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

stabilization and regulation of nonlinear singularly perturbed systems composite control for a general class of nonlinear singularly perturbed systems a two time scale analysis and design procedure for stabilization and regulation is presented it is shown that under a set of conditions the composite control proposed by chow and kokotovic 5 asymptotically stabilizes the desired equilibrium and produces a finite cost j uc which tends to the cost of the slow regulator as the perturbation parameter e tends to zero thus the well posedness of the full regulator problem is established furthermore under different stability requirements on the fast subsystem explicit upper and lower bounds on j uc are obtained finally for each result in this paper an upper bound on the perturbation parameter e is provided under which the result is valid

lmi based designs for robust state and output derivative feedback guaranteed cost controllers in reciprocal state space form in some practical problems state derivative variables are more easily obtained than state variables solution of guaranteed cost control problem using derivative feedback for continuous linear ti

pareto optimal strategy for stochastic weakly coupled large scale systems with state dependent system noise this note is concerned with the decentralized infinite horizon stochastic pareto optimal static output feedback strategy for a class of weakly coupled systems with state dependent noise first pareto optimal control problems are formulated using a static output feedback strategy the necessary conditions are given by the cross coupled stochastic algebraic riccati type equations csares for proving the existence of the static output feedback strategy that minimizes the quadratic cost function after determining the asymptotic structure of the solutions of the csares a new sequential numerical algorithm and newton s method for solving the csares are described the resulting numerical solution is used to develop the pareto optimal strategy finally the efficiency of the proposed algorithm is demonstrated by solving a numerical example for a practical megawatt frequency control problem

near optimum steady state regulators for stochastic linear weakly coupled systems abstract this paper presents an approach to the decomposition and approximation of the linear quadratic gaussian estimation and control problems for weakly coupled systems the global kalman filter is decomposed into separate reduced order local filters via the use of a decoupling transformation a near optimal control law is derived by approximating the coefficients of the truly optimal control law the order of approximation of the optimal performance is o en where n is the order of approximation of the coefficients a real world power system example demonstrates the failure of o e2 and o e4 approximations and the necessity for the existence of the o en theory the proposed method produces the reduction in both off line and on line computational requirements and leads to convergence under mild assumptions in addition only low order systems are involved in algebraic calculations and no analyticity requirement a standard assumption for the power series method is imposed on system coefficients

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

improving stability of mps method by a computational scheme based on conceptual particles abstract excessive pressure oscillation and particle clustering are two obstacles that limit the computational stability of the moving particle semi implicit mps method specifically particles on free surfaces are assumed to have zero pressure and not involved in the solution of the pressure poisson equation the zero pressure tends to drive these surface particles to form clusters the inaccurate distance assessment between these clustered particles would result in incorrect particle number density and an ill pressure poisson equation leading to an unstable computation in this paper a computational scheme based on conceptual particles is proposed to replace the widely adopted surface detection techniques in the enforcement of the dirichlet boundary condition unlike traditional ghost particles conceptual particles are the only concept which is introduced to complement the calculation of the particle number density this leads to a new discretization of the pressure poisson equation and a new framework of the mps method nsd mps which requires no information about the positions of the conceptual particles the effectiveness of the nsd mps method is demonstrated by three verification examples the demonstrated advantages include 1 pressure oscillation suppressed in both spatial and time domains 2 uniform pressure distribution on free surfaces and 3 minimized clustering of surface particles

enhancement of stability and accuracy of the moving particle semi implicit method as a lagrangian gridless particle method the mps moving particle semi implicit method has been proven useful in a wide range of engineering applications up to now most of mps applications have been limited to problems with compressive stress states this paper investigates the performance and stability of mps method in simulation of more general hydrodynamic problems including those characterized by tensile stresses or by changes in the stress states it is shown that mps based simulations are prone to become destabilized in presence of attractive interparticle forces this instability appears to be similar to the so called tensile instability in sph method two new modifications namely a modified poisson pressure equation and a corrective matrix for pressure gradient model are proposed to resolve this shortcoming these two new modifications together with two previously proposed improvements are shown to stabilize and enhance the performance of mps method

robustness of dynamic output feedback control for singular perturbation systems abstract the problem of the robustness of dynamic output feedback control for singular perturbation systems is investigated the solution to this problem is reduced to the simultaneous design of static output feedback controllers for the fast subsystem and the so called auxiliary system of the slow subsystem some conditions are proposed to ensure the robustness of the actual closed loop system the exact upper bound of the parasitic parameter for the controlled system is also determined finally an actual model which failed in dynamic output feedback control in 4 is reexamined successfully here

