new results on composite control of singularly perturbed uncertain linear systems abstract we consider the problem of stabilizing uncertain singularly perturbed linear time varying systems whose fast dynamics can be unstable we propose a class of nonlinear composite controllers which assure global uniform ultimate boundedness of the trajectories of the closed loop system provided the singular perturbation parameter is sufficiently small these controllers consist of a fast controller which stabilizes the fast dynamics and a slow controller which yields the desired stability properties for the slow dynamics we consider the structure of the fast controller to be simpler than structures previously proposed in the literature to obtain these controllers we first develop some new results for singularly perturbed systems under output feedback in particular it is shown that the matching assumption which deals with the manner in which the uncertainties enter the system and is made on the reduced order system is invariant under linear feedback of the fast variable

balancing for a class of non linear singularly perturbed systems in this work a balancing method is investigated for a class of non linear singularly perturbed systems the main result presented here shows that the well known two stages strategy used with singular perturbations in control theory can be extended to compute a balancing form of non linear singularly perturbed systems so an approximate balancing form is derived from the balancing forms of the slow and fast subsystems both computed separately this two stage method avoids the difficult task of solving high dimensional and ill conditioned hamilton jacobi equations due to the presence of the small singular perturbation parameter

multivariable circle criteria for multiparameter singularly perturbed systems a direct approach to the lur e problem for singularly perturbed systems sps is proposed in contrast to previous results the feedback connection between the linear and nonlinear parts of sps is allowed to depend essentially on both the slow and the fast variables the lur e problem for multiparameter sps is studied by the same framework

robust stabilization of singularly perturbed systems abstract we discuss the problem of designing stabilizing controllers for singularly perturbed systems on the basis of simplified models in 1 it was shown that a constant gain output feedback controller designed on the basis of the simplified model need not stabilize the true system containing both fast and slow modes this phenomenon was then expanded to include the case where the simplified system is strictly proper in 2 the objectives of this note are threefold i to show that given any proper system and any stabilizing controller for it that is proper but not strictly proper there exists a singular perturbation of the system that is destabilized by that controller ii to show that any strictly proper controller for a singularly perturbed system designed on the basis of a reduced order model will stabilize the true system for sufficiently small values of the fast dynamics parameter and iii to provide a characterization in the same spirit as 3 4 of the set of all strictly proper controllers that stabilize a given proper plant by combining these results it is possible to generate the class of all robustly stabilizing controllers for a given singularly perturbed system

the guaranteed cost control problem of uncertain singularly perturbed systems abstract in this paper we study the algebraic riccati equation corresponding to the guaranteed cost control theory for an uncertain singularly perturbed system the construction of the controller involves solving the full order algebraic riccati equation with small parameter e under control oriented assumptions we first provide the sufficient conditions such that the full order algebraic riccati equation has a positive semi definite stabilizing solution next we propose an iterative algorithm based on the kleinman algorithm to solve the algebraic riccati equation which depends on the parameter e our new idea is to use the solutions of the reduced order algebraic riccati equations for the initial condition by using the iterative algorithm we can easily obtain a required solution of the algebraic riccati equation moreover using the initial conditions without e we show that there exists an e such that the proposed algorithm has quadratic convergence finally in order to show the effectiveness of the proposed algorithm numerical examples are included

a further note on the robustness of output feedback control methods to modeling errors in an earlier note it was shown that designing a nonstrictly proper output feedback compensator using a model that neglects parasitic elements might lead to an unstable closed loop system even when the neglected modes are asymptotically stable the purpose of this note is to show that this instability phenomenon might take place even when the reduced order design model is strictly proper

numerical study of the langevin theory for fixed energy sandpiles the recently proposed langevin equation aimed to capture the relevant critical features of stochastic sandpiles and other self organizing systems is studied numerically the equation is similar to the reggeon field theory describing generic systems with absorbing states but it is coupled linearly to a second conserved and static nondiffusive field it has been claimed to represent a different universality class including different discrete models the manna as well as other sandpiles reaction diffusion systems etc in order to integrate the equation and surpass the difficulties associated with its singular noise we follow a numerical technique introduced by dickman our results coincide remarkably well with those of discrete models claimed to belong to this universality class in one two and three dimensions this provides a strong backing for the langevin theory of stochastic sandpiles and to the very existence of this meagerly understood universality class

integration of langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions efficient and accurate integration of stochastic partial differential equations with multiplicative noise can be obtained through a split step scheme which separates the integration of the deterministic part from that of the stochastic part the latter being performed by sampling exactly the solution of the associated fokker planck equation we demonstrate the computational power of this method by applying it to the most absorbing phase transitions for which langevin equations have been proposed this provides precise estimates of the associated scaling exponents clarifying the classification of these nonequilibrium problems and confirms or refutes some existing theories

