similarities of the integral pade approximants ii in this paper we show further similarities of the integral pade approximant the similarity of the integral pade approximant with the functional pade approximant and the improved functional epsilon algorithms is demonstrated the purpose of demonstrating the similarity between the integral pade approximant and the functional pade approximant is to verify our conjecture which is the integral pade approximant and the hybrid functional pade approximant produce identical rational functions finally we demonstrate the improvement of the classical functional epsilon algorithms which also has a relationship with the integral pade approximant

stabilizing low complexity feedback control of constrained piecewise affine systems piecewise affine pwa systems are powerful models for describing both non linear and hybrid systems one of the key problems in controlling these systems is the inherent computational complexity of controller synthesis and analysis especially if constraints on states and inputs are present in addition few results are available which address the issue of computing stabilizing controllers for pwa systems without placing constraints on the location of the origin this paper first introduces a method to obtain stability guarantees for receding horizon control of discrete time pwa systems based on this result two algorithms which provide low complexity state feedback controllers are introduced specifically we demonstrate how multi parametric programming can be used to obtain minimum time controllers i e controllers which drive the state into a pre specified target set in minimum time in a second segment we show how controllers of even lower complexity can be obtained by separately dealing with constraint satisfaction and stability properties to this end we introduce a method to compute pwa lyapunov functions for discrete time pwa systems via linear programming finally we report results of an extensive case study which justify our claims of complexity reduction

on the convergence of rows of vector pade approximants we state and prove a de montessus like theorem for vector valued meromorphic functions using vector pade approximants which are defined in the context of clifford algebras the proof is based on that used by saff for the scalar case the theorem may be regarded as an answer to a general problem posed by graves morris and saff

optimization of lyapunov invariants in verification of software systems the paper proposes a control theoretic framework for verification of numerical software systems and puts forward software verification as an important application of control and systems theory the idea is to transfer lyapunov functions and the associated computational techniques from control systems analysis and convex optimization to verification of various software safety and performance specifications these include but are not limited to absence of overflow absence of division by zero termination in finite time absence of dead code and certain user specified assertions central to this framework are lyapunov invariants these are properly constructed functions of the program variables and satisfy certain properties analogous to those of lyapunov functions along the execution trace the search for the invariants can be formulated as a convex optimization problem if the associated optimization problem is feasible the result is a certificate for the specification

quadratic stabilizability of switched linear systems with polytopic uncertainties in this paper we consider quadratic stabilizability via state feedback for both continuous time and discrete time switched linear systems that are composed of polytopic uncertain subsystems by state feedback we mean that the switchings among subsystems are dependent on system states for continuous time switched linear systems we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices then the switched system is quadratically stabilizable via state feedback for discrete time switched linear systems we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of non negative scalars and a common positive definite matrix for both continuous time and discrete time switched systems we propose the switching rules by using the obtained common positive definite matrix

a clustering technique for the identification of piecewise affine systems we propose a new technique for the identification of discrete time hybrid systems in the piecewise affine pwa form this problem can be formulated as the reconstruction of a possibly discontinuous pwa map with a multi dimensional domain in order to achieve our goal we provide an algorithm that exploits the combined use of clustering linear identification and pattern recognition techniques this allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures moreover the clustering step used for classifying the datapoints is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure

hybrid model predictive control application towards optimal semi active suspension the optimal control problem of a quarter car semi active suspension has been studied in the past considering that a quarter car semi active suspension can either be modelled as a linear system with state dependent constraint on control of actuator force input or a bi linear system with a control of variable damping coefficient saturation the seemingly simple problem poses several interesting questions and challenges does the saturated version of the optimal control law derived from the corresponding un constrained system i e clipped optimal remain optimal for the constrained case as suggested in some previous publications or should the optimal deviate from the clipped optimal as suggested in other publications if the optimal control law of the constrained system does deviate from its unconstrained counter part how different are they what is the structure of the optimal control law does it retain the linear state feedback form as the unconstrained case in this paper we attempt to an

