an anisotropic h type mesh refinement strategy abstract an anisotropic h type mesh refinement strategy for finite element approximations is presented the strategy consists of subsecting quadrilateral elements in one of two possible directions the decision which elements should be subsected and in which direction is based on minimization of interpolation errors the method is especially suitable for approximate solutions which in some regions display almost one dimensional behavior for instance solutions with boundary layers

edge elements on anisotropic meshes and approximation of the maxwell equations this paper deals with some edge element methods on a class of anisotropic meshes based on tetrahedra and prismatic pentahedral elements anisotropic local interpolation error estimates are derived for all these types of elements and for functions from classical and weighted sobolev spaces as a particular application the numerical approximation of the maxwell equations in domains with edges is investigated using nedelec s edge elements where anisotropic finite element meshes are appropriate some anisotropic regularity results of the solutions of maxwell equations on such domains are proved some numerical tests are described and inverse estimates are established both showing that our theoretical orders of convergence are optimal

fake algebraic riccati techniques and stability conditions sufficient and necessary for monotonic behavior of the solutions of the riccati differential equation and riccati difference equation are derived for the optimal filtering respectively control equation these results are derived without the usual requirement of detectability respectively stabilizability the monotonic behavior allows proof of stabilizing properties of the solutions subject only to requirements on the initial conditions

constrained linear quadratic regulation the paper is a contribution to the theory of the infinite horizon linear quadratic regulator lqr problem subject to inequality constraints on the inputs and states extending an approach first proposed by sznaier and damborg 1987 a solution algorithm is presented which requires solving a finite number of finite dimensional positive definite quadratic programs the constrained lqr outlined does not feature the undesirable mismatch between open loop and closed loop nominal system trajectories which is present in the other popular forms of model predictive control mpc that can be implemented with a finite quadratic programming algorithm the constrained lqr is shown to be both optimal and stabilizing the solution algorithm is guaranteed to terminate in finite time with a computational cost that has a reasonable upper bound compared to the minimal cost for computing the optimal solution inherent to the approach is the removal of a tuning parameter the control horizon which is present in other mpc approaches and for which no reliable tuning guidelines are available two examples are presented that compare constrained lqr and two other popular forms of mpc the examples demonstrate that constrained lqr achieves significantly better performance than the other forms of mpc on some plants and the computational cost is not prohibitive for online implementation

nonlinear control of constrained linear systems via predictive reference management a method based on conceptual tools of predictive control is described for solving set point tracking problems wherein pointwise in time input and or state inequality constraints are present it consists of adding to a primal compensated system a nonlinear device called command governor cg whose action is based on the current state set point and prescribed constraints the cg selects at any time a virtual sequence among a family of linearly parameterized command sequences by solving a convex constrained quadratic optimization problem and feeds the primal system according to a receding horizon control philosophy the overall system is proved to fulfill the constraints be asymptotically stable and exhibit an offset free tracking behavior provided that an admissibility condition on the initial state is satisfied though the cg can be tailored for the application at hand by appropriately choosing the available design knobs the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem

analysis of a finite element method for maxwell s equations the use of finite elements to discretize the time dependent maxwell equations on a bounded domain in three dimensional space is analyzed energy norm error estimates are provided when general finite element methods are used to discretize the equations in space in addition it is shown that if some curl conforming elements due to nedelec are used error estimates may also be proved in the l 2 norm

a receding horizon generalization of pointwise min norm controllers control lyapunov functions clfs are used in conjunction with receding horizon control to develop a new class of receding horizon control schemes in the process strong connections between the seemingly disparate approaches are revealed leading to a unified picture that ties together the notions of pointwise min norm receding horizon and optimal control this framework is used to develop a clf based receding horizon scheme of which a special case provides an appropriate extension of sontag s formula the scheme is first presented as an idealized continuous time receding horizon control law the issue of implementation under discrete time sampling is then discussed as a modification these schemes are shown to possess a number of desirable theoretical and implementation properties an example is provided demonstrating their application to a nonlinear control problem finally stronger connections to both optimal and pointwise min norm control are proved

