continuous representation and control of hybrid systems this article introduces a continuous representation for controlled model and state jump hybrid systems such a representation is valuable in that it manages to cope with the difficulties related to discontinuities by replacing the study of these systems by that of continuous ones which is simple the studied hybrid systems are first introduced together with their associated continuous systems some localized and global convergences of the states of continuous systems to those of hybrid systems are proved then the continuous representation is used within the optimal control framework free end time and trajectory pursuit hybrid problems are studied as well as their respective continuous versions convergences of solutions between continuous and hybrid problems are established which shows that the resolution of a problem ensuing from the representation enables one to obtain an approximation of the solution of the initial hybrid problem finally the formalism of calculus of variations is used to obta

stability analysis and control of rigid body systems with impacts and friction many critical tasks in robotics such as locomotion or manipulation involve collisions between a rigid body and the environment or between multiple bodies methods based on sums of squares sos for numerical computation of lyapunov certificates are a powerful tool for analyzing the stability of continuous nonlinear systems and can additionally be used to automatically synthesize stabilizing feedback controllers here we present a method for applying sums of squares verification to rigid bodies with coulomb friction undergoing discontinuous inelastic impact events the proposed algorithm explicitly generates lyapunov certificates for stability positive invariance and safety over admissible non penetrating states and contact forces we leverage the complementarity formulation of contact which naturally generates the semialgebraic constraints that define this admissible region the approach is demonstrated on multiple robotics examples including simple models of a walking robot a perching aircraft and control design of a balancing robot

limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and poincare maps the verge and foliot escapement mechanism of a mechanical clock is a classical example of a feedback regulator in this paper we analyse the dynamics of this mechanism to understand its operation from a feedback perspective using impulsive differential equations and poincare maps to model the dynamics of this closed loop system we determine conditions under which the system possesses a limit cycle and we analyse the period and amplitude of the oscillations in terms of the inertias of the colliding masses and their coefficient of restitution

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

on the equivalence between dissipativity and optimality of discontinuous nonlinear regulators for filippov dynamical systems in this paper we derive guaranteed gain sector and disk margins for nonlinear optimal and inverse optimal discontinuous feedback regulators that minimize a nonlinear nonquadratic performance functional for filippov dynamical systems specifically we consider dynamical systems with lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving filippov set valued maps in addition we extend classical dissipativity theory to address the problem of dissipative discontinuous dynamical systems these results are then used to derive extended kalman yakubovich popov conditions for characterizing necessary and sufficient conditions for dissipativity of discontinuous systems using clarke gradients and locally lipschitz continuous storage functions furthermore using the newly developed dissipativity notions we develop a return difference inequality to provide connections between dissipativity and optimality of nonlinear discontinuous controllers for filippov dynamical systems specifically using the extended kalman yakubovich popov conditions we show that our discontinuous feedback control law satisfies a return difference inequality if and only if the controller is dissipative with respect to a quadratic supply rate

optimal disturbance rejection control for nonlinear impulsive dynamical systems in this paper we develop an optimality based framework for addressing the problem of nonlinear nonquadratic hybrid control for disturbance rejection of nonlinear impulsive dynamical systems with bounded exogenous disturbances specifically we transform a given nonlinear nonquadratic hybrid performance criterion to account for system disturbances as a consequence the disturbance rejection problem is translatedinto an optimal hybridcontrol problem furthermore the resulting optimal hybrid control law is shown to render the closed loop nonlinear input output map dissipative with respect to general supply rates in addition the lyapunov function guaranteeing closed loop stability is shown to be a solution to a stead y state hybridhamilton jacobi isaacs equation andthus guaranteeing optimality 2005 elsevier ltd all rights reserved

deterministic impulse control problems in this paper we study a deterministic infinite horizon mixed continuous and impulse control problem in r n with general impulses and cost of impulses we assume that the cost of impulses is a positive function we prove that the value function of the control problem is the unique viscosity solution of the related first order hamilton jacobi quasi variational inequality 11qvi we then propose time discretization schemes of this qvi where we consider two approximations of the hamiltonian h h including a natural one we prove that the approximate value function u h exists that it is the unique solution of the approximate qvi and that it forms a uniformly bounded and uniformly equicontinuous family we also prove that the approximate value function converges locally uniformly towards the value function of the control problem when the discretization step h goes to zero the rate of convergence is proved to be in h where 0 1 2