equivalence of the digital waveguide and finite difference time domain schemes it has been previously understood that the finite difference time domain fdtd method for numerically solving partial differential equations is equivalent to the digital waveguide dw method over the dw solution space however prior references have assumed that the dw solution space is a strict subset of the fdtd solution space so that the fdtd method exhibits solutions not available in the dw method in this talk based on arxiv org e print physics 0407032 we show that there is in fact a one to one correspondence between the two solution spaces and we give a simple explicit transformation for the 1d case e g for modeling vibrating strings the ability to transform fdtd models to dw models and back provides a means of guaranteeing passivity and or stability of specific fdtd models with specific boundary conditions furthermore wide classes of passive boundary conditions can be specified for the fdtd method based on the linear transformation of known passive terminations in the digital waveguide case similarly physically precise fdtd excitations input signals can be defined based on their dw counterparts

absorbing boundary conditions for difference approximations to the multi dimensional wave equation construction des conditions aux limites absorbantes pour l equation des ondes multidimensionnelle a l aide d approximations aux differences formulation sous forme canonique des conditions aux limites absorbantes analytiques

clifford algebras and vector valued rational forms i we demonstrate how the use of clifford algebras in the theory of vector valued rational forms leads to practical recurrence relations which do not involve representations of the algebras

equivalent piecewise affine models of linear hybrid automata in this technical note we examine the relationship between linear hybrid automata lha and piecewise affine pwa systems while a lha is an autonomous non deterministic model a pwa is a deterministic model with inputs through the key idea of modeling the uncertainty associated with lha transitions as input disturbances in a pwa model by extending continuous time pwa models to include the dynamics of discrete states and resets we show in a constructive way that a lha can be equivalently represented as a pwa system where equivalent means that the two systems generate the same trajectories besides filling in a missing theoretical link between the lha modelling framework and the pwa modelling framework the result has the practical advantage of enabling the use of several existing control theoretical tools developed for pwa models to a wider class of hybrid systems

an extension of a row convergence theorem for vector pade approximants abstract a row convergence theorem of de montessus type is established for vector pade approximants to a vector valued meromorphic function f while in a previous paper the authors established such a theorem for the case when f has simple poles the essential feature of the present paper is to treat the situation when f has multiple poles

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

row convergence theorems for generalised inverse vector valued pade approximants abstract the approximants mentioned in the title are related to vector valued continued fractions and the vector algorithm devised by wynn in 1963 here we establish a unitary invariance property of these approximants and describe how the classical 1 dimensional pade approximants can be obtained as a special case the main results of the paper consist of de montessus de ballore type convergence theorems for row sequences having fixed denominator degree of vector valued approximants to meromorphic vector functions

improved algorithm for mixed integer quadratic programs and a computational study in a recent paper 6 we suggested an algorithm for solving complicated mixed integer quadratic programs based on an equivalent formulation that employs a nonsingular transformation of variables the objectives of the present paper are two first to present an improved version of this algorithm which reduces substantially its computational requirements second to report on the results of a computational study with the revised algorithm

switching stabilizability for continuous time uncertain switched linear systems this paper investigates the switching stabilizability problem for a class of continuous time switched linear systems with time variant parametric uncertainties first a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived under the assumption that the closed loop switched system does not generate sliding motions then an additional condition is introduced to exclude the possibility of unstable sliding motions finally a necessary and sufficient for the asymptotic stabilizability of such continuous time uncertain switched linear systems is presented this result improves upon conditions found in the literature which are either sufficient only or necessary only

iterative learning control for non linear systems described by a blended multiple model representation this paper deals with the design of gain scheduling based iterative learning controllers for continuous time non linear systems described by a blended multiple model representation sufficient conditions guaranteeing the convergence of the infinity norm as well as the u norm of the tracking error are derived the effectiveness of the proposed control scheme is illustrated on an example of a non affine in input system