fosll method for the eddy current problem with three dimensional edge singularities in the case that the domain has reentrant edges the standard finite element method loses its global accuracy because of singularities on the boundary to overcome this difficulty foslla is applied in this paper foslla is a methodology for solving pdes using the dual operator here a modified foslla method is developed that employs a partially weighted functional and allows the use of a standard finite element scheme without losing global accuracy

a numerically robust state space approach to stable predictive control strategies recent work with predictive control strategies has shown that the stable gpc sgpc approach has significant computational and numerical advantages however sgpc is cast in the transfer function framework which limits its application here we develop a means of extending the results to state space models and show that improved numerical conditioning can be obtained for many stable predictive control strategies

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

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

unconstrained receding horizon control of nonlinear systems it is well known that unconstrained infinite horizon optimal control may be used to construct a stabilizing controller for a nonlinear system we show that similar stabilization results may be achieved using unconstrained finite horizon optimal control the key idea is to approximate the tail of the infinite horizon cost to go using as terminal cost an appropriate control lyapunov function roughly speaking the terminal control lyapunov function clf should provide an incremental upper bound on the cost in this fashion important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers the absence of constraints allows a significant speedup in computation furthermore it is shown that in order to guarantee stability it suffices to satisfy an improvement property thereby relaxing the requirement that truly optimal trajectories be found we provide a complete analysis of the stability and region of attraction operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class it is shown that the guaranteed region of operation contains that of the clf controller and may be made as large as desired by increasing the optimization horizon restricted of course to the infinite horizon domain moreover it is easily seen that both clf and infinite horizon optimal control approaches are limiting cases of our receding horizon strategy the key results are illustrated using a familiar example the inverted pendulum where significant improvements in guaranteed region of operation and cost are noted

lyapunov based model predictive control of stochastic nonlinear systems in this work we design a lyapunov based model predictive controller lmpc for nonlinear systems subject to stochastic uncertainty the lmpc design provides an explicitly characterized region from where stability can be probabilistically obtained the key idea is to use stochastic lyapunov based feedback controllers with well characterized stabilization in probability to design constraints in the lmpc that allow the inheritance of the stability properties by the lmpc the application of the proposed lmpc method is illustrated using a nonlinear chemical process system example

fulfilling hard constraints in uncertain linear systems by reference managing a method based on conceptual tools of predictive control is described for tackling tracking problems of uncertain linear systems wherein pointwise in time input and or state inequality constraints are present the method consists of adding to a primal compensated system a nonlinear device called predictive reference filter which manipulates the desired reference in order to fulfill the prescribed constraints provided that an admissibility condition on the initial state is satisfied the control scheme is proved to fulfill the constraints as well as stability and set point tracking requirements for all systems whose impulse step responses lie within given uncertainty ranges

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

stabilization of nonlinear systems with state and control constraints using lyapunov based predictive control this work considers the problem of stabilization of nonlinear systems subject to state and control constraints for cases where the state constraints need to be enforced at all times hard constraints and where they can be relaxed for some time soft constraints we propose a lyapunov based predictive control design that guarantees stabilization and state and input constraint satisfaction for all times from an explicitly characterized set of initial conditions an auxiliary lyapunov based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation for the case when the state constraints are soft we propose a switched predictive control strategy that reduces the time during which state constraints are violated driving the states into the state and input constraints feasibility region of the lyapunov based predictive controller we demonstrate the application of the lyapunov based predictive controller designs through a chemical process example

a discontinuous galerkin method on refined meshes for the two dimensional time harmonic maxwell equations in composite materials in this paper a discontinuous galerkin method for the two dimensional time harmonic maxwell equations in composite materials is presented the divergence constraint is taken into account by a regularized variational formulation and the tangential and normal jumps of the discrete solution at the element interfaces are penalized due to an appropriate mesh refinement near exterior and interior corners the singular behaviour of the electromagnetic field is taken into account optimal error estimates in a discrete energy norm and in the l 2 norm are proved in the case where the exact solution is singular

