nonlinear state feedback for l 1 optimal control this paper considers l1 optimal control problems with full state feedback in contrast to h optimal control previous work has shown that linear l1 optimal controllers can be dynamic and arbitrarily high order however this paper shows that continuous memoryless nonlinear state feedback perform as well as dynamic linear state feedback the derivation which is nonconstructive relies on concepts from viability theory

quadratic stabilizability of uncertain linear systems existence of a nonlinear stabilizing control does not imply existence of a linear stabilizing control this note is concerned with the problem of stabilizing an uncertain linear system via state feedback control an uncertain system which admits a stabilizing state feedback control and some associated quadratic lyapunov function is said to be quadratically stabilizable in a number of recent papers conditions are given under which quadratic stabilizability via nonlinear control implies quadratic stabilizability via linear control these papers restrict the manner in which the uncertain parameters are permitted to enter structurally into the state equation in order to establish this result this note presents an example which shows that this implication is not true for more general uncertain linear systems to this end we describe an uncertain linear system which is quadratically stabilizable via nonlinear control but not quadratically stabilizable via linear control

petri net controllers for generalized mutual exclusion constraints with floor operators in this paper a special type of nonlinear marking specifications called stair generalized mutual exclusion constraints stair gmecs is defined a stair gmec can be represented by an inequality whose left hand is a linear combination of floor functions stair gmecs have higher modeling power than classical gmecs and can model legal marking sets that cannot be defined by or and gmecs we propose two algorithms to enforce a stair gmec as a closed loop net in which the control structure is composed by a residue counter remainder counters and duplicate transitions we also show that the proposed control structure is maximally permissive since it prevents all and only the illegal trajectories of a plant net this approach can be applied to both bounded and unbounded nets several examples are proposed to illustrate the approach

robust stability of uncertain linear systems with saturating actuators we consider the robust stability of uncertain linear systems with saturating actuators and present two sufficient conditions to guarantee the stability of the closed loop system we assume that the bound of the initial state is known and that the uncertainty is unstructured the obtained results meet our intuition that the lower bound of initial state and the higher bound of saturation level make it easy to design a controller finally we show the usefulness by an example

quadratic stabilizability of uncertain systems a two level optimization setup abstract the problem of stabilizing linear systems subject to possibly fast time varying uncertainties is investigated necessary and sufficient conditions of quadratic stabilizability are discussed the design process is formulated as a two level optimization process which can be simplified if the uncertainty is bounded by a hyperpolyhedron

robust linear regulator design for discrete time systems under polyhedral constraints the robust linear constrained regulation problem for uncertain linear discrete time systems a b is investigated using the theory of positively invariant polyhedral sets closed and bounded polyhedral uncertain domains are considered involving parameters of both a and b matrices and polyhedral constraints on both state and control vectors new sufficient conditions for the solvability of the regulation problem are presented for computational solution of the regulation problem a linear programming approach is proposed where the constraints are given by the solvability conditions and the performance index represents a guaranteed trade off between the closed loop stability margin and the level of control effort

control effort considerations in the stabilization of uncertain dynamical systems abstract this paper investigates the problem of designing a state feedback control to stabilize an uncertain nonlinear system we focus attention on the amplitude norm of the controller which is used to achieve this end the uncertain system is described by a state equation which contains uncertain parameters which are unknown but bounded a lyapunov function is used to establish the stability of the closed loop system the paper gives necessary and sufficient concitions for the uncertain system to be stabilizable with a given lyapunov function furthermore a procedure is indicated for the construction of the desired feedback control law

adaptive l tracking for a class of infinite dimensional systems abstract for a class of high gain stabilizable multivariable linear infinite dimensional systems we present an adaptive control law which achieves approximate asymptotic tracking in the sense that the tracking error tends asymptotically to a ball centred at 0 and of arbitrary prescribed radius 0 this control strategy called tracking combines proportional error feedback with a simple nonlinear adaptation of the feedback gain it does not involve any parameter estimation algorithms nor is it based on the internal model principle the class of reference signals is w 1 the sobolev space of absolutely continuous functions which are bounded and have essentially bounded derivative the control strategy is robust with respect to output measurement noise in w 1 and bounded input disturbances we apply our results to retarded systems and integrodifferential systems