stochastic hybrid control the objective of this paper is to study the stochastic version of a previous paper of the authors in which hybrid control for deterministic systems was considered the modelling is quite similar to the deterministic case we have a system whose state is composed of a continuous part and a discrete part they are affected by a continuous type control and an impulse control the dynamics is moreover perturbed by noise also a continuous and a discrete noise process the markovian character of the sate process is preserved we develop the model and show how the dynamic programming approach leads to some involved quasi variational inequality

the application of dynamic programming to optimal inventory control this paper concerns a class of deterministic impulse control problems arising in inventory control a notable feature of the problem formulation is the presence of an end point constraint in consequence the value function may be discontinuous viability theory provides a characterization of the value function as the unique lower semicontinuous solution to a bensoussan lions type quasi variational inequality qvi suitably interpreted for nondifferentiable extended valued functions yet there are few examples in the literature of the use of this analytical machinery this paper provides such an example the example which concerns a problem for which the value function is neither everywhere finite valued nor continuously differentiable on the interior of its effective domain illustrates what is involved in calculating subdifferentials and checking satisfaction of qvi in a generalized sense this paper also provides a summary of the underlying theory and gathers in the appendix proofs of key results

technical communique optimally switched linear systems in this paper we address the problem of optimal switching for switched linear systems the uniqueness of our approach lies in describing the switching action by multiple control inputs this allows us to embed the switched system in a larger family of systems and apply pontryagin s minimum principle for solving the optimal control problem this approach imposes no restriction on the switching sequence or the number of switchings this is in contrast to search based algorithms where a fixed number of switchings is set a priori in our approach the optimal solution can be determined by solving the ensuing two point boundary value problem results of numerical simulations are provided to support the proposed method

controllability and observability for a class of controlled switching impulsive systems in this note we study the controllability and observability problem for a class of controlled switching impulsive systems by proposing several formula of variation of parameters for this type of time varying systems and employing the characteristic polynomial theory of matrix we establish necessary and sufficient conditions for controllability and controlled observability with respect to a given switching time sequence specializing the obtained results to the case of time invariant linear switching impulsive systems we derive some simple algebraic criteria which include the results reported in the literature for time invariant linear switching systems linear impulsive systems and classical linear systems one example is worked out for illustration

unknown input observers for switched nonlinear discrete time descriptor systems in this paper a linear matrix inequality technique for the state estimation of discrete time nonlinear switched descriptor systems is developed the considered systems are composed of linear and nonlinear parts an observer giving a perfect unknown input decoupled state estimation is proposed sufficient conditions of global convergence of observers are proposed numerical examples are given to illustrate this method

fault estimation for a class of nonlinear systems based on intermediate estimator this technical note investigates the problem of fault estimation for a class of nonlinear systems with lipschitzian nonlinearities in most of the existing fault estimation approaches the observer matching condition should be satisfied however this condition is hard to meet for many systems to overcome this restriction a new fault estimation method is proposed where an intermediate variable is introduced and a specially designed intermediate estimator is proposed to estimate the state and the faults simultaneously by exploiting the properties of fault distribution matrix it is proved that the states of the error system are uniformly ultimately bounded simulation examples verify the effectiveness of the proposed method

target problems under state constraints for nonlinear controlled impulsive systems we study the problem of reaching a target without leaving a prescribed constraint set for a dynamical system described by a controlled differential equation and a controlled instantaneous reset function we characterize all initial conditions from which the objective can be reached then we characterize the value function associated with the optimal reaching time problem