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

two guaranteed equilibrated error estimators for harmonic formulations in eddy current problems abstract in this paper a guaranteed equilibrated error estimator is developed for the 3d harmonic magnetodynamic problem of maxwell s system this system is recasted in the classical a potential formulation and solved by the finite element method the error estimator is built starting from the a numerical solution by a local flux reconstruction technique its equivalence with the error in the energy norm is established a comparison of this estimator with an equilibrated error estimator already developed through a complementary problem points out the advantages and drawbacks of these two estimators in particular an analytical benchmark test illustrates the obtained theoretical results and a physical benchmark test shows the efficiency of these two estimators

output feedback control of switched nonlinear systems using multiple lyapunov functions abstract this work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints the key feature of the proposed methodology is the integrated synthesis via multiple lyapunov functions of lower level bounded nonlinear feedback controllers together with upper level switching laws that orchestrate the transitions between the constituent modes and their respective controllers both the state and output feedback control problems are addressed under the assumption of availability of full state measurements a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed loop modes and provide an explicit characterization of the corresponding stability region for each mode a set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed loop system when complete state measurements are unavailable a family of output feedback controllers are synthesized using a combination of bounded state feedback controllers high gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain a different set of switching rules based on the evolution of the state estimates generated by the observers is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes the differences between the state and output feedback switching strategies and their implications for the switching logic are discussed and a chemical process example is used to demonstrate the proposed approach

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

multiscale asymptotic method for maxwell s equations in composite materials in this paper we discuss the multiscale analysis of maxwell s equations in composite materials with a periodic microstructure the new contributions in this paper are the determination of higher order correctors and the explicit convergence rate for the approximate solutions see theorem 2 3 consequently we present the multiscale finite element method and derive the convergence result see theorem 4 1 the numerical results demonstrate that higher order correctors are essential for solving maxwell s equations in composite materials

weighted norm first order system least squares fosls for div curl systems with three dimensional edge singularities a weighted norm first order system least squares fosls method for div curl problems with edge singularities is presented traditional finite element methods including least squares methods often suffer from a global loss of accuracy due to the influence of a nonsmooth solution near polyhedral edges by minimizing a modified least squares functional optimal accuracy in weighted and nonweighted norms is recovered error estimates with and without mesh refinements are presented and numerical results are given to confirm the theory

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

augmented formulations for solving maxwell equations we consider augmented variational formulations for solving the static or time harmonic maxwell equations for that a term is added to the usual h curl conforming formulations it consists of a weighted l2 scalar product between the divergence of the em and the divergence of test fields in this respect the methods we present are h curl div conforming we also build mixed augmented variational formulations with either one or two lagrange multipliers to dualize the equation on the divergence and when applicable the relation on the tangential or normal trace of the field it is proven that one can derive formulations which are equivalent to the original static or time harmonic maxwell equations in the latter case spurious modes are automatically excluded numerical analysis and experiments will be presented in the forthcoming paper augmented formulations for solving maxwell equations numerical analysis and experiments in preparation

a functional equations approach to nonlinear discrete time feedback stabilization through pole placement abstract the present work proposes a new approach to the nonlinear discrete time feedback stabilization problem with pole placement the problem s formulation is realized through a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived using tools from functional equations theory one can prove that the solution to the above system of nonlinear functional equations is locally analytic and an easily programmable series solution method can be developed under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear discrete time state feedback control law that are both computed through the solution of the system of nonlinear functional equations the feedback stabilization with pole placement design objective can be attained under rather general conditions the key idea of the proposed single step design approach is to bypass the intermediate step of transforming the original system into a linear controllable one with an external reference input associated with the classical exact feedback linearization approach however since the proposed method does not involve an external reference input it cannot meet other control objectives such as trajectory tracking and model matching

