riesz potentials

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

non wiener solutions for the lms algorithm a time domain approach a time domain analysis of the lms algorithm is presented for a sinusoidal deterministic reference input for the sinusoidal reference input only the n dimensional time varying linear matrix recursion for the weight vector is solved using a 2 d orthogonal subspace decomposition using this weight vector solution it is shown that there exists a linear time invariant relationship between the desired input and the filter output

brief paper affine and predictive control policies for a class of nonlinear systems the input state linear horizon islh for a nonlinear discrete time system is defined as the smallest number of time steps it takes the system input to appear nonlinearly in the state variable in this paper we employ the latter concept and show that the class of constraint admissible n step affine state feedback policies is equivalent to the associated class of constraint admissible disturbance feedback policies provided that n is less than the system s islh the result generalizes a recent result in goulart p j kerrigan e c maciejowski j m 2006 optimization over state feedback policies for robust control with constraints automatica 42 4 523 533 and is significant because it enables one i to determine a constraint admissible state feedback policy by employing well known convex optimization techniques and ii to guarantee robust recursive feasibility of a class of model predictive control mpc policies by imposing a suitable terminal constraint in particular we propose an input to state stabilizing mpc policy for a class of nonlinear systems with bounded disturbance inputs and mixed polytopic constraints on the state and the control input at each time step the proposed mpc policy requires the solution of a single convex quadratic programme parameterized by the current system state

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

stabilizing receding horizon control of nonlinear time varying systems a receding horizon control scheme for nonlinear time varying systems is proposed which is based on a finite horizon optimization problem with a terminal state penalty the penalty is equal to the cost that would be incurred over an infinite horizon by applying a locally stabilizing linear control law to the nonlinear system assuming only stabilizability of the linearized system around the desired equilibrium the new scheme ensures exponential stability of the equilibrium as the length of the optimization horizon goes from zero to infinity the domain of attraction moves from the basin of attraction of the linear controller toward the basin of attraction of the infinite horizon nonlinear controller stability robustness in the face of system perturbations is also established

the effect of transfer function estimation errors on the filtered x lms algorithm the filtered x lms algorithm which is commonly implemented in active noise and vibration control systems requires an estimate of the cancellation path transfer function to maintain algorithm stability this correspondence considers the effect of errors in this estimate on the stability of the algorithm implemented in the time domain concluding that while a maximum phase error of spl plusmn 90 spl deg is a bound for stability there is no simple relationship between error and stability within this region

robustness of the filtered x lms algorithm part i necessary conditions for convergence and the asymptotic pseudospectrum of toeplitz matrices errors in the secondary path model of the filtered x lms fxlms algorithm will lead to its divergence when the eigenvalues of the cross correlation matrix between the estimated filtered reference and the true filtered reference signals are not all located in the right half plane this cross correlation matrix has a block toeplitz structure whose dimension is determined by the number of adaptive filter coefficients using results on the asymptotic pseudospectrum of toeplitz matrices a frequency domain condition on the model is derived to ensure stability the condition is sufficient and necessary for a large number of filter coefficients a transient analysis shows that the sufficient condition given by wang and ren 1999 is only necessary to prevent an initial increase of the error in the adaptive filter coefficients critical behavior

enlarging the domain of attraction of mpc controllers this paper presents a method for enlarging the domain of attraction of nonlinear model predictive control mpc the usual way of guaranteeing stability of nonlinear mpc is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated lyapunov function the domain of attraction of the controller depends on the size of the terminal region and the control horizon by increasing the control horizon the domain of attraction is enlarged but at the expense of a greater computational burden while increasing the terminal region produces an enlargement without an extra cost in this paper the mpc formulation with terminal cost and constraint is modified replacing the terminal constraint by a contractive terminal constraint this constraint is given by a sequence of sets computed off line that is based on the positively invariant set each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one step set this property allows us to use one step approximations with a trade off between accuracy and computational burden for the computation of the sequence this strategy guarantees closed loop stability ensuring the enlargement of the domain of attraction and the local optimality of the controller moreover this idea can be directly translated to robust mpc