secret sharing schemes from three classes of linear codes secret sharing has been a subject of study for over 20 years and has had a number of real world applications there are several approaches to the construction of secret sharing schemes one of them is based on coding theory in principle every linear code can be used to construct secret sharing schemes but determining the access structure is very hard as this requires the complete characterization of the minimal codewords of the underlying linear code which is a difficult problem in general in this paper a sufficient condition for all nonzero codewords of a linear code to be minimal is derived from exponential sums some linear codes whose covering structure can be determined are constructed and then used to construct secret sharing schemes with nice access structures

a linear code based on resilient boolean maps whose dual is a platform for a robust secret sharing scheme abstract a linear code based on resilient maps on vector spaces over finite fields is introduced and lower bounds for its minimal distance are given the dual code is used to define a secret sharing scheme sss according to massey construction since the dual code satisfies the conditions stated by padro and saez the generalization to a vector space sss is robust against cheaters

optimal control of hybrid systems and a system of quasi variational inequalities optimal control of a class of hybrid dynamical systems is studied using the method of dynamic programming it is proved that the value function is a discontinuous viscosity solution of the corresponding hamilton jacobi bellman hjb equation which appears as a system of quasi variational inequalities sqvi coupled by a nonlocal operator with a variable boundary condition the comparison theorems are established for the sub and super solutions of the sqvi

applying discrete time proportional integral observers for state and disturbance estimations in this note we apply the proportional integral observer to simultaneously estimate system states and unknown disturbances for discrete time nonminimum phase systems conditions for providing the existence of such observer are given when the disturbances do not vary too much between two consecutive sampling instances the proposed method can render the estimation errors of system states and disturbances to be constrained in a small bounded region simulation results support the theoretical developments

functional unknown input reconstruction of descriptor systems the problem of finding conditions for the reconstruction of a linear combination of the vector of unknown inputs is tackled appropriate definitions are given in order to address formally the analysis thus necessary and sufficient conditions are obtained for two cases when the reconstruction may be achieved in finite time and when it is possible to do it asymptotically the results are applied for the fault detection with the respective deduction of analogous conditions

time periodic optimal policy for operation of a water storage tank using the dynamic programming approach abstract operation of a water storage tank in a specific environment motivates mathematical studies on a discrete time deterministic dynamic programming problem the operator decides whether or not to open the valve releasing the water in the tank to a drip irrigation system based on the information on the storage volume of the tank two cases of functional regularity which are lipschitz continuous and of bounded variations are considered for the reward defining the performance index to be maximized firstly it is shown that the value function inherits the lipschitz continuity of the reward in the infinite time horizon problem with discounting then time periodic value functions are discussed in terms of the fixed point theorem discrete approximation of value functions is discussed as well to conduct numerical experiments with a posteriori error estimation applied to the real world problem where the discount rate approaches to unity it is found that a skiba point appears as a threshold of valve opening for each day in an optimal policy for operation practically setting a constant threshold throughout the period is quite reasonable and acceptable for the operator of the water storage tank to irrigate the farmland

finite time stabilization of linear systems via impulsive control this paper introduces a new concept of finite time stability of linear time invariant impulsive systems the sufficient condition of finite time stability of the system via impulsive control at fixed times and variable times is obtained respectively such sufficient conditions of finite time stabilization are given in terms of matrix inequalities a numerical example is presented to illustrate the efficiency of the proposed results

a nonlinear luenberger like observer for nonlinear singular systems this paper investigates observer design problem for a large class of nonlinear singular systems with multiple outputs we firstly regularize the singular system by injecting the derivative of outputs into the system then differential geometric method is applied to transform the regularized system into a simple normal form for which a luenberger like observer is proposed

energy dissipating hybrid control for impulsive dynamical systems abstract a novel class of fixed order energy based hybrid controllers is proposed as a means for achieving enhanced energy dissipation in nonsmooth euler lagrange hybrid port controlled hamiltonian and lossless impulsive dynamical systems these dynamic controllers combine a logical switching architecture with hybrid dynamics to guarantee that the system plant energy is strictly decreasing across switchings the general framework leads to hybrid closed loop systems described by impulsive differential equations special cases of energy based hybrid controllers involving state dependent switching are described and an illustrative numerical example is given to demonstrate the efficacy of the proposed approach