systems of controlled functional differential equations and adaptive tracking an adaptive servomechanism is developed in the context of the problem of approximate or practical tracking with prescribed asymptotic accuracy by the system output of any admissible reference signal absolutely continuous and bounded with essentially bounded derivative for every member of a class of controlled dynamical systems modelled by functional differential equations

reachability in input constrained discrete time linear systems abstract a complete picture of dynamic system theory and optimization should include the study of linear constrained systems surprising little work has been done so far in this area in this paper a rather complete theory of linear discrete time systems with general constraints on the input is developed it covers reachability theory and gives also the discrete time version of the bang bang principle for convex constraints

design of controllers for mg3 compressor models with general characteristics using graph backstepping we discuss the design of controllers for compressors with general characteristics including the right skewed ones the controllers can be represented graphically by plotting their throttle surfaces the graphical representation of controllers enhances understanding of controller action and allows to compare various controllers we discuss the issue of the right skewness of a compressor characteristic we show how to design controllers using a graph backstepping procedure involving the construction of the throttle surface we show that for a quite general compressor characteristic every potential axisymmetric equilibrium on the decreasing part of the compressor characteristic the peak of the characterisitic and every rotating stall equilibrium close to the peak can be globally or semi globally stabilized by an appropriate choice of the throttle surface and the controller gains we obtain lower bounds on the gains of the controller in terms of the divided differences related to compressor characteristic these bounds can be expressed using some bounds on the first and second derivatives of the characteristic in the region of operation in this way we establish a direct relationship between the shape of the compressor characteristic and the required controller gains we discuss controllers that stabilize a range of the desired equilibria and guarantee a soft bifurcation of the equilibria as a set point parameter varies we give an example of controller design for a right skew compressor we provide simple general guidelines for choosing the throttle surface

growth and fluctuations of personal income pareto s law states that the distribution of personal income obeys a power law in high income range many researchers have proposed models over a century since its discovery but the dynamical understanding of hie phenomenon necessitates empirical study on growth of individual income here we uncovered several properties in the fluctuations of individual income growth derived from income tax data including all taxpayers more than 80 000 with high income iii japan for two consecutive years 1997 and 1998 in a relatively stable period of economics in this work 8 we show i that the dynamics has approximate time reversal symmetry in the period ii that the distribution of growth rate is independent of income tax in the past yearm and iii that the pareto s law breaks down in bubble collapse of japanese economy in 1990 it is shown in 3 how these phenomenological facts are consistent with pareto law these findings provide first direct observation of dynamical process of ruuirey flow in an economic network and its relation to risky assets price fluctuations of lands and stocks

shape of growth rate distribution determines the type of non gibrat s property abstract in this study the authors examine exhaustive business data on japanese firms which cover nearly all companies in the mid and large scale ranges in terms of firm size to reach several key findings on profits sales distribution and business growth trends here profits denote net profits first detailed balance is observed not only in profits data but also in sales data furthermore the growth rate distribution of sales has wider tails than the linear growth rate distribution of profits in log log scale on the one hand in the mid scale range of profits the probability of positive growth decreases and the probability of negative growth increases symmetrically as the initial value increases this is called non gibrat s first property on the other hand in the mid scale range of sales the probability of positive growth decreases as the initial value increases while the probability of negative growth hardly changes this is called non gibrat s second property under detailed balance non gibrat s first and second properties are analytically derived from the linear and quadratic growth rate distributions in log log scale respectively in both cases the log normal distribution is inferred from non gibrat s properties and detailed balance these analytic results are verified by empirical data consequently this clarifies the notion that the difference in shapes between growth rate distributions of sales and profits is closely related to the difference between the two non gibrat s properties in the mid scale range

a lagrange approach to set theoretic control synthesis a lagrange approach to solving the nonlinear constrained optimization problem arising in the set theoretic control problem is described by introducing matrix lagrange multipliers the problem is reduced to that of solving a set of nonlinear simultaneous matrix equations one of which is the familiar matrix riccati equation frequently encountered in linear quadratic control theory the structural similarities and differences between set theoretic and linear quadratic control methods are identified the results obtained from the set theoretic control approach are compared with those obtained from the linear quadratic control approach