near optimal output feedback regulation of ill conditioned linear systems a two time scale approximation for the linear quadratic optimal output feedback regulator program is examined necessary conditions for optimality as well as an algorithm for computing locally near optimal gains are derived if it is assumed that the slow and fast subsystem initial conditions are uniformly distributed optimal gains for the two time scale problem provide a second order approximation to optimal closed loop performance in the unperturbed system this is verified with a numerical example

composite control of a singularly perturbed uncertain system with slow non linearities a practical stability controller for a class of non linear singularly perturbed uncertain dynamical systems is designed using the composite control technique the class of systems considered has non linearities that depend upon the slow dynamics of the system the system is uncertain in the slow dynamics as only a nominal slow behaviour is assumed to be known together with some bound on the non linearities the controller guarantees practical stability in the sense that it drives the state of the system in a sufficiently small neighbourhood of the origin

new iterative algorithm for algebraic riccati equation related to h sub spl infin control problem of singularly perturbed systems we present the solution to the algebraic riccati equation are with indefinite sign quadratic term related to the h sub spl infin control problem for singularly perturbed systems by means of a kleinman type algorithm the resulting algorithm is very efficient from the numerical point of view because the are is solvable even if the quadratic term has an indefinite sign moreover the resulting iterative algorithm is quadratically convergent we also present an algorithm for solving the generalized algebraic lyapunov equation on the basis of the fixed point algorithm

robust model tracking control for a class of nonlinear plants we propose a new model following control scheme for a class of nonlinear plants the feedback control signal is a continuous function of all its arguments it is shown that this scheme guarantees that tracking error remains bounded and tends to a neighborhood of the origin with a rate not inferior to an exponential one furthermore it allows the designer to arbitrarily prescribe the rate of convergence and the size of the set of ultimate boundedness

asymptotic expansions for game theoretic riccati equations and stabilization with disturbance attenuation for singularly perturbed systems abstract if the systems to be controlled are singularly perturbed then the riccati equations which appear in h problems are difficult to solve due to the presence of the small parameter the present paper describes and validates asymptotic expansions showing how they may be used in h control furthermore we construct a composite controller based on the solution of slow and fast problems which guarantees a desired achievable performance level for the full order plant as e approaches zero

on the robustness of output feedback control methods to modeling errors singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time invariant systems the effect of designing the control strategy using a model that neglects unknown parasitic elements is considered it is shown that such a strategy may in general be destabilizing even when the neglected modes are asymptotically stable special structures that will not permit this situation and will guarantee asymptotic stability are illustrated

feedback control of two time scale nonlinear systems this article concerns a class of two time scale single input single output nonlinear systems for such systems combination of singular perturbation and geometric methods is employed to synthesize well conditioned static state feedback laws that induce a well characterized input output behaviour and guarantee stability of the closed loop system the developed control laws are applied to two nonlinear chemical processes with time scale multiplicity and their performance is evaluated through simulations

absorbing phase transition in contact process on fractal lattices abstract we investigate the critical behavior of nonequilibrium phase transition from an active phase to an absorbing state on two selected fractal lattices i e on a checkerboard fractal and on a sierpinski carpet the checkerboard fractal is finitely ramified with many dead ends while the sierpinski carpet is infinitely ramified we measure various critical exponents of the contact process with a diffusion reaction scheme a aa and a 0 characterized by a spreading with a rate and an annihilation with a rate and the results are confirmed by a crossover scaling and a finite size scaling the exponents compared with the expansion results assuming 4 d f d f being the fractal dimension of the underlying fractal lattice exhibit significant deviations from the analytical results for both the checkerboard fractal and the sierpinski carpet on the other hand the exponents on a checkerboard fractal agree well with the interpolated results of the regular lattice for the fractional dimensionality while those on a sierpinski carpet show marked deviations