bounded amplitude performance of switched lpv systems with applications to hybrid systems this paper discusses recent results on multiple linear agent control for systems satisfying a bounded amplitude performance constraint the plant is assumed to be a linear parameter varying lpv system scheduled along a nominal parameter trajectory in this respect the control problem represents a plant operating between a prespecified set of operating conditions linear controllers are designed at setpoints along this scheduling trajectory to satisfy bounded amplitude performance constraints this paper discusses an approach to analyze the switched system behavior under practical assumptions on the structure of the switching rule the approach combines the scheduling parameter with lpv system properties to derive bounds on the switching behavior of the system these estimates are then used to construct a logical model of the switched system behavior in the form of a timed automaton in this respect this paper presents a way of extracting logical models of continuous time system behavior

hybrid control systems and viscosity solutions we investigate a model of hybrid control system in which both discrete and continuous controls are involved in this general model discrete controls act on the system at a given set interface the state of the system is changed discontinuously when the trajectory hits predefined sets namely an autonomous jump set a or a controlled jump set c where the controller can choose to jump or not at each jump the trajectory can move to a different euclidean space we prove the continuity of the associated value function v with respect to the initial point using the dynamic programming principle satisfied by v we derive a quasi variational inequality satisfied by v in the viscosity sense we characterize the value function v as the unique viscosity solution of the quasi variational inequality by the comparison principle method

uniqueness of unbounded viscosity solutions for impulse control problem we study here the impulse control problem in infinite as well as finite horizon we allow the cost functionals and dynamics to be unbounded and hence the value function can possibly be unbounded we prove that the value function is the unique viscosity solution in a suitable subclass of continuous functions of the associated quasivariational inequality our uniqueness proof for the infinite horizon problem uses stopping time problem and for the finite horizon problem comparison method however we assume proper growth conditions on the cost functionals and the dynamics

differential automata and their discrete simulators on presente la notion d automate differentiel pour la formulation d une classe de problemes aux valeurs initiales sur des champs vectoriels hysteretiques

impulsive modes and causality in singular systems the concepts of impulsive modes and causality in singular systems are considered their properties relations and applications are studied matrix rank criteria are presented thus all controllabilities and observabilities and related concepts have matrix rank criteria based on the original system coefficient matrices

a new scheme of fault detection for linear discrete time varying systems in this note a new scheme of fault detection fd is proposed for linear discrete time varying ldtv systems subject to l 2 norm bounded unknown inputs the basic idea is to find an optimal estimation of the l 2 norm of the unknown inputs including the unknown initial state variables this leads to a natural design of the fd system with the l 2 norm boundedness of the unknown inputs as a threshold and the l 2 norm of the unknown input estimate as the evaluation function to avoid heavy computational burden projection technique in krein space is applied which allows a recursive computation of the evaluation function it is shown that the achieved fd system satisfies both the worst case and best case sensitivity robustness ratio criteria and further applications to observer based fd lead to an alternative design of h infty h infty and or h h infty fault detection filter

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

optimality in accelerated life tests we formulate a stochastic control problem arising from the optimal design of accelerated life tests the model is obtained in a natural way in the setup of point processes the cost functional depends on the total number of items under test at time t the observed number of items failed up to time t and the stress level applied to the items under test at time t the optimal policy minimizing the cost functional is characterized via the dynamic programming equation after a further specification of the model we prove that the solution is of bang bang type in some specific cases we also prove that the control problem is equivalent to an optimal stopping problem this amounts to simply running the test with the number of items and the stress level at their highest available value up to the exit time of the state process from a given region in this special case we exhibit an explicit solution and give a criterion in order to decide whether to let the experiment run or to stop it

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

nonfragile h state estimation for recurrent neural networks with time varying delays on proportional integral observer design in this article a novel proportional integral observer pio design approach is proposed for the nonfragile h state estimation problem for a class of discrete time recurrent neural networks with time varying delays the developed pio is equipped with more design freedom leading to better steady state accuracy compared with the conventional luenberger observer the phenomena of randomly occurring gain variations which are characterized by the bernoulli distributed random variables with certain probabilities are taken into consideration in the implementation of the addressed pio attention is focused on the design of a nonfragile pio such that the error dynamics of the state estimation is exponentially stable in a mean square sense and the prescribed h performance index is also achieved sufficient conditions for the existence of the desired pio are established by virtue of the lyapunov krasovskii functional approach and the matrix inequality technique finally a simulation example is provided to demonstrate the effectiveness of the proposed pio design scheme