swinging control of nonlinear oscillations the speed gradient method of control design used previously for problems of regulation and tracking is extended to oscillating systems with energy based objective functions the concept of swinging control is introduced meaning achievement of arbitrary large level of the objective function by arbitrary small control level the existence of swinging control for hamiltonian systems is established simulation results for pendulum swinging problem are demonstrated

stability and stabilization of delay differential systems the delay systems considered here are represented by linear delay differential equations the system parameters and the delays are assumed to be imperfectly known the instantaneous state vector is perturbed by a bounded external disturbance vector the problem addressed is that of characterizing conditions that guarantee that the trajectory of the instantaneous state vector remains in a domain defined by a set of symmetrical linear constraints it is shown that the positive invariance property can be used to solve this problem and that positive invariance of a compact domain of the instantaneous state space implies delay independent asymptotic stability of the associated deterministic system the possible use of these results for the control of a multiple delay mimo differential model is then presented finally an example is given

approach for transforming linear constraints on petri nets an efficient supervisor synthesis method is proposed based on the constraint transformation since enforcing a logic expression of linear constraints on petri nets essentially involves finding admissible constraints it consists of cooperative algorithms that are used to obtain the logic expression of constraints for any set of forbidden markings to remove redundant constraints using the quantity information of constraints to judge the existence of a permissive supervisor to equivalently reduce multiple constraints into a single one using net structural properties and to approach the admissible constraints from the original ones for ordinary petri nets these algorithms are derived from a series of theorems and lemmas presented to construct the theory of constraint transformation or reduction in addition the linear constraint whose uncontrollable subnet is a forward concurrent free net can be equivalently transformed into an admissible linear constraint using this method

derivation of the distribution from extended gibrat s law abstract employing profits data of japanese companies in 2002 and 2003 we identify the non gibrat s law which holds in the middle profits region from the law of detailed balance in all regions gibrat s law in the high region and the non gibrat s law in the middle region we kinematically derive the profits distribution function in the high and middle range uniformly the distribution function accurately fits with empirical data without any fitting parameter

regulator problem for linear continuous time delay systems with nonsymmetrical constrained control the regulator problem is studied for linear continuous time delay systems with nonsymmetrical constrained control necessary and sufficient conditions allowing the autors to obtain the largest nonsymmetrical polyhedral positively invariant with respect to w r t the system in the closed loop are given the case of symmetrical constrained control is obtained as a particular case

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

stabilization of linear controllable systems by means of bounded continuous nonlinear feedback control abstract using an inner ellipsoidal approximation to the controllable set of controllable linear systems a bounded continuous nonlinear stabilizing feedback control is designed the resulting control is a smooth local approximation to the time optimal control in particular this design approach is used to globally stabilize the n th order integrator system

output feedback model reference adaptive control for multi input multi output plants with state delay two new output feedback adaptive control schemes based on model reference adaptive control mrac and adaptive laws for updating the controller parameters are developed for a class of linear multi input multi output mimo systems with state delay an effective controller structure established on a new error equation parametrization is proposed to achieve tracking with the error tending to zero asymptotically to achieve exact asymptotical tracking we introduce in the standard mrac structure for plants without delay a new additional adaptive feedforward control component as an output of a dynamical system driven by the reference signal adaptive laws are developed using the spr lyapunov design approach and two assumptions regarding the prior knowledge of the high frequency matrix kp this work is the first asymptotic exact zero tracking results for this class of systems in the framework of the certainty equivalence approach 2005 elsevier b v all rights reserved

bifurcation analysis of axial flow compressor stability with a one mode truncation it is possible to reduce the moore greitzer model for compressor instability to a set of three ordinary differential equations these are approached from the point of view of bifurcation theory most of the bifurcations emerge from a degenerate takens bogdanov bifurcation point the bifurcation sets are completed using the numerical branch tracking scheme auto despite the severity of the truncation the agreement with experimental results is excellent

regulation of control systems under inequality constraints abstract a velocity controlled viability theory for control systems with inequality constraints is introduced we do this by constructing a velocity controlled regulation map and change the control problem in that sense by doing that the solutions to the differential inclusion are prevented from running into the border of the viability domain too fast this leads to a marchaud system which provides for an application of the viability theorem as well as the smooth control theorem