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

discrete time stability with perturbations application to model predictive control exponential stability and asymptotic perturbed stability results are derived for nonlinear discrete time systems some related results are available in the literature but proofs for the discrete time case are difficult to find our motivation for obtaining these results was to determine conditions under which discrete time nonlinear model predictive control is stabilizing in the face of perturbations this problem has particular relevance when output rather than state feedback is used a nonlinear state estimator is then required to reconstruct the state and it is necessary to identify the class of reconstruction errors for which the cascaded estimator controller assembly is stabilizing

a nodal based finite element approximation of the maxwell problem suitable for singular solutions a new mixed finite element approximation of maxwell s problem is proposed its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term which yields a very weak control on the divergence of the unknown the method is shown to be stable and convergent in the natural h rm mathbf curl 0 omega norm for this unknown in particular convergence also applies to singular solutions for which classical nodal based interpolations are known to suffer from spurious convergence upon mesh refinement

sufficient conditions for stabilization of sampled data nonlinear systems via discrete time approximations given a parameterized by sampling period t family of approximate discrete time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all t sufficiently small we present conditions which guarantee that the same family of controllers semi globally practically stabilizes the exact discrete time model of the plant for sufficiently small sampling periods when the family of controllers is locally bounded uniformly in the sampling period the inter sample behavior can also be uniformly bounded so that the time varying sampled data model of the plant is uniformly semi globally practically stabilized the result justifies controller design for sampled data nonlinear systems based on the approximate discrete time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied our analysis is applicable to a wide range of time discretization schemes and general plant models

analysis of a continuous finite element method for h mathrm curl mathrm div elliptic interface problem in this paper we develop a continuous finite element method for the curlcurl grad div vector second order elliptic problem in a three dimensional polyhedral domain occupied by discontinuous nonhomogeneous anisotropic materials in spite of the fact that the curlcurl grad div interface problem is closely related to the elliptic interface problem of vector laplace operator type the continuous finite element discretization of the standard variational problem of the former generally fails to give a correct solution even in the case of homogeneous media whenever the physical domain has reentrant corners and edges to discretize the curlcurl grad div interface problem by the continuous finite element method we apply an element local l 2 projector to the curl operator and a pseudo local l 2 projector to the div operator where the continuous lagrange linear element enriched by suitable element and face bubbles may be employed it is shown that the finite element problem retains the same coercivity property as the continuous problem an error estimate mathcal o h r in an energy norm is obtained between the analytical solution and the continuous finite element solution where the analytical solution is in prod l 1 l h r omega l 3 for some r in 1 2 1 due to the domain boundary reentrant corners and edges e g nonconvex polyhedron and due to the interfaces between the different material domains in omega bigcup l 1 l omega l

a universal formula for stabilization with bounded controls abstract we provide a formula for stabilizing feedback law using a bounded control under the assumption that an appropriate control lyapunov function is known such a feedback smooth away from the origin and continuous everywhere is known to exist via artstein s theorem as in the unbounded control case treated in a previous note we provide an explicit and universal formula given by an algebraic function of lie derivatives in particular we extended to the bounded case the result that the feedback can be chosen analytic if the lyapunov function and the vector fields defining the system are analytic

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

the maximum angle condition for mixed and nonconforming elements application to the stokes equations for the lagrange interpolation it is known that optimal order error estimates hold for elements satisfying the maximum angle condition the objective of this paper is to obtain similar results for the raviart thomas interpolation arising in the analysis of mixed methods we prove that optimal order error estimates hold under the maximum angle condition for this interpolation both in two and three dimensions and moreover that this condition is indeed necessary to have these estimates error estimates for the mixed approximation of second order elliptic problems and for the nonconforming piecewise linear approximation of the stokes equations are derived from our results

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

computation approximation and stability of explicit feedback min max nonlinear model predictive control this paper presents an approximate multi parametric nonlinear programming mp nlp approach to explicit solution of feedback min max nmpc problems for constrained nonlinear systems in the presence of bounded disturbances and or parameter uncertainties it is based on an orthogonal search tree structure of the state space partition and consists in constructing a piecewise nonlinear pwnl approximation to the optimal sequence of feedback control policies conditions guaranteeing the robust stability of the closed loop system in terms of a finite l 2 gain are derived