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

a sampled data control scheme for stabilization of systems with unmodeled high frequency dynamics the output feedback stabilization problem is considered for linear sampled data control systems in the presence of unmodeled high frequency dynamics sufficient conditions for stabilization of such systems were given by m vidyasagar 1985 for strictly proper systems this paper extends the class of systems in order to include the proper systems case and proposes a conceptually novel digital control scheme in this scheme the control law based on the reduced order system is applied to the full system only during a short fraction of the sampling period during the second part of the sampling period the control is taken equal to zero such that without control the neglected fast states have sufficient time to converge to their equilibrium point

a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

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

a new stable compensator design for exact and approximate loop transfer recovery abstract in this paper a new compensator structure for loop transfer recovery ltr is proposed the proposed compensator a is open loop stable b guarantees closed loop stability and above all c requires much smaller values of gain than the conventional observer based controller for the same degree of loop transfer recovery the fact that the new compensator requires much smaller values of gain than the conventional controller results in several practical advantages the most important among them being the reduction in controller band width and freedom from the woes of saturation the trade off between the value of gain and the degree of loop transfer recovery as well as the bounds on singular values of sensitivity and complementary sensitivity functions is shown clearly both full and reduced order compensators for ltr when the design specifications are reflected either at the input or at the output point of the given plant are considered numerical examples illustrate the advantages of the new compensator structure the new compensator structure is inspired by a careful and clear understanding of how loop transfer recovery occurs when conventional observer based controllers are used to motivate and deduce our new compensator structure a unified treatment of observer theory for ltr is presented in the context of such a unification some new results are also given

solving the matrix differential riccati equation a lyapunov equation approach in this technical note we investigate a solution of the matrix differential riccati equation that plays an important role in the linear quadratic optimal control problem unlike many methods in the literature the approach that we propose employs the negative definite anti stabilizing solution of the matrix algebraic riccati equation and the solution of the matrix differential lyapunov equation an illustrative numerical example is provided to show the efficiency of our approach

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

the recursive reduced order numerical solution of the singularly perturbed matrix differential riccati equation under stability observability conditions imposed on a singularly perturbed system an efficient numerical method for solving the corresponding matrix differential riccati equation is obtained in terms of the reduced order problems the order reduction is achieved via the use of the chang transformation applied to the hamiltonian matrix of a singularly perturbed linear quadratic control problem an efficient numerical recursive algorithm with a quadratic rate of convergence is developed for solving the algebraic equations comprising the chang transformation

a new filtering method for linear singularly perturbed systems in this paper we present a new method which allows complete decomposition of the optimal global kalman filter for linear singularly perturbed systems into pure slow and pure fast local optimal filters both driven by the system measurements the method is based on the exact decomposition of the global singularly perturbed algebraic riccati equation into pure slow and pure fast local algebraic riccati equations an f 8 aircraft example demonstrates the proposed method

on conservation laws of continuum mechanics abstract a unified variational formulation is advanced leading to field equations and conservation laws in general mechanical continua the formulation is applicable to dynamic processes in any medium which admits a lagrangian as a result of the procedure employed physical or canonical momenta emerge on the same level as material momenta the simplicity and transparency of the relations derived is a consequence of strict separation of descriptions in physical and material space which precludes the use of displacement as a field variable one of the results shows that a distinction between field equations or equations of motion and conservation laws is no longer essential and all basic relations are in fact balance laws

robust redesign of adaptive control effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed in the regulation problem global stability properties are no longer guaranteed but a region of attraction exists for exact adaptive regulation the dependence of the region of attraction on unmodeled parasitics is examined first then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties a modified adaptive law is proposed guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking the size of this set depends on design parameters the frequency range of parasitics and the reference input signal characteristics