distributed control design for parabolic evolution equations application to compressor stall control we present a theoretical study of distributed control design for semilinear parabolic nonlocal evolution equations with an application to axial compressor stall control using air injection by taking advantage of the spatial invariance of the equations a linear controller is constructed following bamieh et al via linear quadratic control of each fourier mode we derive sufficient conditions for the linear controller to stabilize the full nonlinear system concepts such as controller decentralization finite dimensional implementation inverse optimality and beneficial nonlinearities are discussed in the second part of this paper these developments are applied to a model of axial compressor control with air injection the unactuated model is derived following the work of moore and greitzer and the model coupled with air injection actuation follows the works of behnken et al and weigl et al a numerical study of the control designs is pursued and the comparison of controller performance is discussed the techniques presented here are expected to be useful for distributed control design of a much broader class of nonlinear reaction diffusion systems

feedback control of linear discrete time systems under state and control constraints in this paper the problem of stabilizing linear discrete time systems under state and control linear constraints is studied based on the concept of positive invariance existence conditions of linear state feedback control laws respecting both the constraints are established these conditions are then translated into an algorithm of linear programming

basic control for the viscous moore greitzer partial differential equation the notions of basic controllability and basic control are defined a quadratic optimal control of the linearized viscous moore greitzer equation is presented and it is confirmed that stall is uncontrollable in this model a basic control is constructed for the nonlinear viscous moore greitzer equation which can control both surge and stall some extensions of this construction are discussed numerical simulations of the basic control are presented and its performance is compared to the performance of a backstepping control constructed by banaszuk hauksson and mezic siam j control optim 37 1999 pp 1503 1537 it is shown that the viscous moore greizer equation with throttle control is not basically controllable but under certain conditions adding air injection control will make the equation basically controllable

an eigenstructure assignment approach for constrained linear continuous time singular systems abstract this paper establishes necessary and sufficient algebraic conditions for positive invariance of convex polyhedra with respect to some linear continuous time singular systems they can be considered as an extension for linear singular systems of the classical positive invariance relations for regular linear systems for a stabilizable and impulse controllable singular system with constrained inputs a stabilizing state feedback control guaranteeing the closed loop positive invariance of some polyhedral sets determined from the feedback matrix is studied an analysis of the closed loop positive invariance relations is thus presented in terms of eigenstructure and stability properties an eigenstructure assignment technique is proposed depending on the number of stable finite poles of the singular system

maximum entropy formalism fractals scaling phenomena and 1 f noise a tale of tails in this report on examples of distribution functions with long tails we a show that the derivation of distributions with inverse power tails from a maximum entropy formalism would be a consequence only of an unconventional auxilliary condition that involves the specification of the average value of a complicated logarithmic function b review several models that yield log normal distributions c show that log normal distributions may mimic 1 f noise over a certain range and d present an amplification model to show how log normal personal income distributions are transformed into inverse power pareto distributions in the high income range

a finite dimensional attractor of the moore greitzer pde model the moore greitzer pde model with viscosity is presented and the equations are rewritten as an evolution equation on a hilbert space it is proven that the model has a unique global solution which is smooth in space and time furthermore it is proven that there exists a global attractor i e a compact set which attracts all bounded sets finally it is shown that the attractor has a finite fractal dimension

optimization of the l sup spl infin induced norm under full state feedback this paper considers the l sup spl infin optimal control problem i e minimization of the effects of disturbances as measured by the l sup spl infin induced norm earlier work showed that even in the case of full state feedback optimal and near optimal linear controllers may be dynamic and of arbitrarily high order however previous work by the author derived the existence of near optimal nonlinear controllers which are static this paper presents a constructive algorithm for such nonlinear controllers the main idea is to construct a certain subset of the state space such that achieving disturbance rejection is equivalent to restricting the state dynamics to this set a construction of this subset requires the solution of several finite linear programs with the number of variables being at least the number of states but less than the number of states plus the number of controls the concept of controlled invariance plays a central role throughout