on stability of multiobjective nmpc with objective prioritization this paper proposes a new multiobjective model predictive control mo mpc of constrained nonlinear systems according to objective prioritization the mo mpc problem is formulated as a lexicographic optimization problem the optimal solutions are obtained by solving a hierarchy of single objective optimization problems the conditions guaranteeing the recursive feasibility of the optimization problem and stability of the closed loop system are derived which depend only on the most important objective moreover a suboptimal algorithm is presented to reduce the computational demand of mo mpc one characteristic of the proposed mo mpc is that the given objective prioritization is automatically satisfied the theoretical results are illustrated by a comparison study of an example

observation for markov jump piecewise affine systems with admissible region switching paths the technical note investigates the problem of state observation for discrete time markov jump piecewise affine pwa systems which cover both markov jump systems and traditional pwa systems as two special classes a new method for determining the admissible region switching paths between adjacent time instants is proposed for both the plant state and the estimator state so that both the computation cost and the conservatism of the theoretical results are reduced to analyze the mean square stability of the observation error system a novel piecewise lyapunov function is constructed which depends on the current mode and the region indices of both the system and observer states as the partitions of the state space are different for different modes the region indices are dependent on the system mode then mode dependent pwa observers are designed by means of s procedure and ellipsoidal outer approximation such that the observation error system is mean square stable the proposed observation strategy is demonstrated via an illustrative example

a control problem for affine dynamical systems on a full dimensional polytope given an affine system on a full dimensional polytope the problem of reaching a particular facet of the polytope using continuous piecewise affine state feedback is studied necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope special attention is paid to affine systems on full dimensional simplices in this case the necessary and sufficient conditions are equivalent and a constructive procedure yields an affine feedback control law that solves the reachability problem under consideration

cardinality constrained linear quadratic optimal control as control implementation often incurs not only a variable cost associated with the magnitude or energy of the control but also a setup cost we consider a discrete time linear quadratic lq optimal control problem with a limited number of control implementations termed in this technical note the cardinality constrained linear quadratic optimal control cclq we first derive a semi analytical feedback policy for cclq problems using dynamic programming dp due to the exponential growth of the complexity in calculating the action regions however dp procedure is only efficient for cclq problems with a scalar state space recognizing this fact we develop then two lower bounding schemes and integrate them into a branch and bound bnb solution framework to offer an efficient algorithm in solving general cclq problems adopting the devised solution algorithm for cclq problems we can solve efficiently the linear quadratic optimal control problem with setup costs

enumeration based approach to solving parametric linear complementarity problems this paper presents a solution method for parametric linear complementarity problems plcp that relies on an enumeration technique to discover all feasible bases the enumeration procedure is based on evaluating all possible combinations of active constraints and testing for feasibility although the enumeration approach is known to grow exponentially in the number of constraints the formulation of the plcp allows incorporation of cheap rank tests to quickly prune the infeasible directions in the exploration the motivation for the development of the enumeration based plcp solver is that it represents a direct method to solve parametric linear and quadratic optimization problems as well as their mixed integer counterparts these types of problems often arise in the field of model predictive control for linear and hybrid systems the enumeration based plcp solver offers another alternative to compute explicit solutions in the field of hybrid model predictive control that can be extremely effective in some important cases

pathloss calculation using the transmission line matrix and finite difference time domain methods with coarse grids numerical simulations of the wave equation that are intended to provide accurate time domain solutions require a computational mesh with grid points separated by a distance less than the wavelength of the source term and initial data however calculations of radio signal pathloss generally do not require accurate time domain solutions this paper describes an approach for calculating pathloss by using the finite difference time domain and transmission line matrix models of wave propagation on a grid with points separated by distances much greater than the signal wavelength the calculated pathloss can be kept close to the true value for freespace propagation with an appropriate selection of initial conditions this method can also simulate diffraction with an error governed by the ratio of the signal wavelength to the grid spacing