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

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

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

on 4 generated bundles and directly linked subcanonical curves abstract given a subcanonical curve in p 3 we study conditions under which is directly linked to another subcanonical curve we show that this happens when the rank 2 bundle e associated to admits a surjection 4op3 ai e ai z we give an explicit construction of such a starting with surjection u and we prove that the numbers ai appearing in u are uniquely determined by e this implies that we have at most 3 possibilities for the numerical characters of a subcanonical curve directly linked to

brief paper a predictive controller with artificial lyapunov function for linear systems with input state constraints this paper copes with the problem of satisfying input and or state hard constraints in set point tracking problems stability is guaranteed by synthesizing a lyapunov quadratic function for the system and by imposing that the terminal state lies within a level set of the function procedures to maximize the volume of such an ellipsoidal set are provided and interiorpoint methods to solve on line optimization are considered

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

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

a mixed method for approximating maxwell s equations a semidiscrete mixed finite element approximation to the time dependent maxwell s equations on a bounded smooth domain is analyzed a variational problem for the electric and magnetic fields in which the boundary conditions are enforced naturally is derived then a general convergence result for mixed methods is proven and it is shown how this result may be used to prove various error estimates when nedelec s curl conforming finite elements are used jz3 with connected boundary f and unit outward normal n let e x and 1 x denote respectively the dielectric constant and magnetic permeability of the medium occupying q let a x denote the conductivity of the medium then if e x t and h x t denote respectively the electric and magnetic fields maxwell s equations 10 state that

stability of model predictive control with mixed constraints we derive stability conditions for model predictive control mpc with hard constraints on the inputs and soft constraints on the outputs for an infinitely long output horizon we show that with state feedback mpc is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk with output feedback we show that the results hold if all the eigenvalues are strictly inside the unit circle the online optimization problem defining mpc can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon

a singular field method for the solution of maxwell s equations in polyhedral domains it is well known that in the case of a regular domain the solution of the time harmonic maxwell s equations allows a discretization by means of nodal finite elements this is achieved by solving a regularized problem similar to the vector helmholtz equation the present paper deals with the same problem in the case of a nonconvex polyhedron it is shown that a nodal finite element method does not approximate in general the solution to maxwell s equations but actually the solution to a neighboring variational problem involving a different function space indeed the solution to maxwell s equations presents singularities near the edges and corners of the domain that cannot be approximated by lagrange finite elements a new method is proposed involving the decomposition of the solution field into a regular part that can be treated numerically by nodal finite elements and a singular part that has to be taken into account explicitly this singular field method is presented in various situations such as electri

a delta regularization finite element method for a double curl problem with divergence free constraint to deal with the divergence free constraint in a double curl problem rm curl mu 1 rm curl u f and rm div varepsilon u 0 in omega where mu and varepsilon represent the physical properties of the materials occupying omega we develop a delta regularization method rm curl mu 1 rm curl u delta delta varepsilon u delta f to completely ignore the divergence free constraint rm div varepsilon u 0 we show that u delta converges to u in h rm curl omega norm as delta rightarrow 0 the edge finite element method is then analyzed for solving u delta with the finite element solution u delta h a quasioptimal error bound in the h rm curl omega norm is obtained between u and u delta h including a uniform with respect to delta stability of u delta h in the h rm curl omega norm all the theoretical analysis is done in a general setting where mu and varepsilon may be discontinuous an

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

a posteriori error indicators for maxwell s equations abstract in this paper we shall analyze a class of a posteriori error indicators for an electromagnetic scattering problem for maxwell s equations in the presence of a bounded inhomogeneous and anisotropic scatterer problems of this type arise when computing the interaction of electromagnetic radiation with biological tissue we briefly recall existence and uniqueness theory associated with this problem then we show how a posteriori error indicators can be derived using an adjoint equation approach the error indicators use both the jump in normal and tangential components of the field across faces in the mesh