a razumikhin type lemma for functional differential equations with application to adaptive control a lemma of razumikhin type pertaining to boundedness of solutions of functional differential equations is presented this lemma is subsequently invoked in the analysis of adaptive strategies that guarantee approximate tracking with prescribed asymptotic error bound of reference signals of sobolev class w 1 for two classes of uncertain systems modelled by controlled nonlinear functional differential equations

an integral invariance principle for differential inclusions with applications in adaptive control the byrnes martin integral invariance principle for ordinary differential equations is extended to differential inclusions on bbb r n the extended result is applied in demonstrating the existence of adaptive stabilizers and servomechanisms for a variety of nonlinear system classes

characterization of admissible marking sets in petri nets with conflicts and synchronizations in this paper we study the problem of constraint transformation for petri nets with uncontrollable transitions and containing both conflicts and synchronizations we show that given an arbitrary net and a set of legal markings the admissible marking set cannot always be represented by a finite number of disjunctions of gmecs moreover we characterize the gmec inflation phenomenon that is the case in which the representation of the admissible marking set may be too complex to be efficiently implemented in a closed loop net to rule out the possibility of gmec inflation we consider a subclass of constraints called singular gmecs with an acyclic backward conflict free uncontrollable subnet by these assumptions we propose an algorithm to transform a given singular gmec into a controllable or gmec which precisely characterizes its admissible marking set

a design approach for constrained regulation in discrete singular systems abstract in the present study the problem of designing controllers for linear discrete time singular descriptor systems under initial state and control constraints is considered the aim is to eliminate any non causalities and make the closed loop system stable while the state feedback control vector must respect appropriate constraints the present approach constitutes an extension to the design of constrained linear state feedback controllers for linear regular discrete time systems

on the computation of reference signal constraints for guaranteed tracking performance abstract this paper concerns the problem of determining constraints on reference signals for tracking systems such that the tracking performance can be guaranteed within a specified tolerance for any reference signal satisfying the constraints we first consider the problem of computing derivative constraints which are linear constraints on the vector valued reference signal and its time derivatives and present an off line algorithm for computing inner approximations to supremal derivative constraint sets based on the hyperplane method for generating inner and outer approximations to the reachable set of states for the controlled system no simulation is required we then consider planning problems in which a finite number of parameters are selected to generate the reference signal the derivative constraints are mapped into this parameter space the simplicial approximation method is proposed as a method for computing an approximation to the set of admissible parameters the resulting linear parameter constraints characterize a class of reference signals which can be successfully executed by the tracking system thereby permitting supervisory planning and control to be carried out in the reference signal parameter space without simulating detailed models of the underlying system dynamics we illustrate the computational algorithm and the application of derivative and parameter constraints for the problem of generating trajectories for a two axis computer numerical control cnc cutting tool

control of vector discrete event systems i the base model a vector discrete event system vdes is a discrete event system model in which the system state is represented by a vector with integer components and state transitions by integer vector addition the authors investigate such structures from the viewpoint of control theory the objective is to specialize to vdes the general automation based control theory of p j ramadge and w m wonham 1987 and w m wonham and p j ramadge 1988 it is shown that within the vdes framework a useful class of control systems can be compactly modeled and some of the associated control problems of ramadge and wonham can be more efficiently solved

an algorithm to find maximal state constraint sets for discrete time linear dynamical systems with bounded controls and states an algorithm to find a polyhedral approximant to the maximal state constraint set given state and input bounds is suggested for linear discrete time dynamical systems

constrained regulation of linear systems abstract in this paper the linear constrained regulation problem without an assigned set of initial states is investigated this problem consists of the determination of a linear state feedback control law and of a set of admissible initial states d so that every trajectory of the resulting closed loop system which emanates from the set converges asymptotically to the origin without violation of the control constraints by applying well known results on the positive invariance of polyhedral sets an eigenstructure assignment approach to this problem is established if the number of unstable open loop eigenvalues does not exceed the number of control variables then this approach enables one to derive a linear state feedback stabilizing control law which makes the set of states where the control constraints are respected positively invariant this positively invariant set is the maximal admissible set of initial states for the control law under consideration for the case where the number of control variables is greater than the number of the unstable open loop eigenvalues a modified algorithm is proposed