negative orlicz sobolev norms and strongly nonlinear systems in fluid mechanics abstract we prove a version of the negative norm theorem in orlicz sobolev spaces a study of boundedness properties of the bogovski operator between orlicz spaces is a crucial step of independent interest in our approach applications to the problem of pressure reconstruction for non newtonian fluids governed by constitutive laws which are not necessarily of power type are presented a key inequality for a numerical analysis of the underlying elliptic system is also derived

a class of orlicz sobolev spaces with applications to variational problems involving nonlinear hill s equations necessary and sufficient conditions are proved for a b 2 young function g with independent variable t to be convex resp concave in t2 in terms of inequalities between the second derivative of g and the first derivative of its legendre transform g with independent variable s it is then proven that a young function g is convex resp concave in t2 if and only if g is concave resp convex in s2 these results along with another set of inequalities for functions g convex resp concave in t2 allow the proof of the uniform convexity and thereby of the reflexivity with respect to luxemburg s norm f g inf k 0 d g f k 1 of the orlicz space lg over an open domain rn with lebesgue measure d when applied to g t t pp and g s s p p with p 1 p 1 1 the preceding results lead to the shortest proof to date of two clarkson s inequalities and of the reflexivity of lp spaces for 1 p finally some of these results are used to solve by direct methods variational problems associated with the existence question of periodic orbits for a class of nonlinear hill s equations these variational problems are formulated on suitable orlicz sobolev spaces wmlg and thereby allow for nonlinear terms which may grow faster than any power of the variable

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

novel adaptive nonlinear predistorters based on the direct learning algorithm the adaptive nonlinear predistorter is an effective technique to compensate for the nonlinear distortion existing in digital communication and control systems however available adaptive nonlinear predistorters using indirect learning are sensitive to measurement noise and do not perform optimally other available types are either slow to converge complicated in structure and computationally expensive or do not consider the memory effects in nonlinear systems such as a high power amplifier hpa in this paper we first propose several novel adaptive nonlinear predistorters based on direct learning algorithms the nonlinear filtered x rls nfxrls algorithm the nonlinear adjoint lms nalms algorithm and the nonlinear adjoint rls narls algorithm using these new learning algorithms we design adaptive nonlinear predistorters for an hpa with memory effects or for an hpa following a linear system because of the direct learning algorithm these novel adaptive predistorters outperform nonlinear predistorters that are based on the indirect learning method in the sense of normalized mean square error nmse bit error rate ber and spectral regrowth moreover our developed adaptive nonlinear predistorters are computationally efficient and or converge rapidly when compared to other adaptive nonlinear predistorters that use direct learning and furthermore can be easily implemented we further simplify our proposed algorithms by exploring the robustness of our proposed algorithm as well as by examining the statistical properties of what we call the instantaneous equivalent linear iel filter simulation results confirm the effectiveness of our proposed algorithms

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

maximum likelihood least squares identification method for active noise control systems with autoregressive moving average noise maximum likelihood methods are significant for parameter estimation and system modeling this paper derives a maximum likelihood principle based least squares identification algorithm for online secondary path modeling in feed forward active noise control systems with autoregressive moving average noise this derivation proves that minimizing the cost function of least squares is equivalent to the maximum of likelihood function proposed method requires tuning of only one parameter in comparison with other recognized methods simulation tests show that proposed algorithm has better estimation accuracy and noise reduction capability than the current state of the art methods in the presence and absence of disturbance at the error microphone

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

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

differentiability properties of functions from higher order orlicz sobolev spaces abstract we analyze pointwise differentiability properties of functions from local orlicz sobolev spaces w loc m a on an open subset of r n n 2 a necessary and sufficient condition on the order of differentiation m and on the young function a is exhibited for any function in w loc m a to admit a differential of order m a e in an optimal approximate differentiability property in integral and norm form is established when such a condition fails

construction of invariant polytopic sets with specified complexity the problem of construction of controlled invariant polytopic sets with specified complexity for linear systems subject to linear state and control constraints is investigated first geometric conditions for the enlargement of a polytopic set by adding a new vertex in order to produce a polytopic set of specified complexity are established next conditions for such an enlargement of controlled invariant sets to preserve the controlled invariance property are presented the established theoretical results are used to develop methods for the construction of admissible controlled invariant sets with specified complexity two numerical examples show how these results can be used for the computation of monotonic sequences of admissible controlled invariant sets of specified complexity

estimates for certain orlicz sobolev capacities of an euclidean ball abstract we calculate certain orlicz sobolev capacities of an euclidian n dimensional ball