numerical experience with lower bounds for miqp branch and bound the solution of convex mixed integer quadratic programming miqp problems with a general branch and bound framework is considered it is shown how lower bounds can be computed efficiently during the branch and bound process improved lower bounds such as the ones derived in this paper can reduce the number of quadratic programming qp problems that have to be solved the branch and bound approach is also shown to be superior to other approaches in solving miqp problems numerical experience is presented which supports these conclusions

brief paper tracking and synchronisation for a class of pwa systems in this paper the tracking problem for a class of discontinuous piecewise affine pwa systems is addressed we propose an observer based output feedback control design consisting of a feedforward a piecewise affine feedback law and a model based observer solving the tracking problem these synthesis results can also be employed to tackle the master slave synchronisation problem for pwa systems it is shown that for certain classes of pwa systems the design is characterised in terms of linear matrix inequalities the results are illustrated by application to mechanical systems with discontinuous friction characteristics

problems and progress in vector pade approximation abstract some open problems in vector pade approximation are stated and some recent de montessus type theorems governing convergence of rows of the vector pade table are contrasted weshow how these results indicate when it is more appropriate to use generalised inverse vector pade approximants or their hybridised form we show how a straightforward analogue of the berlekamp massey algorithm may be used to calculate generalised inverse vector pade approximants this algorithm is applied to the derivation of a new low order hybrid vector approximant related results include the case of a row convergence theorem for a complex valued power series using a clifford inverse instead of the moore penrose inverse

the simulation of piano string vibration from physical models to finite difference schemes and digital waveguides a model of transverse piano string vibration second order in time which models frequency dependent loss and dispersion effects is presented here this model has many desirable properties in particular that it can be written as a well posed initial boundary value problem permitting stable finite difference schemes and that it may be directly related to a digital waveguide model a digital filter based algorithm which can be used for musical sound synthesis techniques for the extraction of model parameters from experimental data over the full range of the grand piano are discussed as is the link between the model parameters and the filter responses in a digital waveguide simulations are performed finally the waveguide model is extended to the case of several coupled strings

stabilizing polynomial approximation of explicit mpc a given explicit piecewise affine representation of an mpc feedback law is approximated by a single polynomial computed using linear programming this polynomial state feedback control law guarantees closed loop stability and constraint satisfaction the polynomial feedback can be implemented in real time even on very simple devices with severe limitations on memory storage

impulsive and hybrid dynamical systems stability dissipativity and control s book review w m haddad v s chellaboina and s g nersesov

extrapolation methods for vector sequences an analogue of aitken s 2 method suitable for vector sequences is proposed aspects of the numerical performance of the vector algorithm based on using the moore penrose inverse are investigated the fact that the denominator polynomial associated with a vector pade approximant is the square of its equivalent in the scalar case is shown to be a source of approximation error in cases where the convergence of the vector sequence is dominated by real eigenvalues a hybrid form of the vector pade approximant having a denominator polynomial of minimal degree is proposed and its effectiveness is demonstrated on several standard examples

optimistic optimization for model predictive control of max plus linear systems model predictive control for max plus linear discrete event systems usually leads to a nonsmooth nonconvex optimization problem with real valued variables which may be hard to solve efficiently an alternative approach is to transform the given problem into a mixed integer linear programming problem however the computational complexity of current mixed integer linear programming algorithms increases in the worst case exponentially as a function of the prediction horizon the focus of this paper is on making optimistic optimization suited to solve the given problem optimistic optimization is a class of algorithms that can find an approximation of the global optimum for general nonlinear optimization a key advantage of optimistic optimization is that one can specify the computational budget in advance and guarantee bounds on the suboptimality with respect to the global optimum we prove that optimistic optimization can be applied for the given problem by developing a dedicated semi metric and by proving it satisfies the necessary requirements for optimistic optimization moreover we show that the complexity of optimistic optimization is exponential in the control horizon instead of the prediction horizon hence using optimistic optimization is more efficient when the control horizon is small and the prediction horizon is large