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

disturbance attenuation using proportional integral observers in this paper we first propose a proportional integral observer design for single output uncertain linear systems which permit us to attenuate either measurement noise or modelling errors we show that when only sensor noise is present in the system an integral observer alone suffices to achieve good convergence and filtering properties on the other hand when modelling errors and sensor noise are present we show that for some classes of linear systems the proportional integral observer allows us to decouple completely the modelling uncertainties while keeping satisfactory convergence properties a comparison of the classical proportional observer to the proposed observers are given via academic simulation examples we next extend the design to the class of single output uniformly observable non linear systems we show through a practical simulation example dealing with a flexible joint robot that the non linear proportional integral has very satisfactory disturbance attenuating properties

unknown input proportional multiple integral observer design for linear descriptor systems application to state and fault estimation in this note the problem of observer design for linear descriptor systems with faults and unknown inputs is considered first it is considered that the fault vector function f is s times piecewise continuously differentiable if the s th time derivative of f is null then s integral actions are included into a luenberger observer which is designed such that it estimates simultaneously the state the fault and its finite derivatives face to unknown inputs second when the fault is not time piecewise continuously differentiable but bounded like actuator noise or s th time derivative of fault is not null but bounded too a high gain observer is derived to attenuate the fault impact in estimation errors the considered faults may be unbounded may not be determinist and faults and unknown inputs may affect the state dynamic and plant outputs sufficient conditions for the existence of such observer are given results are illustrated with a differential algebraic power system

disturbance decoupled observer design a unified viewpoint this paper is concerned with the observer design for linear systems with unknown inputs an equivalent system which is free of unknown inputs is derived for the purpose of the observer design based on the equivalent system description one can design an observer full order reduced order minimal order or functional for linear systems with unknown inputs using well known techniques it is shown that the equivalent system exists as long as there exists a disturbance decoupled observer two sets of the known existence conditions of disturbance decoupled observers are proved to be equivalent

design of proportional integral observer for unknown input descriptor systems this note presents simple methods to design full and reduced order proportional integral observer for unknown inputs ui descriptor systems sufficient conditions for the existence of the observer are given and proven the observer is solvable by any pole placement algorithm it achieves a posteriori robustness state and ui estimation versus to time varying parameters and bounded nonlinear ui an illustrative example is included

the hierarchical lattices of a finite machine the concept of dynamical consistency is introduced to define a high level transition function for an arbitrary partition of the state space of a finite input state machine m the existence of a dynamically consistent transition from a partition member xi to a member xj corresponds to the existence for every state x in xi of some x dependent control sequence which takes that state directly into xj this paper analyses what are termed in block controllable partition machines and between block controllable partition machines and establishes the existence of the associated in block controllable hierarchical lattice ibcp m it is shown that any partition machine in ibcp m is between block controllable if and only if the base machine m is controllable this setting allows the specification of state to state control trajectories of m to be decomposed into high level and low level components

non linear impulsive dynamical systems part i stability and dissipativity in this paper we develop lyapunov and invariant set stability theorems for non linear impulsive dynamical systems furthermore we generalize dissipativity theory to non linear dynamical systems with impulsive effects specifically the classical concepts of system storage functions and supply rates are extended to impulsive dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy dissipated energy over the continuous time system dynamics and dissipated energy over the resetting instants furthermore extended kalman yakubovich popov conditions in terms of the impulsive system dynamics characterizing dissipativeness via system storage functions are derived finally the framework is specialized to passive and non expansive impulsive systems to provide a generalization of the classical notions of passivity and non expansivity for non linear impulsive systems these results are used in the second part of this paper to develop extensions of the small gain and p