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

brief paper on the computation of convex robust control invariant sets for nonlinear systems in this paper we provide a method to compute robust control invariant sets for nonlinear discrete time systems a simple criterion to evaluate if a convex set in state space is a robust control invariant set for a nonlinear uncertain system is presented the criterion is employed to design an algorithm for computing a polytopic robust control invariant set the method is based on the properties of dc functions i e functions which can be expressed as the difference of two convex functions since the elements of a wide class of nonlinear functions have dc representation or at least admit an arbitrarily close approximation the method is quite general the algorithm requires relatively low computational resources

extensions of fisher information and stam s inequality we explain how the classical notions of fisher information of a random variable and fisher information matrix of a random vector can be extended to a much broader setting we also show that stam s inequality for fisher information and shannon entropy as well as the more generalized versions proved earlier by the authors are all special cases of more general sharp inequalities satisfied by random vectors the extremal random vectors which we call generalized gaussians contain gaussians as a limiting case but are noteworthy because they are heavy tailed

multi channel active noise control for periodic sources indirect approach this paper presents a multi channel active noise control algorithm that is designed to reject periodic signals of unknown frequency it is based on a so called indirect approach where the frequency of the disturbance is estimated in real time and the estimate is used in a disturbance rejection scheme designed for a known frequency improvements over an earlier algorithm include an extension to multi channel systems a better frequency estimation algorithm and a thorough experimental evaluation for disturbance rejection a so called inverse g algorithm is proposed and its properties are compared through analysis and experiments to those of a gradient algorithm a new frequency estimator is also considered that is simple and flexible in design and is able to use multiple harmonics or multiple signals in order to estimate the fundamental frequency of the noise source in this manner the algorithm maintains tracking of the fundamental frequency despite significant changes in signal characteristics the ability of the indirect approach to reject periodic noise with fixed or time varying frequency and amplitudes is demonstrated in active noise control experiments the algorithm may also be useful in other control applications where periodic disturbances of unknown frequency must be rejected

a characterization of minimal orlicz sobolev norms in the affine class abstract the orlicz sobolev norm is invariant only under rigid motions but is not invariant under volume preserving affine transformations on r n in this paper we will consider the orlicz sobolev norm in the affine class and characterize its minimum

non wiener mean weight behavior of lms transversal equalizers with sinusoidal interference the least mean square lms algorithm is generally expected to operate near the corresponding wiener filter solution an important exception occurs when the algorithm is used to adapt a transversal equalizer in the presence of additive narrowband interference for this application the steady state lms equalizer behavior does not correspond to that of the fixed wiener equalizer the mean of its weights is different from the wiener weights and its mean square error performance may be significantly better than the wiener performance assuming a large interference to signal ratio isr we present the solution for the mean of the lms weight vector in steady state based on the butterweck expansion of the weight update equation the analytical results are valid for all mean square stable step sizes simulation results are included to support the analytical results and show that the analytical results predict the simulation results accurately over a wide range of isr

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

low complexity polytopic invariant sets for linear systems subject to norm bounded uncertainty we propose a novel algorithm to compute low complexity polytopic robust control invariant rci sets along with the corresponding state feedback gain for linear discrete time systems subject to norm bounded uncertainty additive disturbances and state input constraints using a slack variable approach we propose new results to transform the original nonlinear problem into a convex lmi problem whilst introducing only minor conservatism in the formulation through numerical examples we illustrate that the proposed algorithm can yield improved maximal minimal volume rci set approximations in comparison with the schemes given in the literature

optimal sobolev norms in the affine class abstract optimal sobolev norms under volume preserving affine transformations are considered it turns out that this minimal transform is equivalent to the p 2 fisher information matrix defined by lutwak lv yang and zhang furthermore some analytic inequalities regarding to the l p affine and l p sine energies for the optimal function are investigated