determinantal inequalities for diagonally signed matrices and an application to gram cauchy matrices abstract the condition that a hermitian matrix is diagonally signed complementary has recently been shown to guarantee that its signature is invariant with respect to hadamard products with gram matrices in this paper we establish inequalities for the determinants of these diagonally signed matrices that are analogs of well known inequalities for positive definite matrices because hermitian cauchy matrices and their confluent forms are diagonally signed we can then infer from the new inequalities the existence in general of inverses of the confluent forms of hermitian gram cauchy matrices

technical communique an efficient algorithm for optimal control of pwa systems with polyhedral performance indices we present an algorithm for the computation of explicit optimal control laws for piecewise affine pwa systems with polyhedral performance indices the algorithm is based on dynamic programming dp and represents an extension of ideas initially proposed in kerrigan and mayne 2003 optimal control of constrained piecewise affine systems with bounded disturbances in proceedings of the 41st ieee conference on decision and control las vegas nevada usa december and baotic et al 2003 a new algorithm for constrained finite time optimal control of hybrid systems with a linear performance index in proceedings of european control conference cambridge uk september specifically we show how to exploit the underlying geometric structure of the optimization problem in order to significantly improve the efficiency of the off line computations an extensive case study is provided which clearly indicates that the algorithm proposed in this paper may be preferable to other schemes published in the literature

numerical simulations of piano strings i a physical model for a struck string using finite difference methods the first attempt to generate musical sounds by solving the equations of vibrating strings by means of finite difference methods fdm was made by hiller and ruiz j audio eng soc 19 462 472 1971 it is shown here how this numerical approach and the underlying physical model can be improved in order to simulate the motion of the piano string with a high degree of realism starting from the fundamental equations of a damped stiff string interacting with a nonlinear hammer a numerical finite difference scheme is derived from which the time histories of string displacement and velocity for each point of the string are computed in the time domain the interacting force between hammer and string as well as the force acting on the bridge are given by the same scheme the performance of the model is illustrated by a few examples of simulated string waveforms a brief discussion of the aspects of numerical stability and dispersion with reference to the proper choice of sampling parameters is also included

introduction to the improved functional epsilon algorithm this paper introduces the improved functional epsilon algorithm we have defined this new method in principle of the modified aitken 2 algorithm moreover we have found that the improved functional epsilon algorithm has remarkable precision of the approximation of the exact solution and there exists a relationship with the integral pade approximant the use of the improved functional epsilon algorithm for accelerating the convergence of sequence of functions is demonstrated the relationship of the improved functional epsilon algorithm with the integral pade approximant is also demonstrated moreover we illustrate the similarity between the integral pade approximant and the modified aitken 2 algorithm thus we have shown that the integral pade approximant is a natural generalisation of modified aitken 2 algorithm

lyapunov function construction by linear programming in this paper the lyapunov function given by the infinity norm is considered a new proof of the theorem of molchanov and pyatintskii 1986 is given the presented proof enables us to give an explicit calculation of the matrix which was only demonstrated to exist in the original paper combining the obtained result with the idea of scaling faces of a polytope gives the method of fitting the shape of level surfaces of the lyapunov function given by the infinity norm to the specified demands

optimal control of continuous time switched affine systems this paper deals with optimal control of switched piecewise affine autonomous systems where the objective is to minimize a performance index over an infinite time horizon we assume that the switching sequence has a finite length and that the decision variables are the switching instants and the sequence of operating modes we present two different approaches for solving such an optimal control problem the first approach iterates between a procedure that finds an optimal switching sequence of modes and a procedure that finds the optimal switching instants the second approach is inspired by dynamic programming and identifies the regions of the state space where an optimal mode switch should occur therefore providing a state feedback control law

a family of pade type approximants for accelerating the convergence of sequences we describe a collection of pade type methods for accelerating the convergence of sequence of functions the construction and connections of pade s methods with other similar methods are given we examine the effectiveness of these new methods namely integral pade approximant modified pade approximant and squared pade approximant together with the well established methods namely functional pade approximant and classical pade approximant for approximating the characteristic value and corresponding characteristic function estimates of characteristic value and characteristic function derived using integral pade approximants are found to be substantially more accurate than other similar methods