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

near optimum regulators for stochastic linear singularly perturbed systems this paper presents a new approach to the decomposition and approximation of linear quadratic gaussian estimation and control problems for singularly perturbed systems the kalman filter is decomposed into separate slow mode and fast mode filters via the use of a decoupling transformation a near optimal control law is derived by approximating the coefficients of the optimal control law the order of approximation of the optimal performance is 0 mu n where n is the order of approximation of the coefficients

optimal output feedback regulation with frequency shaped cost functional the theory of optimal output feedback control is extended to a class of quadratic performance measures whose weighting matrices are functions of frequency the incorporation of frequency dependent weighting matrices allows one to emphasise or de emphasise the importance of the variables being penalised over specific bands of frequencies optimization of the frequency shaped performance measure yields optimal compensators that can be more meaningful for certain minimisation problems results are presented for different configurations of frequency shaping feedback control an example is presented to illustrate the usefulness of the design technique

frequency domain results for systems with multiple time scales the mathematical treatment of systems with multiple time scales has traditionally employed the use of singular perturbation theory for differential equations this paper treats such systems from a frequency domain viewpoint previously existing two frequency scale results involving approximation and algebraic characterization are extended in addition an exact frequency scale decomposition is presented

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods

decoupling transformation for weakly coupled linear systems the non singular transformation that completely decouples a weakly coupled linear system under non restrictive conditions is defined the transformation matrices are obtained from two algebraic matrix equations algorithms that efficiently generate solutions to these equations are derived the proposed transformation also completely decouples the corresponding lyapunov matrix differential equation

output feedback control of linear two time scale systems output feedback control of linear time invariant singularly perturbed systems is studied the set of all compensators that stabilize a singularly perturbed system while preserving its two time scale structure is parameterized the parameterization is used to show that any two frequency scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure in this procedure a fast high frequency compensator is designed first to stabilize the fast model of the system then a strictly proper slow low frequency compensator is designed to stabilize a modified slow model the parallel connection of the two compensators forms a two frequency scale stabilizing compensator for the singularly perturbed system

aspects of variational arguments in the theory of elasticity fact and folklore abstract an account of the use of the calculus of variations in elastostatics is given variations of both the independent and dependent variables are used to obtain the equations of balance and natural boundary conditions the meaning and use of the necessary transversality conditions for movable internal or external boundaries are examined satisfaction of the transversality conditions is shown to provide immediate access to the forces that act on such boundaries through a virtual work type argument misconceptions concerning the general form of lagrangian densities for which the field equations are identically satisfied are corrected the complete characterization of such lagrangian densities is shown to lead to methods for realization of a wide class of traction boundary conditions as natural boundary conditions and to a significantly richer class of invariance transformations and associated conservation laws

general transformation for block diagonalization of multitime scale singularly perturbed linear systems in this technical note a general transformation for block diagonalization decoupling of multitime scale singularly perturbed linear systems composed of n subsystems is presented the resulting decoupling corresponds to subsystem time scales and produces n completely independent subsystems operating in different time scales

on output feedback control of singularly perturbed systems we treat the problem of robustness of output feedback controllers with respect to singular perturbations given a singularly perturbed control system whose boundary layer system is exponentially stable and whose reduced order system is exponentially stabilizable via a possibly dynamical output feedback controller we present a sufficient condition which ensures that the system obtained by applying the same controller to the original full order singularly perturbed control system is exponentially stable for sufficiently small values of the perturbation parameter this condition which is less restrictive than those previously given in the literature is shown to be always satisfied when the singular perturbation is due to the presence of fast actuators and or sensors furthermore we show explicitly that in the linear time invariant case if this condition is not satisfied then there exists an output feedback controller which stabilizes the reduced order system but destabilizes the full order system

numerical fixed point solution for near optimum regulators of linear quadratic gaussian control problems for singularly perturbed systems the fixed point method is developed for obtaining an efficient numerical solution of the linear quadratic gaussian problem for singularly perturbed systems it is shown that each iteration step improves the accuracy by an order of magnitude that is the accuracy 0 ek can be obtained by performing only k 1 iterations in addition only low order systems are involved in algebraic manipulations and no analyticity requirements are imposed on the system coefficients