disturbance decoupled observer design for descriptor systems in this paper we study the observer design problem for descriptor systems with partly unknown inputs we give necessary and sufficient conditions for the existence of a solution to the disturbance decoupled estimation problem with or without stable error spectrum requiring at the same time that the resulting combined system is regular and of index at most one all results are proved based on a condensed form that can be computed using orthogonal matrix transformations i e transformations that can be implemented in a numerically stable way

reduced order observer design for descriptor systems with unknown inputs a new method for the design of reduced order observers for descriptor systems with unknown inputs is presented the approach is based on the generalized constrained sylvester equation sufficient conditions for the existence of the observer are given

luenberger like interval observer design for discrete time descriptor linear system abstract in this paper the problem of luenberger like interval observer design for discrete time descriptor linear system is investigated in the first place two ways in which the original descriptor system is transformed into general systems are given and the detectability of the equivalent general systems is discussed in detail a new equivalent general system construction is developed and we prove that the detectability can be kept under this new equivalent transformation after this based on the new equivalent general system a luenberger like interval observer is proposed finally two simulation examples are given to demonstrate the correctness and the effectiveness of the proposed interval observer

nice reachability for planar bilinear control systems with applications to planar linear switched systems corrected we consider planar bilinear control systems with measurable controls we show that any point in the reachable set can be reached by a ldquonicerdquo control specifically a control that is a concatenation of a bang arc with either 1 a bang bang control that is periodic after the third switch or 2 a piecewise constant control with no more than two discontinuities under the additional assumption that the bilinear system is positive or invariant for any proper cone we show that the reachable set is spanned by a concatenation of a bang arc with either 1 a bang bang control with no more than two discontinuities or 2 a piecewise constant control with no more than two discontinuities in particular any point in the reachable set can be reached using a piecewise constant control with no more than three discontinuities several known results on the stability of planar linear switched systems under arbitrary switching follow as corollaries of our result we demonstrate this with an example

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

brief energy based control for hybrid port controlled hamiltonian systems in this paper we develop an energy based hybrid control framework for hybrid port controlled hamiltonian systems in particular we obtain constructive sufficient conditions for hybrid feedback stabilization that provide a shaped energy function for the closed loop system while preserving a hybrid hamiltonian structure at the closed loop level furthermore an inverse optimal hybrid feedback control framework is developed that characterizes a class of globally stabilizing energy based controllers that guarantee hybrid sector and gain margins to multiplicative input uncertainty of hybrid hamiltonian systems

lyapunov based hybrid loops for stability and performance of continuous time control systems we construct hybrid loops that augment continuous time control systems we consider a continuous time nonlinear plant in feedback with a possibly non stabilizing given nonlinear dynamic continuous time state feedback controller the arising hybrid closed loops are guaranteed to follow the underlying continuous time closed loop dynamics when flowing and to jump in suitable regions of the closed loop state space to guarantee that a positive definite function v of the closed loop state and or a positive definite function v p of the plant only state is non increasing along the hybrid trajectories sufficient conditions for the construction of these hybrid loops are given for the nonlinear case and then specialized for the linear case with the use of quadratic functions for the linear case we illustrate specific choices of the functions v and v p which allow for the reduction of the overshoot of a scalar output the proposed approaches are illustrated on linear and nonlinear examples

solution examples of an impulse control problem we study an impulse control problem with switching technology in infinite horizon we solve the impulse control problem in case of deterministic impulse times on specific transition kernel examples our objective is to exhibit an optimal strategy which maximizes the value function in these cases

observability and detectability of singular linear systems with unknown inputs in this paper the strong observability and strong detectability of a general class of singular linear systems with unknown inputs are tackled the case when the matrix pencil is non regular is comprised i e more than one solution for the differential equation is allowed it is shown that under suitable assumptions the original problem can be studied by means of a regular non singular linear system with unknown inputs and algebraic constraints thus it is shown that for purposes of analysis the algebraic equations can be included as part of an extended system output based on this analysis we obtain necessary and sufficient conditions guaranteeing the observability or detectability of the system in terms of the zeros of the system matrix corresponding algebraic conditions are given in order to test the observability and detectability a formula is provided that expresses the state as high order derivative of a function of the output which allows for the reconstruction of the actual state vector it is shown that the unknown inputs may be reconstructed also