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

efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form for hybrid systems described by switched linear difference equations linear threshold conditions automata and propositional logic conditions described in mixed logical dynamical form this note describes two algorithms for transforming such systems into an equivalent piecewise affine form where equivalent means that for the same initial conditions and input sequences the trajectories of the system are identical the proposed techniques exploit ideas from mixed integer programming and multiparametric programming

lyapunov functions stability and input to state stability subtleties for discrete time discontinuous systems in this note we consider stability analysis of discrete time discontinuous systems using lyapunov functions we demonstrate via simple examples that the classical second method of lyapunov is precarious for discrete time discontinuous dynamics also we indicate that a particular type of lyapunov condition slightly stronger than the classical one is required to establish stability of discrete time discontinuous systems furthermore we examine the robustness of the stability property when it was attained via a discontinuous lyapunov function which is often the case for discrete time hybrid systems in contrast to existing results based on smooth lyapunov functions we develop several input to state stability tests that explicitly employ an available discontinuous lyapunov function

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

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

dynamic programming for constrained optimal control of discrete time linear hybrid systems in this paper we study the solution to optimal control problems for constrained discrete time linear hybrid systems based on quadratic or linear performance criteria the aim of the paper is twofold first we give basic theoretical results on the structure of the optimal state feedback solution and of the value function second we describe how the state feedback optimal control law can be constructed by combining multiparametric programming and dynamic programming

on hybrid systems and closed loop mpc systems the following five classes of hybrid systems were recently proven to be equivalent linear complementarity extended linear complementarity mixed logical dynamical systems piecewise affine systems and max min plus scaling systems some of the equivalences were obtained under additional assumptions such as boundedness of certain system variables in this paper for linear or hybrid plants in closed loop with a model predictive control mpc controller based on a linear model fulfilling linear constraints on input and state variables and utilizing a quadratic cost criterion we provide a simple and direct proof that the closed loop system is a subclass of any of the former five classes of hybrid systems this result is of extreme importance as it opens up the use of tools developed for the mentioned hybrid model classes such as robust stability and safety analysis tools to study closed loop properties of mpc

propositional logic in control and monitoring problems by using linear constraints on integer variables logical inference can be incorporated within model predictive control and model based detection problems resulting in mixed integer quadratic or mixed integer linear programming problems qualitative knowledge can be used to prioritize control objectives or to improve performance of detection schemes this article demonstrates some capabilities of combining logic using integer variables with quantitative models

an efficient realization of frequency dependent boundary conditions in an acoustic finite difference time domain model abstract the finite difference time domain fdtd method provides a simple and accurate way of solving initial boundary value problems however most acoustic problems involve frequency dependent boundary conditions and it is not easy to include such boundary conditions in an fdtd model although solutions to this problem exist most of them have high computational costs and stability cannot always be ensured in this work a solution is proposed based on mixing modelling strategies this involves separating the fdtd mesh and the boundary conditions a digital filter representation of the impedance and combining them into a global solution this solution is based on an interaction model that involves wave digital filters the proposed method is validated with several test cases

stability and invariance analysis of uncertain discrete time piecewise affine systems this note proposes a method to analyze uniform asymptotic stability and uniform ultimate boundedness of uncertain piecewise affine systems whose dynamics are only defined in a bounded and possibly non invariant set x of states the approach relies on introducing fake dynamics outside x and on synthesizing a piecewise affine and possibly discontinuous lyapunov function via linear programming the existence of such a function proves stability properties of the original system and allows the determination of a region of attraction contained in x the procedure is particularly useful in practical applications for analyzing the stability of piecewise affine control systems that are only defined over a bounded subset x of the state space and to determine whether for a given set of initial conditions the trajectories of the state vector remain within the domain x

on the input output representation of piecewise affine state space models this paper addresses the conversion of discrete time piecewise affine pwa state space models into input output form necessary and sufficient conditions for the existence of equivalent input output representations of a given pwa state space model are derived connections to the observability properties of pwa models are investigated under a technical assumption it is shown that every finite time observable pwa model admits an equivalent input output representation when an equivalent input output model exists a constructive procedure is presented to derive its equations several examples illustrate the proposed results