robust stability of systems with integral control a number of necessary and sufficient conditions are derived which must be satisfied by the plant d c gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is stable based on these results the robustness of integral control systems is analyzed i e the family of plants is defined which are stable when controlled with the same integral controller conditions for actuator sensor failure tolerance of systems with integral control are also given finally parallels are drawn between the results of this paper and the bifurcation theory of nonlinear systems

exact decomposition of the algebraic riccati equation of deterministic multimodeling optimal control problems in this paper we show how to exactly decompose the algebraic riccati equations of deterministic multimodeling in terms of one pure slow and two pure fast algebraic riccati equations the algebraic riccati equations obtained are of reduced order and nonsymmetric however their o spl epsiv perturbations where spl epsiv spl par sub spl epsiv 2 sup spl epsiv 1 spl par and spl epsiv sub 1 spl epsiv sub 2 are small positive singular perturbation parameters are symmetric the newton method is perfectly suited for solving the nonsymmetric reduced order pure slow and pure fast algebraic riccati equations since excellent initial guesses are available from their o spl epsiv perturbed reduced order symmetric algebraic riccati equations that can be solved rather easily the proposed decomposition scheme might facilitates new approaches to multimodeling control problems that are conceptually simpler and numerically more efficient than the ones previously used

finite horizon optimal control of singularly perturbed systems a differential lyapunov equation approach in this note we study the finite time horizon optimal control problem for singularly perturbed systems the solution is obtained in terms of the corresponding solution of the algebraic riccati equation and the decomposition of the singularly perturbed differential lyapunov equation into reduced order differential lyapunov sylvester equations an illustrative numerical example is provided to show the efficiency of the proposed approach

on the robustness of sampled data control to unmodeled high frequency dynamics robustness of sampled data control designs to unmodeled high frequency dynamics is studied using singular perturbation theory it is argued that when the plant is preceded by a zero order hold a direct transmission term of the reduced order model which results from neglecting high frequency dynamics should be modeled as a delay element in order to ensure robustness

a contoured continuum surface force model for particle methods a surface tension model is essential to simulate multiphase flows with deformed interfaces this study develops a contoured continuum surface force ccsf model for particle methods a color function that varies sharply across the interface to mark different fluid phases is smoothed in the transition region where the local contour curvature can be regarded as the interface curvature the local contour passing through each reference particle in the transition region is extracted from the local profile of the smoothed color function the local contour curvature is calculated based on the taylor series expansion of the smoothed color function whose derivatives are calculated accurately according to the definition of the smoothed color function two schemes are proposed to specify the smooth radius fixed scheme where 2 r e r e particle interaction radius is assigned to all particles in the transition region and varied scheme where r e and 2 r e are assigned to the central and edged particles in the transition region respectively numerical examples including curvature calculation for static circle and ellipse interfaces deformation of square droplet to a circle 2d and 3d droplet deformation in shear flow and droplet coalescence are simulated to verify the ccsf model and compare its performance with those of other methods the ccsf model with the fixed scheme is proven to produce the most accurate curvature and lowest parasitic currents among the tested methods

bounds on the optimum quadratic cost of structure constrained controllers in this note lower and upper bounds are derived on the quadratic cost of optimal output feedback controllers subject to constraints on the controller structure the use of these bounds in forming a comparative assessment of alternative controller confugurations is described and an illustrative example is given the principal advantage of these bounds arises from the fact that they can save considerable computational effort

stabilization and smoothing of pressure in mps method by quasi compressibility in this paper a method to stabilize simulations and suppress the pressure oscillation in moving particle semi implicit method for an incompressible fluid is presented to make the pressure smooth in terms of both of space and time a new representation of the incompressible condition is proposed the incompressible condition consists of two parts the divergence free condition and the particle number density condition the divergence free condition has the effect of making the pressure smooth in terms of both space and time the particle number density condition is necessary to keep the fluid volume constant in this work the quasi compressibility is also introduced for stabilization a dam break is simulated more stably and the space distribution and the time variation of pressure are evaluated more smoothly than the traditional method moreover surface particles are detected more accurately nevertheless the proposed method is computationally cheaper some simulations such as a fluid structure interaction are supposed to be more accurate using this method