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

singular perturbations and input to state stability this paper establishes a type of total stability for the input to state stability property with respect to singular perturbations in particular if the boundary layer system is uniformly globally asymptotically stable and the reduced system is input to state stable with respect to disturbances then these properties continue to hold up to an arbitrarily small offset for initial conditions disturbances and their derivatives in an arbitrarily large compact set as long as the singular perturbation parameter is sufficiently small

on damage spreading transitions we study the damage spreading transition in a generic one dimensional stochastic cellular automaton with two inputs domany kinzel model using an original formalism for the description of the microscopic dynamics of the model we are able to show analytically that the evolution of the damage between two systems driven by the same noise has the same structure as a directed percolation problem by means of a mean field approximation we map the density phase transition into the damage phase transition obtaining a reliable phase diagram we extend this analysis to all symmetric cellular automata with two inputs including the ising model with heat bath dynamics

near optimal control of linear multiparameter singularly perturbed systems in this note the linear quadratic optimal control for multipa rameter singularly perturbed systems is studied the attention is focused on the design of a new near optimal controller the resulting controller achieves approximation of the optimal cost the proposed algorithm has been numerically tested on a real physical example and pro duced useful results

robust semiglobally practical stabilization for nonlinear singularly perturbed systems in this work the problem of semiglobally practical stabilization is considered for nonlinear singularly perturbed systems with unknown parameters the composite lyapunov function for the full systems is established by both that of the slow subsystem and the boundary layer system a state feedback control law for the linear part of the slow subsystem and boundary layer system is proposed which renders the whole closed loop system semiglobally stable the upper bound expression of e is given to obtain the condition of asymptotic stability for the system a simulation example is given to demonstrate the effectiveness and feasibility of the controller

phase structure of systems with infinite numbers of absorbing states critical properties of systems exhibiting phase transitions into phases with infinite numbers of absorbing states are studied we analyze a non markovian langevin equation recently proposed to describe the critical behavior of such systems and also introduce and study a non markovian discrete model which is argued to present the same critical features on the basis of mean field analysis monte carlo simulations and theoretical arguments we conclude that the phenomenology of the non markovian models closely parallels that of systems with many absorbing states in one and two dimensions the bulk or static critical properties of these systems fall in the directed percolation dp universality class by contrast the critical properties associated with the spread of an initially localized seed exhibit a more complex behavior depending on parameter values they can both in one and two dimensions fall either in the dynamical percolation or dp universality class or else exhibit apparently nonuniversal exponents in contrast to previous results however the nonuniversal exponents in 2d are found to satisfy a scaling law which implies that a particular linear combination of them is universal and assumes dp values these results demonstrate the efficacy of the non markovian approach for understanding systems with many absorbing states which are difficult to analyze in their original microscopic formulation

monadic extensions of institutions in this paper we show how partially ordered monads can be used to provide a non classical extension of institutions and entailment systems as appearing in the framework of general logics general logics is an axiomatization of a general framework for logics this framework builds upon traditional power sets of sentences as appearing in satisfaction relations and entailment the underlying power set monad is implicit and the utility of a monadic machinery was therefore not explored making the use of the power set monad more explicit in the satisfaction and entailment relations opens up possibilities to experiment with various non classical representations of sentences as appearing in inference these representations are enabled by partially ordered monads where the partial order attached to the underlying set functor is essential for extending the axiomatization

robust disturbance attenuation with stability for a class of uncertain singularly perturbed systems in this paper the problem of robust stability and robust disturbance attenuation is investigated for a class of singularly perturbed linear systems with norm bounded parameter uncertainties in both state and output equations based on the slow and fast subsystems a composite linear controller is designed such that both robust stability and a prescribed h infinity performance for the full order system are achieved irrespective of the uncertainties our results show that the above problem can be converted to an h infinity control problem for a related singularly perturbed linear system without parameter uncertainty thus the existing results on h infinity control of singularly perturbed systems can be applied to obtain solutions to the problem of robust h infinity control for the uncertain systems which is independent of the singular perturbation epsilon when epsilon is sufficiently small an example is given to show the potential of the proposed technique

h sub 2 guaranteed cost control for singularly perturbed uncertain systems the h sub 2 guaranteed cost control problem for a singularly perturbed norm bounded uncertain system is addressed using the quadratic stabilizability framework after defining the corresponding slow and fast uncertain subsystems the set of quadratic stabilizing composite controls is characterized two riccati equations have to be solved one for the slow subsystem and the other for the fast subsystem choosing appropriately the weighting matrices it is shown how to pick up in the set of quadratic stabilizing composite controls a control minimizing an upper bound on the h sub 2 norm of a certain transfer matrix the case of the guaranteed cost control problem for the reduced system is also investigated

delay dependent guaranteed cost stabilization criterion for neutral delay differential systems matrix inequality approach abstract in this paper we address the problem of the guaranteed cost stabilization for a class of neutral delay differential systems with a given quadratic cost function based on the lyapunov method delay dependent criteria which are expressed in terms of matrix inequalities are proposed to guarantee the asymptotic stability of the system the matrix inequalities can be easily solved by various efficient optimization algorithms