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

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

solution of integral equations using generalised inverse function valued pade approximants i abstract neumann series solutions for the linear integral equation x 1 1 0 1 x y y d y converge for small values of we use generalised inverse function valued pade approximants to accelerate the convergence of the neumann series and to estimate the singular value of these estimates are found to compare very favourably with those from the fredholm determinant method and the pade approximant method

brief paper event driven optimization based control of hybrid systems with integral continuous time dynamics in this paper we introduce a class of continuous time hybrid dynamical systems called integral continuous time hybrid automata icha for which we propose an event driven optimization based control strategy events include both external actions applied to the system and changes of continuous dynamics mode switches the icha formalism subsumes a number of hybrid dynamical systems with practical interest e g linear hybrid automata different cost functions including minimum time and minimum effort criteria and constraints are examined in the event driven optimal control formulation this is translated into a finite dimensional mixed integer optimization problem in which the event instants and the corresponding values of the control input are the optimization variables as a consequence the proposed approach has the advantage of automatically adjusting the attention of the controller to the frequency of event occurrence in the hybrid process a receding horizon control scheme exploiting the event based optimal control formulation is proposed as a feedback control strategy and proved to ensure either finite time or asymptotic convergence of the closed loop

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

data based identification and control of nonlinear systems via piecewise affine approximation the piecewise affine pwa model represents an attractive model structure for approximating nonlinear systems in this paper a procedure for obtaining the pwa autoregressive exogenous arx autoregressive systems with exogenous inputs models of nonlinear systems is proposed two key parameters defining a pwarx model namely the parameters of locally affine subsystems and the partition of the regressor space are estimated the former through a least squares based identification method using multiple models and the latter using standard procedures such as neural network classifier or support vector machine classifier having obtained the pwarx model of the nonlinear system a controller is then derived to control the system for reference tracking both simulation and experimental studies show that the proposed algorithm can indeed provide accurate pwa approximation of nonlinear systems and the designed controller provides good tracking performance

vector valued rational interpolants i it is shown explicitly that the samelson inverse may be used to define vector valued thiele type rational interpolants and the equivalence with claessens algorithm is established for the special case of vector valued pade approximants the general form of mccleod s theorem follows as a corollary

parameter fitting for piano sound synthesis by physical modeling a difficult issue in the synthesis of piano tones by physical models is to choose the values of the parameters governing the hammer string model in fact these parameters are hard to estimate from static measurements causing the synthesis sounds to be unrealistic an original approach that estimates the parameters of a piano model from the measurement of the string vibration by minimizing a perceptual criterion is proposed the minimization process that was used is a combination of a gradient method and a simulated annealing algorithm in order to avoid convergence problems in case of multiple local minima the criterion based on the tristimulus concept takes into account the spectral energy density in three bands each allowing particular parameters to be estimated the optimization process has been run on signals measured on an experimental setup the parameters thus estimated provided a better sound quality than the one obtained using a global energetic criterion both the sound s attack and its brightness were better preserved this quality gain was obtained for parameter values very close to the initial ones showing that only slight deviations are necessary to make synthetic sounds closer to the real ones

the epsilon algorithm and related topics the epsilon algorithm is recommended as the best all purpose acceleration method for slowly converging sequences it exploits the numerical precision of the data to extrapolate the sequence to its limit we explain its connections with pade approximation and continued fractions which underpin its theoretical base then we review the most recent extensions of these principles to treat application of the epsilon algorithm to vector valued sequences and some related topics in this paper we consider the class of methods based on using generalised inverses of vectors and the formulation specifically includes the complex case wherever possible