a contour integral and an energy release rate in thermoelasticity abstract this paper is a sequel to ref 1 in which a material momentum for thermoelasticity was derived our main goal here is to show that in analogy to the elastic case it is possible to relate an integral of the material momentum with a concept of energy release rate however the relation obtained is not local in time it holds during a time interval which agrees with the results obtained in ref 1

the graph metric for unstable plants and robustness estimates for feedback stability in this paper a graph metric is defined that provides a measure of the distance between unstable multivariable plants the graph metric induces a graph topology on unstable plants which is the weakest possible topology in which feedback stability is robust using the graph metric it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of rhp poles if the perturbed and unperturbed systems have the same rhp poles then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations as an application of these results the design of stabilizing controllers for unstable singularly perturbed systems is studied finally the relationship of the graph metric to the gap metric introduced by zames and el sakkary is studied in detail in particular it is shown that the robustness results of zames and el sakkary do not enable one to conclude the causality of the perturbed system whereas the present results do

parallel reduced order controllers for stochastic linear singularly perturbed discrete systems an approach to the decomposition and approximation of linear quadratic gaussian control problems for singularly perturbed discrete systems at steady state is presented the global kalman filter is decomposed into separate reduced order local filters through the use of a decoupling transformation a near optimal control law is derived by approximating coefficients of the optimal control law the proposed method allows parallel processing of information and reduces offline and online computational requirements a real world example demonstrates the efficiency of the proposed method

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

brief paper parameterization of all stabilizing h static state feedback gains application to output feedback design this paper presents a simplified parameterization of all h static state feedback controllers in terms of a single algebraic riccati equation and a free parameter matrix as a special case necessary and sufficient conditions for the existence of an static output feedback gain are given an efficient computational algorithm is given and its correctness proven no initial stabilizing output feedback gain is needed the technique is used to design an h lateral directional command augmentation system for the f 16 aircraft

the recursive algorithm for the optimal static output feedback control problem of linear singularity perturbed systems a recursive algorithm is developed for solving the algebraic equations comprising the solution of the optimal static output feedback control problem of singularly perturbed linear systems the algorithm is very efficient from the numerical point of view since only low order systems are involved in algebraic calculations and the required solution can be easily obtained up to an arbitrary order of accuracy that is o epsilon sup k where epsilon is a small perturbation parameter the real world example demonstrates the failure of o epsilon theory used so far in the study of this problem and the necessity for the existence of o epsilon sup k theory

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

tracking and disturbance rejection of mimo nonlinear systems with pi controller we study tracking and disturbance rejection of a class of mimo nonlinear systems with linear proportional plus integral pi compensator roughly speaking we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady state i o map then a simple pi compensator can be used to yield a stable unity feedback closed loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors

a two time scale neurodynamic approach to constrained minimax optimization this paper presents a two time scale neurodynamic approach to constrained minimax optimization using two coupled neural networks one of the recurrent neural networks is used for minimizing the objective function and another is used for maximization it is shown that the coupled neurodynamic systems operating in two different time scales work well for minimax optimization the effectiveness and characteristics of the proposed approach are illustrated using several examples furthermore the proposed approach is applied for h infty model predictive control

technical communique on the klimushchev krasovskii theorem the klimushchev krasovskii theorem describes a sufficient condition for the asymptotic stability of singularly perturbed systems motivated by some subtle examples this note presents a new necessary and sufficient condition by imposing an additional assumption on the statement of the klimushchev krasovskii theorem this note also extends the main inertia theorem to singularly perturbed systems

frequency domain results for systems with slow and fast dynamics the mathematical treatment of systems with slow and fast dynamics has traditionally involved singular perturbation theory for differential equations this paper suggests a set of conditions to be placed on a frequency domain description of a system to guarantee two time scale behavior some basic stability and approximation results are presented

robust stabilization for composite observer based control of discrete systems abstract design criteria of robust observer based controllers for linear discrete time singularly perturbed systems with slow and fast modes are considered the developed stability measure complements the quantitative information for unmodeled fast modes that cannot be provided by the usual qualitative robustness analyses a numerical example is provided to show the analytical results obtained