cryptographically resilient functions this correspondence studies resilient functions which have applications in fault tolerant distributed computing quantum cryptographic key distribution and random sequence generation for stream ciphers we present a number of new methods for synthesizing resilient functions an interesting aspect of these methods is that they are applicable both to linear and nonlinear resilient functions our second major contribution is to show that every linear resilient function can be transformed into a large number of nonlinear resilient functions with the same parameters as a result we obtain resilient functions that are highly nonlinear and have a high algebraic degree

lqr optimization of linear system switching considers offline optimization of a switching sequence for a given finite set of linear control systems together with joint optimization of control laws a linear quadratic full information criterion is optimized and dynamic programming is used to find an optimal switching sequence and control law the main result is a method for efficient pruning of the search tree to avoid combinatoric explosion a method to prove optimality of a found candidate switch sequence and corresponding control laws is presented

brief paper state and input observability for structured linear systems a graph theoretic approach this paper deals with the state and input observability analysis for structured linear systems with unknown inputs the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure using a particular decomposition of the systems into two subsystems we express in simple graphic terms necessary and sufficient conditions for the generic state and input observability these conditions are easy to check because they are based on comparison of integers and on finding particular subgraphs in a digraph therefore our approach is suited to study large scale systems

universal computation and other capabilities of hybrid and continuous dynamical systems we explore the simulation and computational capabilities of hybrid and continuous dynamical systems the continuous dynamical systems considered are ordinary differential equations odes for hybrid systems we concentrate on models that combine odes and discrete dynamics e g finite automata we review and compare four such models from the literature notions of simulation of a discrete dynamical system by a continuous one are developed we show that hybrid systems whose equations can describe a precise binary timing pulse exact clock can simulate arbitrary reversible discrete dynamical systems defined on closed subsets of r n the simulations require continuous odes in ir2n with the exact clock as input all four hybrid systems models studied here can implement exact clocks we also prove that any discrete dynamical system in rn can be simulated by continuous odes in rt2n 1 we use this to show that smooth odes in ri3 can simulate arbitrary turing machines and hence possess the power of universal computation we use the famous asynchronous arbiter problem to distinguish between hybrid and continuous dynamical systems we prove that one cannot build an arbiter with devices described by a system of lipschitz odes on the other hand all four hybrid systems models considered can implement arbiters even if their odes are lipschitz

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

quasi variational inequalities with dirichlet boundary condition related to exit time problems for impulse control we study degenerate elliptic quasi variational inequalities with dirichlet boundary condition which are related to the value function of the exit time problem for stochastic impulse control by means of the dynamic programming principle the boundary condition in the viscosity solutions sense does not identify a unique solution because in this nonlocal problem the boundary layer gives rise to a loss of information also at the interior points the eventual discontinuities of solutions at the boundary of the domain play an essential role and cannot be removed therefore we superimpose a selection criterion which enforcing the information coming from the boundary datum picks up the value function among all possible viscosity solutions as a result we attain the continuity of the value function up to the boundary in addition we produce a monotone iterative scheme approximating the value function

a numerical method for a class of mixed switching and impulsive optimal control problems in this paper we consider a class of optimal control problems in which the dynamical system involves both switching and impulsive controls the number of switching times are supposed to be finite and without loss of generality to occur together with the impulses we show that this class of optimal control problems is equivalent to a special class of optimal parameter selection problems the gradient formulae for the cost functional and the constraint functional are derived on this basis the control parameterization is shown to be applicable for numerical solution a numerical example is solved for illustration

quasi variational inequalities and first order hamilton jacobi equations on considere des inegalites quasi variationnelles de hamilton jacobi dans r n on introduit pour ce probleme la notion de solution viscosite

unknown input functional observability of descriptor systems with neutral and distributed delay effects in this paper a general class of linear systems with time delays is considered which includes linear classical systems linear systems with commensurate delays neutral systems and singular systems with delays after given a formal definition of functional backward observability bo an easily testable condition is found the fulfillment of the obtained condition allows for the reconstruction of the trajectories of the system under consideration using the actual and past values of the system output and some of its derivatives the methodology we follow consists in an iterative algorithm based upon the classical silverman algorithm used for inversion of linear systems by using basic module theory we manage to prove that the proposed algorithm is convergent a direct application of studying functional observability is that a condition can be derived for systems with distributed delays also we do this as a case of study the obtained results are illustrated by two examples one is merely academic but illustrates clearly the kind of systems which the proposed methodology works for and the other is a practical system with distributed delays