a branch and bound approach for the design of decentralized supervisors in petri net models the paper addresses the design of compact and maximally permissive decentralized supervisors for petri nets based on generalized mutual exclusion constraints decentralization constraints are formulated with respect to the net transitions instructing each local supervisor to detect and disable transitions of its own control site only a solution is characterized in terms of the states it allows and its feasibility is assessed by means of two separate tests one checking the required behavioral properties e g liveness reversibility and controllability of the induced reachability subgraph and the other ensuring the existence of a decentralized supervisor enforcing exactly the considered set of allowed states the second test employs an integer linear programming formulation maximal permissivity is ensured by efficiently exploring the solution space using a branch and bound method that operates on the reachable states particular emphasis is posed on the obtainment of the controllability property both in the structural and the behavioral interpretation

constrained stabilization of continuous time linear systems in this paper we consider the stabilization problem for linear continuous time systems under state and control constraints we show that the largest domain of attraction to the origin can be arbitrarily closely approximated by a polyhedral domain of attraction associated to a certain continuous feedback stabilizing control and we show how to use existing numeric procedures for discrete time systems to solve the continuous time problem we propose a new discontinuous stabilizing control law for scalar input systems which has the advantage of being successfully applicable to systems with quantized control

paper linear ultimate boundedness control of uncertain dynamical systems given a state equation whose description includes uncertain parameters it is often desirable to design a feedback controller which renders all solutions uniformly and ultimately bounded when facing such a problem one often has available or assumes an upper bound for the excursions of the uncertain parameters within this framework the objective is to guarantee no matter how nature selects the uncertainty that the state will eventually end up and remain within some pre specified region when this region is a small neighborhood about the origin the concept of uniform ultimate boundedness is tantamount to practical asymptotic stability the objectives of this paper are twofold first and foremost our goal is to show that a class of ultimate boundedness problems which have been solved to date via nonlinear control can in point of fact be solved via linear control this is the main result and is given in theorem 4 1 secondly we show that some of the so called matching assumptions which have been required in the earlier literature can be weakened somewhat this enables one to design controllers for a larger class of dynamical systems than previously considered

feedback control logic for backward conflict free choice nets this paper discusses the forbidden state problem as specified by generalized mutual exclusion constraints in the context of supervisory control of discrete event systems modelled by petri nets the case of backward conflict free and free choice uncontrollable subnets is considered and it is shown how to transform such subnets in well formed free choice nets then the well formed free choice nets are decomposed in marked graph components by recurring to minimal t invariants the forbidden state problem is so reformulated for the obtained marked graph components into an equivalent one which is shown to be a linear programming problem thus improving existing results in literature a polynomial complexity solution suitable for on line control is achieved free choice relationship and cycle modelling that frequently occur in real life situations are so allowed in the uncontrollable subnet

the uniqueness of firm size distribution function from tent shaped growth rate distribution abstract employing profits data of japanese firms in 2003 and 2004 we report the proof that a non gibrat s law in the middle scale region of profits is unique under the law of detailed balance this uniquely leads to the probability distribution function pdf of profits in the proof two approximations are employed the pdf of growth rate is described as tent shaped exponential functions and the value of the origin of the growth rate distribution is constant these approximations are confirmed in the database the resultant profits pdf fits with the empirical data consistently this guarantees the validity of the approximations

on the positive invariance of polyhedral sets for discrete time systems abstract in this note necessary and sufficient conditions for a polyhedral set to be a positively invariant set of a linear discrete time system are established

the growth of business firms theoretical framework and empirical evidence we introduce a model of proportional growth to explain the distribution pg g of business firm growth rates the model predicts that pg g is exponential in the central part and depicts an asymptotic power law behavior in the tails with an exponent 3 because of data limitations previous studies in this field have been focusing exclusively on the laplace shape of the body of the distribution in this article we test the model at different levels of aggregation in the economy from products to firms to countries and we find that the predictions of the model agree with empirical growth distributions and size variance relationships