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

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

a quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability we present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed loop stability the scheme can be applied to both stable and unstable systems with input constraints the objective functional to be minimized consists of an integral square error ise part over a finite time horizon plus a quadratic terminal cost the terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate lyapunov equation furthermore the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region if the jacobian linearization of the nonlinear system to be controlled is stabilizable we prove that feasibility of the open loop optimal control problem at time t 0 implies asymptotic stability of the closed loop system the size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense

novel fxlms convergence condition with deterministic reference a novel analysis of fxlms convergence when the reference signal is deterministic is presented in this paper the simple case of a sinusoidal reference is considered first to be later extended to any combination of multiple sinusoids in both cases we derive an upper bound for the algorithm step size which ensures convergence in the derivation of this result there is no need of any of the usual approximations such as independence between reference and weights or slow convergence which are not suitable for deterministic references instead we consider the common cases where the adaptive system shows linear time invariant behavior the upper bound obtained for the step size is in good agreement with empirical measurements

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

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

a novel approach to feedforward higher harmonic control a novel adaptive filter structure is proposed for the control of systems characterized by higher harmonic response the control approach has been designated the higher harmonic least mean squares hlms algorithm to differentiate it from the standard multifrequency filtered x version of the least mean squares approach in the hlms algorithm a single frequency reference at that of the fundamental is all that is required to implement the controller the remaining harmonics are generated internally based upon simple trigonometric relationships the filtered x lms algorithm is implemented in parallel for each frequency to be controlled minimizing or totally eliminating the contribution of the time varying terms during the convergence process and increasing the rate of convergence for the higher harmonic control application results from the simulation demonstrate that the hlms approach is far superior to the standard multifrequency filtered x lms algorithm in adaptive feedforward higher harmonic control

an active noise control algorithm for controlling multiple sinusoids the filtered x lms algorithm and its modified versions have been successfully applied in suppressing acoustic noise such as single and multiple tones and broadband random noise this paper presents an adaptive algorithm based on the filtered x lms algorithm which may be applied in attenuating tonal acoustic noise in the proposed method the weights of the adaptive filter and estimation of the phase shift due to the acoustic path from a loudspeaker to a microphone are computed simultaneously for optimal control the algorithm possesses advantages over other filtered x lms approaches in three aspects 1 each frequency component is processed separately using an adaptive filter with two coefficients 2 the convergence parameter for each sinusoid can be selected independently and 3 the computational load can be reduced by eliminating the convolution process required to obtain the filtered reference signal simulation results for a single input single output siso environment demonstrate that the proposed method is robust to the changes of the acoustic path between the actuator and the microphone and outperforms the filtered x lms algorithm in simplicity and convergence speed

orlicz sobolev boundary trace embeddings we prove a sharp trace embedding theorem for orlicz sobolev spaces into orlicz spaces on the boundary an optimal trace embedding into more general rearrangement invariant spaces on the boundary is also established

weighted sobolev spaces and embedding theorems in the present paper we study embedding operators for weighted sobolev spaces whose weights satisfy the well known muckenhoupt a p condition sufficient conditions for boundedness and compactness of the embedding operators are obtained for smooth domains and domains with boundary singularities the proposed method is based on the concept of generalized quasiconformal homeomorphisms homeomorphisms with bounded mean distortion the choice of the homeomorphism type depends on the choice of the corresponding weighted sobolev space such classes of homeomorphisms induce bounded composition operators for weighted sobolev spaces with the help of these homeomorphism classes the embedding problem for non smooth domains is reduced to the corresponding classical embedding problem for smooth domains examples of domains with anisotropic holder singularities demonstrate the sharpness of our machinery comparatively with known results