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

robust observer design for unknown inputs takagi sugeno models this paper deals with the observer design for takagi sugeno t s fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system sufficient conditions to design an unknown input t s observer are given in linear matrix inequality lmi terms both continuous time and discrete time cases are studied relaxations are introduced by using intermediate variables extension to the case of unmeasured decision variables is also given a numerical example is given to illustrate the effectiveness of the given results

interval observer for a class of uncertain nonlinear singular systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantee the existence of a luenberger like observer for the general system

optimal control of switching time in switched stochastic systems with multi switching times and different costs abstractin this paper we solve an optimal control problem for a class of time invariant switched stochastic systems with multi switching times where the objective is to minimise a cost functional with different costs defined on the states in particular we focus on problems in which a pre specified sequence of active subsystems is given and the switching times are the only control variables based on the calculus of variation we derive the gradient of the cost functional with respect to the switching times on an especially simple form which can be directly used in gradient descent algorithms to locate the optimal switching instants finally a numerical example is given highlighting the validity of the proposed methodology

linear codes from perfect nonlinear mappings and their secret sharing schemes in this paper error correcting codes from perfect nonlinear mappings are constructed and then employed to construct secret sharing schemes the error correcting codes obtained in this paper are very good in general and many of them are optimal or almost optimal the secret sharing schemes obtained in this paper have two types of access structures the first type is democratic in the sense that every participant is involved in the same number of minimal access sets in the second type of access structures there are a few dictators who are in every minimal access set while each of the remaining participants is in the same number of minimal access sets

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

filtering and fault estimation of descriptor switched systems in this paper the problems of state and fault estimation are addressed for a class of switched descriptor systems subject to lipschitz nonlinearities and unknown inputs ui the ui appear both on the dynamic and on the measurement equations two problems are addressed by l 2 gain minimization with the use of switched lyapunov functions and formulated by lmi first a functional observer for switched lipschitz nonlinear descriptor system is proposed for robust state estimation second fault estimation is performed by filtering the output estimation error as usually done in the residual generation framework moreover frequency weighting functions can be used to shape the response to the fault and thus improve the estimation

non linear impulsive dynamical systems part ii stability of feedback interconnections and optimality in a companion paper nonlinear impulsive dynamical systems part i stability and dissipativity lyapunov and invariant set stability theorems and dissipativity theory were developed for non linear impulsive dynamical systems in this paper we build on these results to develop general stability criteria for feedback interconnections of non linear impulsive systems in addition a unified framework for hybrid feedback optimal and inverse optimal control involving a hybrid non linear non quadratic performance functional is developed it is shown that the hybrid cost functional can be evaluated in closed form as long as the cost functional considered is related in a specific way to an underlying lyapunov function that guarantees asymptotic stability of the non linear closed loop impulsive system furthermore the lyapunov function is shown to be a solution of a steady state hybrid hamilton jacobi bellman equation

path following for nonlinear systems with unstable zero dynamics in the path following problem formulated in this note it is required that the error between the system output and the desired geometric path eventually be less than any prespecified constant if in a nonlinear multiple input multiple output mimo system the output derivatives do not enter into its zero dynamics a condition relating path geometry and stabilizability of the zero dynamics is given under which a solution to this problem exists the solution is obtained by combining input to state stability and hybrid system methodologies

deterministic impulse control problems we prove that the optimal cost function of a deterministic impulse control problem is the unique viscosity solution of a first order hamilton jacobi quasi variational inequality in mathbb r n