brief paper local l2 gain of bifurcation stabilization local l 2 gain analysis of a class of stabilizing controllers for nonlinear systems with both stationary and hopf bifurcations is studied in particular a family of lyapunov functions is first constructed for the corresponding critical system and simplified sufficient conditions to compute the l 2 gain are derived by solving the hamilton jacobi bellman hjb inequalities local robust analysis for a class of bifurcation stabilizing controllers can then be conducted through computing the local l 2 gain achieved by these controllers at the critical situation the results obtained in this paper provide useful guidance for selecting a robust controller from a given class of stabilizing controllers in terms of l 2 gain as an example application to an axial flow compressor control is discussed in detail

brief paper suboptimal supervisory control of petri nets in presence of uncontrollable transitions via monitor places this paper deals with the problem of enforcing generalized mutual exclusion constraints gmec on place transition nets with uncontrollable transitions an efficient control synthesis technique which has been proposed in the literature enforces gmec constraints by introducing monitor places to create suitable place invariants the method has been shown to be maximally permissive and to give a unique control structure in the case that the set of legal markings is controllable this paper investigates on and formally shows that the class of controllers obtained by this technique may not have a supremal element for uncontrollable specifications moreover it is shown that the family of monitor places enforcing an uncontrollable specification can be parameterized with respect to the solution of a linear system of equation an algorithm to obtain such parameterization is presented here

stabilization of minimum phase nonlinear systems by dynamic output feedback in this paper the stabilization problem of minimum phase nonlinear systems by dynamic output feedback is investigated it is shown that if the zero dynamics of an affine nonlinear system is asymptotically stable according to the kth approximation then the system is stabilizable by dynamic output feedback the proof is constructive which provides a method to design the stabilizer the result is applied to investigating the stabilization problem of the rotating stall in axial flow compressors

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

brief adaptive control of compressor surge instability in this paper we propose a simple high gain type adaptive control scheme for surge stabilization in a compression system we consider a typical configuration in which the plenum throttle position is the control input while the measured output is given by the total pressure at the compressor inlet we prove convergence of the control scheme using a simplified but widely accepted second order model the system does not satisfy strict minimum phase assumptions usually introduced in the high gain type adaptive control context and therefore the proof has been tailored to the specific problem we finally validate the proposed controller by means of both numerical simulation and experiments on a real plant

computer aided analysis of imperfect bifurcation diagrams i simple bifurcation point and isola formation centre quantitative information from the theory for imperfect bifurcation by golubit sky and schaeffer singularities and groups in bifurcation theory vol i springer verlag new york 1985 can be obtained at the cost of some numerical effort the information is used to get a local approximation of the imperfect bifurcation diagrams for simple bifurcation points or isola formation centres

controlled functional differential equations and adaptive tracking abstract adaptive tracking control of a class n of single input single output systems described by nonlinear functional differential equations is considered the control objective is that of tracking by the system output of reference signals of class r absolutely continuous and bounded with essentially bounded derivative a n r universal servomechanism in the form of an adaptive error feedback strategy incorporating gains of nussbaum type is developed which for every system of class n and every reference signal of class r ensures either i practical tracking in the sense that prespecified asymptotic tracking accuracy quantified by 0 is assured or ii asymptotic tracking in the sense that the tracking error approaches zero the first case i is achievable by continuous feedback the second case ii necessitates discontinuous feedback both cases are developed within a framework of functional differential inclusions

piecewise linear lq control for systems with input constraints abstract a piecewise linear control plc law based on lq theory is derived ths law raises an lq gain as the controlled error converges towards the origin it can be computed off line and it guarantees that input bounds are never exceeded without causing input saturation a succession of positively invariant sets are defined of diminishing size and associated with each is the corresponding highest lq gain possible in the presence of the input bounds the formulation gives rise to an iteration function whose solution is a fixed point fp the fp defines the optimal gain and the invariant set which comprise ellipsoids fp existence uniqueness and convergence properties are proven we explain the algorithms for the generation and subsequent implementation of the plc law the notion of a switching function is introduced consideration is given to the computational aspects of the fp the plc scheme is demonstrated for the linearized dynamics of the simple pendulum and the puma 560 robot a discrete time plc law can also be derived using the discrete time algebraic riccati equation