paper optimal output feedback design of systems with ill conditioned dynamics singular perturbation concepts are exploited to develop a procedure for designing a constant gain output feedback control system it is assumed that the original system is ill conditioned in the sense that the plant contains widely separated dynamics and that an accurate description for the high frequency behavior may not be available the design procedure attempts to stabilize the system by minimizing a quadratic cost function made up of the control and states associated with a reduced order low frequency model for the plant and a measure of stability for the neglected fast dynamics the resulting design procedure does not require knowledge of the fast dynamics

reliable h control of multiple time scales singularly perturbed systems with sensor failure this paper studies the reliable h control for linear time invariant multiparameter singularly perturbed systems against sensor failures by time scale decomposition the full order system is decomposed into slow and fast subsystems after designing a reliable h controller for the global system three reduced reliable h sub controllers based on the slow and fast problems are obtained through the manipulation of the algebraic riccati equations the resulting control systems are reliable in that they provide guaranteed asymptotic stability and h performance when all control components are operational as well as when sensor failures occur

linear compensator designs based exclusively on input output information are never robust with respect to unmodeled dynamics the effects of unmodeled higher order dynamics or parasitics on the stability of linear control systems are investigated a description is first given of a class of perturbations of a given state equation that cannot be distinguished from the original on the basis of input output measurements alone then it is shown that given any plant compensator pair perturbations of each system of this type can always be found that destabilize the closed loop configuration the effect of destabilizing perturbations on output behavior is explored

applications of singular perturbation techniques to control problems this paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years the first three sections are devoted to the standard model and its time scale stability and controllability properties the next two sections deal with linear quadratic optimal control and one with cheap near singular control then the composite control and trajectory optimization are considered in two sections and stochastic control in one section the last section returns to the problem of modeling this time in the context of large scale systems the bibliography contains more than 250 titles

comparisons of weakly compressible and truly incompressible algorithms for the sph mesh free particle method in the smoothed particle hydrodynamics sph discretisation method for the navier stokes equations the most widespread method to solve for pressure and mass conservation is the weakly compressible assumption wcsph this includes hydraulics applications and leads to some drawbacks such as severe artificial pressure fluctuations and a limitation to very small time steps related to the wcsph mach number and explicit method this paper presents comparisons of a semi implicit and truly incompressible sph isph algorithm with the classical wcsph method showing how some of the problems encountered in wcsph have been resolved by using isph to simulate incompressible flows mathematical models are presented before describing sph formalism several standard boundary conditions are introduced and special attention is given to tracking the surface particles the lid driven cavity flow re 400 and 1000 is performed as a benchmarking test a bluff body test case a square cylinder in a closed channel re d 20 and 100 based on the cylinder diameter shows that pressure fields extracted from wcsph are very unreliable whereas isph predict pressures and forces in closer agreement with classical finite volume cfd methods dam breaking cases with dry or wet beds downstream are then presented to highlight free surface flow and rapid dynamics effects the wcsph and isph results are generally verified with reference data from experiment and or another numerical method all the comparisons show improvement with isph and good agreement in general

exact slow fast decomposition of the singularly perturbed matrix differential riccati equation in this paper the hamiltonian matrix formulation of the riccati equation is used to derive the reduced order pure slow and pure fast matrix differential riccati equations of singularly perturbed systems these pure slow and pure fast matrix differential riccati equations are obtained by decoupling the singularly perturbed matrix differential riccati equation of dimension n 1 n 2 into the pure slow regular matrix differential riccati equation of dimension n 1 and the pure fast stiff matrix differential riccati equation of dimension n 2 a formula is derived that produces the solution of the original singularly perturbed matrix differential riccati equation in terms of solutions of the pure slow and pure fast reduced order matrix differential riccati equations and solutions of two reduced order initial value problems in addition to its theoretical importance the main result of this paper can also be used to implement optimal filtering and control schemes for singularly perturbed linear time invariant systems independently in pure slow and pure fast time scales

singular perturbation analysis of high frequency filter design the control design of systems with lightly damped high frequency oscillatory modes is treated systems exhibiting these lightly damped modes include turbine generators and large flexible structures frequently the dynamics of these high frequency modes are not known very accurately as a result the design objective is to improve the slow dynamics without destabilizing the high frequency modes from a classical frequency domain design viewpoint this is in part a filtering problem requiring some kind of high frequency filter the singular perturbation method is used to systematically develop a two time scale method to design these high frequency filters and provides guidelines on the kind of high frequency filter to be used in addition the method provides an asymptotic error analysis the design is illustrated with an example representative of a power system model with a two mass turbine generator model