comparison and extensions of control methods for narrow band disturbance rejection techniques for designing and implementing algorithms for the control of periodic narrowband disturbances are discussed and the strong similarities between the different methodologies are shown the analysis of linear time invariant feedback systems results in a suggestion of how to extend two of the lq based multiple input multiple output methodologies to achieve improved performance and stability robustness properties in the analysis of the adaptive feedforward methods it is concluded that the popular filtered x lms algorithm is useful for implementation but is best analyzed from a classical linear time invariant feedback perspective this perspective results in a suggestion of how to extend the multiple error lms algorithm to achieve improved performance and stability robustness stability bounds of the adaptive feedforward approaches are derived in terms of allowable model error

enlargement of polytopic terminal region in nmpc by interpolation and partial invariance this paper uses the concept of partial invariance to derive a sequence of linear programs in order to maximize offline the volume of an invariant polytopic set with an arbitrary predefined number of vertices subject to a bound on closed loop performance interpolation techniques are used to determine a nonlinear control law which is optimal with respect to a closed loop cost bound through the on line solution of a linear program the invariant polytope is also used to define a receding horizon control law through an appropriate terminal constraint and cost

vanishing exponential integrability for functions whose gradients belong to ln log e l α if the gradient of u x is nth power locally integrable on euclidean n space then the integral average over a ball b of the exponential of a constant multiple of u x ub n n 1 ub average of u over b tends to 1 as the radius of b shrinks to zero for quasi almost all center points this refines a result of n trudinger 1967 we prove here a similar result for the class of gradients in ln log e l 0 n 1 the results depend on a capacitary strong type inequality for these spaces

an improved lattice based adaptive iir notch filter a novel lattice based adaptive infinite impulse response iir notch filter is developed which features independent tuning of the notch frequency and attenuation bandwidth the internal structure is based on planar rotators ensuring reliable numerical behaviour and high processing rates in cordic environments a simple update law allows a simpler implementation than previously proposed designs rather than minimizing an output error cost function the algorithm is designed to achieve a stable associated differential equation resulting in a globally convergent unbiased frequency estimator in the single sinusoid case independent of the notch filter bandwidth using a second order structure in the multiple sinusoid case unbiased estimation of one of the input frequencies is achieved by thinning the notch bandwidth the tracking behavior is superior to conventional output error designs and the estimation of extremal frequencies is less prone to overflow instability than previously reported structures

adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency abstract two algorithms are presented for the rejection of sinusoidal disturbances with unknown frequency the first is an indirect algorithm where the frequency of the disturbance is estimated and the estimate is used in another adaptive algorithm that adjusts the magnitude and phase of the input needed to cancel the effect of the disturbance a direct algorithm that uses the concept of a phase locked loop is also presented in which frequency estimation and disturbance cancellation are performed simultaneously approximate analyses are presented for both schemes and the results are found useful for the selection of the design parameters simulations are given which demonstrate the validity of the analytical results and the ability of the algorithms to reject sinusoidal disturbances with unknown frequency the indirect algorithm is found to have a larger capture region for the parameter estimates whereas the direct algorithm has superior convergence properties locally about the optimum parameter estimates

mean weight behavior of the filtered x lms algorithm a new stochastic analysis is presented for the filtered x lms fxlms algorithm the analysis does not use independence theory an analytical model is derived for the mean behavior of the adaptive weights the model is valid for white or colored reference inputs and accurately predicts the mean weight behavior even for large step sizes the constrained wiener solution is determined as a function of the input statistics and the impulse responses of the adaptation loop filters effects of secondary path estimation error are studied monte carlo simulations demonstrate the accuracy of the theoretical model

invariant sets computation for convex difference inclusions systems in this paper we introduce the convex difference inclusion cdi systems as a modeling framework useful to analyze set theory and invariance related issues for nonlinear and uncertain systems the dynamics of a cdi system is given by a set valued map whose values are convex compact subsets of the space and are determined by convex bounding functions necessary and sufficient boundary type conditions for invariance and contractiveness characteristic of the linear systems are given for the cdi systems lyapunov functions are proved to be induced by contractive sets for cdi systems as in the linear context a computational procedure for obtaining polytopic invariant and contractive sets for nonlinear systems based on the properties of the cdi systems is presented

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