on invariant polyhedra of continuous time systems subject to additive disturbances this paper presents new necessary and sufficient algebraic conditions on the existence of positively d invariant polyhedra of continuous time linear systems subject to additive disturbances in particular for a convex unbounded polyhedron containing the origin in its interior it is also shown that the positive d invariance conditions can be split into two lower dimensional sets of algebraic relations the first corresponds to disturbance decoupling conditions and the second to positive d invariance conditions for bounded polyhedra of a reduced order system the stability of the overall system is discussed as well by exploring the results obtained an lp approach is proposed for solution of a state constrained regulator problem in the presence of additive disturbances

brief paper design of a maximally permissive liveness enforcing supervisor with a compressed supervisory structure for flexible manufacturing systems in this paper a deadlock prevention policy for flexible manufacturing systems fms is proposed which can obtain a maximally permissive liveness enforcing petri net supervisor while the number of control places is compressed by using a vector covering approach the sets of legal markings and first met bad markings fbm are reduced to two small ones i e the minimal covering set of legal markings and the minimal covered set of fbm a maximally permissive control purpose can be achieved by designing control places such that all markings in the minimal covered set of fbm are forbidden and no marking in the minimal covering set of legal markings is forbidden an integer linear programming problem is designed to minimize the number of control places under an assumption that a control place is associated with a p semiflow the resulting net has the minimal number of control places on the premise that the assumption holds and possesses all permissive states of a plant the only problem of the proposed method is its computational complexity that makes it inapplicable to large scale petri net models an fms example from the literature is presented to illustrate the proposed method

constrained regulation of linear continuous time dynamical systems abstract in this paper the linear constrained regulation problem lcrp for continuous time dynamical systems is studied the first part of the paper deals with the existence of linear state feedback control laws that transfer asymptotically to the origin all initial states belonging to a given polyhedral subset of the state space while respecting linear constraints on both state and control vectors then the lcrp is formulated as an optimization problem which can be solved by applying linear programming techniques

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

bifurcation control via state feedback for systems with a single uncontrollable mode the state feedback control of bifurcations with quadratic or cubic degeneracy is addressed for systems with a single uncontrollable mode based on normal forms and invariants the classification of bifurcations for systems with a single uncontrollable mode is obtained table 1 using invariants stability characterizations are derived for a family of bifurcations including saddle node bifurcations transcritical bifurcations pitchfork bifurcations and bifurcations with a cusp or hysteresis phenomenon bifurcations in systems under perturbed feedbacks are also addressed in the case of a saddle node bifurcation continuous but not differentiable feedbacks are introduced to locally remove the bifurcation and to achieve the stability

analysis and control of hopf bifurcations in this paper control systems with two uncontrollable modes on the imaginary axis are studied the main contributions include the local orientation control of periodic solutions and center manifolds the quadratic normal form of systems with two imaginary uncontrollable modes the stabilization of the hopf bifurcation by state feedback and the quadratic invariants that characterize the nonlinearity of a system and its hopf bifurcation

quadratic boundedness of nominally linear systems a non linear uncertain system is quadratically bounded if all its solutions are bounded and this is guaranteed by a quadratic lyapunov function we obtain easily checkable conditions which are necessary and sufficient for a class of nominally linear systems to be quadratically bounded the results are applied to the rotational motion of an axisymmetric spacecraft subject to unknown but bounded disturbance torques

vector norms as lyapunov functions for linear systems a unified theory of quadratic and piecewise linear lyapunov functions for continuous and discrete time linear systems is presented the key to this work is the description of these lyapunov functions by vector norms the main results are sufficient and necessary conditions for a vector norm to be a lyapunov function as well as a method based on these conditions of constructing such lyapunov functions

reduced conservatism in stability robustness bounds by state transformation this note addresses the issue of conservatism in the time domain stability robustness bounds obtained by the lyapunov approach a state transformation is employed to improve the upper bounds on the linear time varying perturbation of an asymptotically stable linear time invariant system for robust stability this improvement is due to the variance of the conservatism of the lyapunov approach with respect to the basis of the vector space in which the lyapunov function is constructed improved bounds are obtained using a transformation on elemental and vector norms of perturbations i e structured perturbations as well as on a matrix norm of perturbations i e unstructured perturbations for the case of a diagonal transformation an algorithm is proposed to find the optimal transformation several examples are presented to illustrate the proposed analysis