recursive algorithm for the optimal static output feedback control problem of linear weakly coupled systems a recursive algorithm is developed for solving the algebraic equations comprising the solution of the optimal static output feedback control problem of linear weakly coupled systems the proposed algorithm is very efficient from the numerical point of view since only low order systems are involved in algebraic calculations and the required solution can easily be obtained up to an arbitrary order of accuracy that is 0 e2k where e is a small weak coupling parameter the real world example demonstrates the effectiveness of the proposed reduced order algorithm and its advantages over the global full order algorithm

two time scale distributions and singular perturbations two time scale tts distributions are introduced for a class of stable systems it is shown that every tts distribution has a two frequency scale tfs laplace transform conversely it is shown that the impulse response of any stable tfs transfer function and hence any stable standard singularly perturbed system can be characterized in terms of a stable tts distribution a time domain decomposition for tts distributions is obtained which parallels the slow and fast decomposition of singularly perturbed systems and also the frequency domain decomposition of tfs transfer functions it is shown that every stable tts distribution can be decomposed in terms of two simpler distributions represented in two different time scales a composite distribution is constructed from these two which approximates the tts distribution arbitrarily closely in the l 1 norm

h model matching problem for singularly perturbed systems abstract the model matching problem for single input single output singularly perturbed systems is considered two sets of sufficient conditions are obtained to guarantee the existence of a two frequency scale solution one for the optimal and one for a suboptimal case both the minimum phase and the non minumum phase cases are treated the sub optimal two frequency scale solution constructed in this paper uses the solutions of two well defined lower order problems and therefore it is numerically better conditioned and computationally less demanding than the traditional optimal methods a two stage algorithm for the computation of the suboptimal tfs solution is presented

characterization of zeros in two frequency scale systems we study the asymptotic behavior of the zeros of a two frequency scale transfer function in terms of the zeros of its slow and fast transfer functions by introducing the notion of type index we will show that all zeros of a two frequency scale transfer function with the type index of either spl nu spl ges 0 or spl nu 1 can be completely characterized in a manner that is quite similar to the characterization of the poles we also give a partial characterization for all other zeros in terms of the cardinality of their zero sets

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

robustness of linear feedback control systems to unmodelled high frequency dynamics a basic issue in the control of linear time invariant plants is the effect of neglected high frequency dynamics on the performance in particular on the closed loop stability of the control system in this paper the robustness of various output feedback control designs based on a reduced order model with neglected high frequency dynamics is investigated using singular perturbation techniques a general robust design rule is to avoid static output feedback for systems with unmodelled high frequency dynamics from a frequency domain standpoint the robust design rule is to avoid closing high frequency plant loops by using strictly proper controllers or controllers with a low pass filtering property

optimal output feedback control of discrete linear singularly perturbed stochastic systems the static output feedback control problem for discrete linear singularly perturbed stochastic systems is studied a recursive algorithm is presented to solve the corresponding coupled non linear algebraic equations the algorithm removes the ill conditioning by decomposing the higher order equations into lower order equations and develops a technique which enables us to obtain an arbitrary accuracy that is 0 ej j 1 2 3 a approximation for this problem a numerical example is presented to support the theoretical results communicated by professor a a ioannou

singular perturbation of strictly positive realness abstract the robustness of the strictly positive real spr condition of linear time invariant multi input multi output lti mimo singularly perturbed systems is examined a necessary and sufficient condition under which the full system is spr is proved this robustness result is an extension of the analysis for the popov kalman yakubovich lemma by v r saksena and p v kokotovic 7

fast suboptimal solution to the static output control problem of linear singularly perturbed systems abstract the reduced order suboptimal solution to the static output control problem of linear singularly perturbed system is obtained in terms of the fast variables only assuming the special structure of initial conditions for the slow and fast variables the problem of big initial conditions of the fast variables is considered