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

incompressible finite element methods for navier stokes equations with nonstandard boundary conditions in r 3 application des methodes a elements finis incompressibles aux equations de navier stokes avec des conditions aux limites non standards dans r 3 utilisation du potentiel vecteur de la vorticite et de la pression estimations d erreurs

on the stabilizing property of siorhc it is shown that the stabilizing property of siorhc stabilizing i o receding horizon control holds for general stabilizable discrete time linear plants irrespective of the condition that the plant has no poles at the origin

biliaison of sheaves we define an equivalence relation among coherent sheaves on a projective variety called biliaison we prove the existence of sheaves that are minimal in a biliaison class in a suitable sense and show that all sheaves in the same class can be obtained from a minimal one using certain deformations and other basic moves our results generalize the main theorems of liaison theory of subvarieties to sheaves and provide a framework to study sheaves and subvarieties simultaneously

explicit reference governor for constrained nonlinear systems this technical note introduces a novel control law that dynamically modifies the reference of a pre compensated nonlinear system to ensure the satisfaction of constraints this is done by translating the state space constraints into an upper bound on the value of the lyapunov function and by manipulating the velocity of the applied reference to enforce this bound the main advantage of this approach is that it systematically provides a closed form control law able to enforce constraints the theory is introduced for general nonlinear systems subject to constraints and is then specialized to the large and highly relevant class of nonlinear systems admitting a lyapunov function lower bounded by a quadratic form and subject to linear constraints numerical simulations show the effectiveness of the proposed method

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

isogeometric methods for computational electromagnetics b spline and t spline discretizations in this paper we introduce methods for electromagnetic wave propagation based on splines and on t splines we define spline spaces which form a de rham complex and following the isogeometric paradigm we map them on domains which are piecewise spline or nurbs geometries we analyze their geometric and topological structure as related to the connectivity of the underlying mesh and we present degrees of freedom together with their physical interpretation the theory is then extended to the case of meshes with t junctions leveraging on the recent theory of t splines the use of t splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose

adaptive finite element techniques for the maxwell equations using implicit a posteriori error estimates we consider an implicit a posteriori error estimation technique for the adaptive solution of the maxwell equations with nedelec edge finite element methods on three dimensional domains on each element of the tessellation an equation for the error is formulated and solved with a properly chosen local finite element basis the discrete bilinear form of the local problems is shown to satisfy an inf sup condition which ensures the well posedness of the error equations an adaptive solution algorithm is developed based on the obtained error estimates the performance of the method is tested on various problems including non convex domains with non smooth boundaries the numerical results show that the estimated error computed by the implicit a posteriori error estimation technique correlates well with the actual error on the meshes generated adaptively with the help of the error estimator the achieved accuracy is higher than on globally refined meshes with comparable number degrees of freedom moreover the rate of the error convergence on the locally adapted meshes is faster than that on the globally refined meshes

stability margins of nonlinear receding horizon control via inverse optimality using the nonlinear analog of the fake riccati equation developed for linear systems we derive an inverse optimality result for several receding horizon control schemes this inverse optimality result unifies stability proofs and shows that receding horizon control possesses the stability margins of optimal control laws

on the robustness of receding horizon control with terminal constraints robustness properties of nonlinear receding horizon controllers with zero terminal state constraints are investigated with respect to gain and additive perturbations some robustness margins are derived by extending to the receding horizon case the analysis originally proposed by geromel and da cruz for infinite horizon controllers in the linear case it is shown that the zero terminal state receding horizon controller exhibits worse robustness margins compared to standard infinite horizon lq control

heuristically enhanced feedback control of constrained discrete time linear systems recent advances in computer technology have spurred new interest in the use of feedback controllers based upon on line minimization for the control of constrained linear systems still the use of computers in the feedback loop has been hampered by the fact that the amount of time available for computation in most sampled data systems is not enough to achieve a complete solution using conventional algorithms several ad hoc techniques have been proposed but their applicability is restricted by the lack of supporting theory in this paper we present a theoretical framework to analyze the stability of the closed loop system resulting from the use of on line optimization in the feedback loop using these results we show that a suboptimal algorithm based upon the use of heuristic search techniques yields asymptotically stable systems provided that enough computation power is available to solve at each sampling interval an optimization problem considerably simpler than the original the controller presented in this paper is valuable for situations where the customary approaches of using pontryagin s minimum principle or storing a family of extremal curves are not applicable due to limitations in the computational resources available