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

two point quasifractional approximant in physics truncation error the quasifractional approximation method is developed in a systematic manner this method uses simultaneously the power series and at a second point the asymptotic expansion the usual form of the approximants is two or more rational fractions in terms of a suitable variable combined with auxiliary nonfractional functions coincidence in the singularities in the region of interest is pursued equal denominators in the rational fractions is required so that the solution of only linear algebraic equations is needed to determine the parameters of the approximant an upper bound is obtained for the truncation error for a certain class of functions which contains most of the functions for which this method has been applied so far it is shown that quasifractional approximants can be derived as a mixed german and latin polynomial problem in the context of hermite pade approximation theory

confluent hermitian cauchy matrices are diagonally signed abstract it is shown that cauchy matrices admit a confluent extension in much the same way that confluent vandermonde matrices or cauchy alternants have confluent forms cauchy matrices formed from distinct elements have been proved recently to be diagonally signed and this is equivalent to showing that they are complementary matrices we show here that this property extends to the confluent case too

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

lyapunov stability of a class of discrete event systems discrete event systems des are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals logical des are a class of discrete time des with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences recently there has been much interest in studying the stability properties of logical des and several definitions for stability and methods for stability analysis have been proposed here the authors introduce a logical des model and define stability in the sense of lyapunov and asymptotic stability for logical des then the authors show that more conventional analysis of stability which employs appropriate lyapunov functions can be used for logical des the authors provide a general characterization of the stability properties of automata theoretic des models petri nets and finite state systems furthermore the lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of n different types of parts according to a priority scheme to prove properties related to the machine s ability to reorient itself to achieve safe operation and a load balancing problem in computer networks to study the ability of the system to achieve a balanced load to minimize underutilization

control to facet by piecewise affine output feedback the control to facet problem plays an important role in the design of feedback controllers for piecewise affine hybrid systems on polytopes in the literature necessary conditions and sufficient conditions for solvability by static state feedback exist in this paper we extend these results to the case of continuous piecewise affine static output feedback for the construction of a controller a triangulation of the output polytope is made which satisfies additional conditions to guarantee compatibility with the induced subdivision of the state polytope in the state feedback case the use of this special type of triangulation is not required

brief analysis of discrete time piecewise affine and hybrid systems in this paper we present various algorithms both for stability and performance analysis of discrete time piece wise affine pwa systems for stability different classes of lyapunov functions are considered and it is shown how to compute them through linear matrix inequalities that take into account the switching structure of the systems we also show that the continuity of the lyapunov function is not required in discrete time moreover the tradeoff between the degree of conservativeness and computational requirements is discussed finally by using arguments from the dissipativity theory for nonlinear systems we generalize our approach to analyze the l 2 gain of pwa systems

on the necessity of the invariance conditions for reach control on polytopes abstract we study the reach control problem rcp to make the solutions of an affine system defined on a polytopic state space reach and exit a prescribed facet of the polytope in finite time without first leaving the polytope so called invariance conditions are used to prevent solutions from leaving the polytope through facets which are not designated as the exit facet these conditions are known to be necessary for solvability of the rcp on polytopes by continuous state feedback we study whether the invariance conditions are also necessary for solvability of the rcp on polytopes by open loop controls we show by way of a counterexample that surprisingly the answer is negative we identify a suitable class of polytopes for which the invariance conditions remain necessary conditions

a lyapunov method for stability analysis of piecewise affine systems over non invariant domains this paper analyses stability of discrete time piecewise affine systems defined on possibly non invariant domains taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system an algorithm based on linear programming is proposed in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction the results are based on the definition of a piecewise affine lyapunov function which is in general discontinuous on the boundaries of the regions the proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach two numerical examples are shown among which a case where the proposed method is applied to a closed loop system to which model predictive control was applied without a priori guarantee of stability