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

suboptimal constant output feedback and its application to modern flight control system design this paper describes an applications oriented approach to the generation of optimal output feedback gains for linear time invariant systems which is independent of the open loop stability the standard requirement for the provision of initial stabilizing output feedback gains for priming the computational process is circumvented in lieu of initial stabilizing gains the proposed algorithm employs the full state feedback solution which guarantees stability under the mild condition of stabilizabitity in this paper the problem of the generation of sub optimal output feedback is cast in the setting of a constrained parameter optimization problem the solution of this constrained optimization employs hestenes method of multipliers with some modifications a primal dual problem is considered where the primal minimization employs a davidon fletcher powell method and the dual maximization is accomplished via a quasi newton procedure this approach provides the designer with a means of suppressing to zero sele

feedback systems and multiple time scales we study feedback design for systems with multiple time scale structure uncovering an intrinsic time scale structure for a state feedback system with full state output from this we construct a multiple time scale asymptotic observer and consider a system with state feedback via a two time scale asymptotic observer finally we obtain more general results for a restricted class of systems

the discrete time h sub spl infin control problem with strictly proper measurement feedback this paper is concerned with the discrete time h sub spl infin control problem with strictly proper measurement feedback we derive necessary and sufficient conditions for the existence of a strictly proper compensator which achieves a given h sub spl infin norm bound note that contrary to the continuous time in discrete time there might exist a suitable proper compensator but no suitable strictly proper compensator finally we give an explicit formula for one controller which achieves this bound

brief paper eigenvector approach for order reduction of singularly perturbed linear quadratic optimal control problems in this paper we show how to decompose the singularly perturbed algebraic riccati equation and the corresponding linear quadratic optimal control problem at steady state in terms of reduced order pure slow and pure fast problems by using the eigenvector approach the eigenvector approach should be used for decomposition of singularly perturbed control systems in the cases when the singular perturbation parameter is not very small in such cases the decomposition methods based on series expansions fixed point iterations subspace iterations and newton iterations either fail to produce solutions of the corresponding algebraic equations or display very slow convergence

stability constraints of active magnetic bearing control systems direct lyapunov stability method is employed to analyse the closed loop stability of an electromagnetically suspended rotor system in which non linearity and singular perturbation nature are embedded five explicit sets of stability constraints are proposed so that the state feedback loop is not over designed under impact of modeling inaccuracy due to neglected higher order terms stability conditions for equilibrium point slow mode manifold and boundary layer are studied in addition the singular perturbation order reduction technique is used to simplify the feedback loop and reduce the order of a state feedback controller the stability margin can be numerically evaluated as long as the upper bound of the singular perturbation parameter is available the proposed state feedback controller is verified by intensive computer simulations such that superior performance in terms of stiffness rise time and overshoot is illustrated in comparison to output feedback law and deadbeat control the reported st

on the design of stabilizing controllers for singularly perturbed systems the robustness of output feedback control designs for singularly perturbed systems based on the reduced systems is discussed a frequency domain approach is presented to determine the conditions for the stability of linear time invariant systems subject to neglected high frequency dynamics in contrast with the qualitative analyses for robust stability that have appeared in the literature this approach gives an explicit computable bound on unmodeled dynamics which does not destabilize the systems stability conditions for various feedback control schemes are presented it is noted that the approach extended to systems with mixed singular regular perturbations can be used to derive the robust stability condition

convergence of a numerical algorithm for calculating optimal output feedback gains a sequential numerical algorithm is described which obtains gains minimizing a broad class of performance indexes including the standard lq case the primary contribution is a proof that the algorithm converges to a local minimum under nonrestrictive assumptions numerical examples illustrate the theory the second example demonstrates an important lq design technique which permits the designer to prespecify the feedback structure subject to the requirement of output feedback stabilizability

study of the discrete singularly perturbed linear quadratic control problem by a bilinear transformation this paper presents a new approach in the study of the linear quadratic control problem of singularly perturbed discrete systems by applying a bilinear transformation the algebraic discrete riccati equation is converted into a continuous one which can be solved by using the reduced order recursive method already documented in the control literature this method produces the reduced order near optimal solution up to an arbitrary order of accuracy and reduces the size of required computations the method is very suitable for parallel programming a real world example an f 8 aircraft demonstrates the efficiency of the proposed method