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

feedback linearization of sampled data systems it is shown that feedback linearizability of a continuous time system can be destroyed through the introduction of the usual sample and hold devices a method whereby a feedback linearizable discrete time model can be recovered is given

suboptimal model predictive control feasibility implies stability practical difficulties involved in implementing stabilizing model predictive control laws for nonlinear systems are well known stabilizing formulations of the method normally rely on the assumption that global and exact solutions of nonconvex nonlinear optimization problems are possible in limited computational time in the paper we first establish conditions under which suboptimal model predictive control mpc controllers are stabilizing the conditions are mild holding out the hope that many existing controllers remain stabilizing even if optimality is lost second we present and analyze two suboptimal mpc schemes that are guaranteed to be stabilizing provided an initial feasible solution is available and for which the computational requirements are more reasonable

uniting bounded control and mpc for stabilization of constrained linear systems in this work a hybrid control scheme uniting bounded control with model predictive control mpc is proposed for the stabilization of linear time invariant systems with input constraints the scheme is predicated upon the idea of switching between a model predictive controller that minimizes a given performance objective subject to constraints and a bounded controller for which the region of constrained closed loop stability is explicitly characterized switching laws implemented by a logic based supervisor that constantly monitors the plant are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under mpc reconciles the stability and optimality properties of both controllers and guarantees asymptotic closed loop stability for all initial conditions within the stability region of the bounded controller the hybrid control scheme is shown to provide irrespective of the chosen mpc formulation a safety net for the practical implementation of mpc for open loop unstable plants by providing a priori knowledge through off line computations of a large set of initial conditions for which closed loop stability is guaranteed the implementation of the proposed approach is illustrated through numerical simulations for an exponentially unstable linear system

robust model predictive control of stable linear systems a new robust model predictive control mpc algorithm is presented for stable constrained linear plants that is a direct generalization of the nominally stabilizing regulator presented by rawlings and muske model uncertainty is parametrized by a list of possible plants robust stability is achieved through the addition of constraints that prevent the sequence of optimal controller costs from increasing for the true plant asymptotic stability is demonstrated through a lyapunov argument simulation experiments demonstrate the performance of the algorithm for two example processes

receding horizon revisited an easy way to robustly stabilize an ltv system stabilization schemes are often based on infinite horizon optimization of a non singular cost functional for such schemes to make sense in a time varying context a fairly good knowledge of the system parameters at all times is a prerequisite that is a major disadvantage in adaptive implementations when applicable the receding horizon approach overcomes this difficulty as though it relies on general qualitative long term properties such as controllability it requires quantitative knowledge only of temporally local parameter values work done on receding horizon stabilization during the 1970 s focused on lq h2 optimization criteria looking for a stabilization method which carries also the robustness properties of infinite horizon h design we consider here local minimization of the l2 induced i o norm h optimization as the design objective both state and observation based feedback scheme are derived and relations to finite and infinite horizon optimization are discussed

on finite gain lp stability of nonlinear sampled data systems abstract it is shown that uniform global exponential stability of the input free discrete time model of a globally lipschitz sampled data time varying nonlinear system with inputs implies finite gain l p stability of the sampled data system for all p 1 this result generalizes results on l p stability of sampled data linear systems and it is an important tool for analysis of robustness of sampled data nonlinear systems with inputs

predictive control of switched nonlinear systems with scheduled mode transitions in this work a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times the main idea is to design a lyapunov based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed loop system this is achieved as follows for each constituent mode a lyapunov based model predictive controller mpc is designed and an analytic bounded controller using the same lyapunov function is used to explicitly characterize a set of initial conditions for which the mpc irrespective of the controller parameters is guaranteed to be feasible and hence stabilizing then constraints are incorporated in the mpc design which upon satisfaction ensure that 1 the state of the closed loop system at the time of the transition resides in the stability region of the mode that the system is switched into and 2 the lyapunov function for each mode is nonincreasing wherever the mode is reactivated thereby guaranteeing stability the proposed control method is demonstrated through application to a chemical process example