a new approach to robust guaranteed cost control for uncertain multimodeling systems the guaranteed cost control problem for multimodeling systems with norm bounded uncertainty is investigated the main contribution in this paper is that a new independent controller is derived by solving the reduced order slow and fast algebraic riccati equations ares whose dimension is smaller than the dimension of full order multiparameter algebraic riccati equation mare it is shown that if these ares have a positive definite stabilizing solution then the closed loop system is quadratically stable and has the cost bound

robust semi global output tracking for nonlinear singularly perturbed systems in this work a robust controller design methodology for a broad class of singularly perturbed nonlinear systems with time varying uncertainties is developed when the fast subsystem is stabilizable and the slow subsystem is input output linearizable with input to state stable iss inverse dynamics the developed state feedback controller guarantees boundedness of the trajectories of the closed loop system and robust output tracking with arbitrary degree of asymptotic attenuation of the effect of uncertainty on the output for initial conditions and uncertainties in an arbitrarily large compact set so long as the singular perturbation parameter is sufficiently small the controller is a continuous function of the state of the system and its construction requires the knowledge of bounding functions on the size of uncertainty the developed method is applied to a non isothermal continuous stirred tank reactor with fast jacket dynamics

bibo stabilization of time delayed system with nonlinear perturbation time delayed control system with the nonlinear perturbation is considered novel bibo stabilization criteria are established by the lyapunov functional and formulated in terms of existence of a positive definite solution to an auxiliary algebraic riccati matrix equation the robust quadratic stability for such systems is also discussed a numerical example is given to illustrate the effectiveness of our result

brief paper h control for singularly perturbed systems this paper derives a set of e independent sufficient and necessary conditions for the h control problem for singularly perturbed systems in a different approach from previous ones a sub optimal controller is explicitly constructed we observe that the controller is also singularly perturbed with its fast slow part being an h sub optimal controller for the fast slow sub system of the original system respectively e independent h controller design is also considered the main contribution of this paper is that our results apply to both standard and non standard singularly perturbed systems

sticky grains do not change the universality class of isotropic sandpiles we revisit the sandpile model with sticky grains introduced by mohanty and dhar phys rev lett 89 104303 2002 whose scaling properties were claimed to be generically in the universality class of directed percolation for both isotropic and directed models while for directed models this conclusion is unquestionable for isotropic models we present strong evidence that the asymptotic scaling in the self organized regime in which a stationary critical state exists in the limit of slow driving and vanishing dissipation rate is like other stochastic sandpiles generically in the manna universality class this conclusion is drawn from extensive monte carlo simulations and is strengthened by the analysis of the langevin equations proposed by the same authors to account for this problem argued to converge upon coarse graining to the well established set of langevin equations for the manna class

fuzzy terms in this paper we will show how purely categorical constructions of terms are advantageous when investigating situations concerning uncertainty more specifically where uncertainty comes from and how uncertainty is integrated when dealing with terms over selected signatures there are basically two ways of invoking uncertainty for terms on one hand we may proceed by building composed monads where uncertainty is provided by some suitable monad composed with the traditional term monad on the other hand we can provide a strictly formal basis for term monads being created over categories themselves carrying uncertainty this is the distinction between computing with fuzzy and fuzzy computing and the fundamental question raised by these constructions is where uncertainty resides in language constructions for logic this paper also shows how the notion of signature often needs to be expanded to levels of signatures in particular when dealing with type constructors such levels allow us to strictly delineate e g primitive operations type terms and value level terms levels of signature will in this paper be exemplified by the construction of the signature of simply typed lambda calculus

simulation of spatial systems with demographic noise the demographic shot noise in population dynamics scales with the square root of the population size this process is very important as it yields an absorbing state at zero field but simulating it especially on spatial domains is a nontrivial task here we analyze two similar methods that were suggested for simulating the corresponding langevin equation one by pechenik and levine and the other by dornic chate and munoz dcm these methods are based on operator splitting techniques and the essential difference between them lies in which terms are bundled together in the splitting process both these methods are first order in the time step so one may expect that their performance will be similar we find surprisingly that when simulating the stochastic ginzburg landau equation with two deterministic metastable states the dcm method exhibits two anomalous behaviors first the stochastic stall point moves away from its deterministic counterpart the maxwell point when decreasing the noise second the errors induced by the finite time step are larger by a significant factor i e 10 in the dcm method we show that both these behaviors are the result of a finite time step induced shift in the deterministic maxwell point in the dcm method due to the particular operator splitting employed in light of these results care must be exercised when computing quantities like phase transition boundaries as opposed to universal quantities such as critical exponents in such stochastic spatial systems

numerical study of a field theory for directed percolation a numerical method is devised for the study of stochastic partial differential equations describing directed percolation the contact process and other models with a continuous transition to an absorbing state owing to the heightened sensitivity to fluctuations attending multiplicative noise in the vicinity of an absorbing state a useful method requires discretization of the field variable as well as of space and time when applied to the field theory for directed percolation in 1 1 dimensions the method yields critical exponents which compare well against accepted values

powersets of terms and composite monads composing various powerset functors with the term monad gives rise to the concept of generalized terms this in turn provides a technique for handling many valued sets of terms in a framework of variable substitutions thus being the prerequisite for categorical unification in many valued logic programming using an extended notion of terms as constructions of monads involve complicated calculations with natural transformations proofs are supported by a graphical approach that provides a useful tool for handling various conditions such as those well known for distributive laws

institutional semantics for many valued logics we develop many valued logic including a generic abstract model theory over a fully abstract syntax we show that important many valued logic model theories such as traditional first order many valued logic and fuzzy multi algebras may be conservatively embedded into our abstract framework our development is technically based upon the so called theory of institutions of goguen and burstall and may serve as a template for defining at hand many valued logic model theories over various concrete syntaxes or from another perspective to combine many valued logic with other logical systems we also show that our generic many valued logic abstract model theory enjoys a couple of important institutional model theory properties that support the development of deep model theory methods

optimal control for a new class of singularly perturbed linear systems singularly perturbed linear control systems have been traditionally studied with one vector input that controls both the slow and fast state variables motivated by examples of real physical systems in this paper we extend the study to corresponding two vector input systems we have identified several classes of real physical singularly perturbed systems that can be more efficiently controlled using two vector inputs in such systems one vector input is used to control the slow state space variables and the other vector input is used to control the fast state variables this control structure offers more flexibility controlling given systems and appears to be more effective we study the linearquadratic regulator lqr problem for this new class of singularly perturbed systems and develop a numerical algorithm based on fixed point iterations to obtain its solution the latter is obtained in terms of reduced order sub problems which avoid possible numerical stiffness issues and are computationally advantageous for large scale systems

robust stability of singularly perturbed systems the robust stability problem of linear time invariant singularly perturbed systems is discussed where the system matrix may have a parameter perturbation bounded by the h norm a sufficient condition for the upper bound of e is given such that the stability of the actual system or the full order model can be inferred from the analysis of the reduced order system or the slow model in separate time scales

asymptotic expansions and a new numerical algorithm of the algebraic riccati equation for multiparameter singularly perturbed systems abstract in this paper we study a continuous time multiparameter algebraic riccati equation mare with an indefinite sign quadratic term the existence of a unique and bounded solution of the mare is newly established we show that the kleinman algorithm can be used to solve the sign indefinite mare the proof of the convergence and the existence of the unique solution of the kleinman algorithm is done by using the newton kantorovich theorem furthermore we present new algorithms for solving the generalized multiparameter algebraic lyapunov equation gmale by means of the fixed point algorithm

compensation of measurable disturbances for two time scale nonlinear systems this paper deals with a class of two time scale nonlinear systems with time varying disturbances modeled within the framework of singular perturbations systems in both standard and nonstandard form are considered for these systems we synthesize well conditioned control laws that utilize feedback of the full state vector and feedforward compensation of disturbances to exponentially stabilize the fast dynamics and enforce a pre specified input output behavior independently of the disturbances in the closed loop slow subsystem singular perturbation methods are employed to establish that the discrepancy between the output of the closed loop full order system and the output of the closed loop slow subsystem is proportional to the value of the singular perturbation parameter the stability of the closed loop system is analyzed using lyapunov s direct method and precise conditions that guarantee boundedness of the trajectories for sufficiently small values of the singular perturbation parameter are derived the application of the developed methodology is illustrated through a catalytic continuous stirred tank reactor example modeled as a singularly perturbed system in nonstandard form

guaranteed cost stabilization of neutral differential systems with parametric uncertainty in this paper we address the problem of the guaranteed cost stabilization for a class of neutral systems with parametric uncertainties and a given quadratic cost function the parametric uncertainties are real time varying norm bounded and state delay is a constant the problem is to design the state feedback control laws such that the closed loop system is asymptotically stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainty and delay two criteria for the existence of such controllers are derived based on the matrix inequality approach combined with the lyapunov method the developed guaranteed cost controllers can be synthesized in terms of the feasible solutions to the certain matrix inequalities

robust stability of two time scale systems with nonlinear uncertainties this note is concerned with the robust stability problem of uncertain two time scale systems where the only information available for system uncertainties is their norm upper bounds the stability bound spl epsiv sup is derived via a state transformation and the constructive use of a lyapunov function finally examples are given to illustrate the applications of the proposed results