system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

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

decentralized guaranteed cost dynamic control for synchronization of a complex dynamical network with randomly switching topology this paper considers synchronization problem of a complex dynamical network with randomly switching topology which means that the topology of a complex network probabilistically switches for this problem a decentralized guaranteed cost dynamic feedback controller is designed to achieve the synchronization of the network based on lyapunov stability theory and linear matrix inequality framework the existence condition for feasible controllers is derived in terms of linear matrix inequalities finally the proposed method is applied to two numerical examples in order to show the effectiveness of our result

a new perspective on static and low order anti windup synthesis by viewing the anti windup problem as a decoupled set of subsystems and relating this configuration to a general static anti windup set up lmi conditions are established which guarantee stability and performance of the resulting closed loop system the approach taken and the mapping used for the performance index are logical and intuitive and it is argued central to the true anti windup objective the approach enables one to construct static anti windup compensators in a systematic and numerically tractable manner the idea is extended to allow low order anti windup compensators to be synthesized which while being sub optimal can improve transient performance and possess several desired properties such as low computational overhead and sensible closed loop pole locations in addition low order anti windup synthesis is often feasible when the corresponding static synthesis is not

an observer based anti windup scheme for non linear systems with input constraints this article addresses the problem of anti windup design for feedback linearizable non linear systems with input constraints subject to dynamic controllers with linear dynamics and non linear gains a method for designing the controller gains and a non linear observer based anti windup modification is proposed which allows reducing the behaviour of the closed loop system under the dynamic feedback controller to that under a given static feedback linearizing controller arbitrarily fast the proposed anti windup method allows thus to attenuate the effect of windup arbitrarily fast and guarantee that the region of closed loop asymptotic stability under the dynamic controller is limited only by the corresponding region under the static feedback linearizing controller the application and advantages of the method are illustrated through a simulation study on a methyl methacrylate polymerization reactor

sufficient conditions for the filtration of a stationary processes to be standard let x be a stationary process with values in some sigma finite measured state space e mathcal e pi indexed by mathbb z call mathcal f x its natural filtration in 3 sufficient conditions were given for mathcal f x to be standard when e is finite and the proof used a coupling of all probabilities on the finite set e in this paper we construct a coupling of all laws having a density with regard to pi which is much more involved then we provide sufficient conditions for mathcal f x to be standard generalizing those in 3

generalized sector synthesis of output feedback control with anti windup structure this paper considers the control synthesis problem for linear time invariant lti continuous time systems with actuator saturation nonlinearities the control architecture is standard a nominal lti output feedback with an anti windup aw mechanism traditional approaches have focused on aw synthesis where the nominal controller is first designed to achieve a local performance in the linear region of the actuators and then the aw compensator is added to guarantee stability performance properties when the actuators saturate in contrast this paper proposes a synthesis method to design both the nominal controller and the aw compensator simultaneously using the generalized sector gs approach in the multiplier setting a sufficient condition is given in terms of linear matrix inequalities so that a given ellipsoid is synthesized as a domain of attraction for the closed loop system our result is shown to include the existing results on the simultaneous circle synthesis and the anti windup gs synthesis as special cases this paper also shows that the direct feed through term in the aw compensator does not contribute to enlarging the achievable domain of attraction within the multiplier gs framework

power law decay and the ergodic nonergodic transition in simple fluids it is well known that mode coupling theory mct leads to a two step power law time decay in dense simple fluids we show that much of the mathematical machinery used in the mct analysis can be taken over to the analysis of the systematic theory developed in the fundamental theory of statistical particle dynamics mazenko in phys rev e 81 6 061102 2010 we show how the power law exponents can be computed in the second order approximation where we treat hard sphere fluids with statics described by the percus yevick solution

lpv system analysis via quadratic separator for uncertain implicit systems this paper considers a class of linear systems containing time varying parameters whose behavior is not known exactly we assume that the parameters vary within known intervals and there are known bounds on their rates of variation our objective is to give a computationally verifiable condition that guarantees stability of the system for all possible parameter variations we first point out that the information on the rate bounds can be exploited by considering an augmented system described by an implicit model we then develop a tool called the quadratic separator for stability analysis of uncertain implicit systems using this tool a sufficient stability condition is obtained for the original linear parameter varying system moreover we show that the stability condition obtained is equivalent to the existence of a lyapunov function that depends on the parameters in a linear fractional manner finally the computational aspects of the proposed stability conditions are addressed

brief paper anti windup and bumpless transfer schemes this paper considers the problem of windup which occurs when a controller with unstable integrator modes is subjected to input saturation or multi mode operation an optimal strategy for the so called model based approach is proposed based on an h optimisation framework this has been found to give good results on numerical examples taken from the literature

technical communique a fast nonlinear control method for linear systems with input saturation we present a novel fast saturating nonlinear feedback law for single input systems with linear dynamics and input saturation it is fast in the sense that it yields a better performance than a saturating linear control law the control law is based on implicit soft variable structure control a convex optimization procedure for the controller synthesis based on linear matrix inequalities lmis is derived at the price of some conservatism as an example we consider the control of a submarine

brief an analysis and design method for linear systems subject to actuator saturation and disturbance we present a method for estimating the domain of attraction of the origin for a system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant this condition is shown to be less conservative than the existing conditions which are based on the circle criterion or the vertex analysis moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis this condition is then extended to determine the invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements the effectiveness of the developed methods is illustrated with examples

observer based anti windup compensator design for saturated control systems using an lmi approach in practical control systems actuator saturation usually induces a windup phenomenon and potentially results in system instability accordingly this paper develops an observer based auxiliary anti windup compensation scheme to mitigate the effects of actuator limitations on the performance and stability of the controlled system in the proposed approach the controller output signal passing through the saturation element is treated as an external disturbance imported to the designed controller and an auxiliary controller is designed to minimize the difference between the controller output signal and the system input signal the conditions required to maintain the system performance in the presence of actuator saturation are formulated as an lmi criterion the l 2 stability criterion of the anti windup compensator design is also formulated as an lmi condition it is shown that by integrating the two lmi conditions and solving the resulting optimization problem the resulting anti windup controller both minimizes the performance attenuation of the saturated control system and guarantees its l 2 stability

output feedback control of saturated discrete time linear systems using parameter dependent lyapunov functions in this paper we present a new output feedback control approach for discrete time linear systems subject to actuator saturations using parameter dependent lyapunov functions the saturation level indicator serves as a scheduling parameter the resulting nonlinear controller is expressed in a quasi lpv linear parameter varying form and the stabilization and disturbance attenuation problems are formulated and solved as finite dimensional linear matrix inequality lmi optimization problems our approach is less conservative than a single quadratic lyapunov function method specifically the proposed output feedback control law asymptotically stabilizes the open loop system with a larger domain of attraction and achieves better disturbance attenuation under energy and magnitude bounded disturbances

nonlinear bounded control for norm bounded uncertain systems in this paper a method to derive a bounded continuous feedback control function which stabilizes a norm bounded uncertain linear system in a certain region is proposed the aim is to ensure a certain performance level in a neighborhood ellipsoid of the origin through a guaranteed cost state feedback control outside this neighborhood a linear like control with state dependent gains is obtained from the solutions of a family of parameter dependent algebraic riccati equation similar to the one arising in h sub spl infin control

technical communique an anti windup scheme with closed loop stability considerations this paper considers the so called model based approach to anti windup compensation and analyses the stability of the closed loop system for a class of input nonlinearities the degrees of freedom in the anti windup scheme are used to minimise the h norm of the transfer function around the nonlinearity and the small gain theorem is used to prove stability

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

technical communique a convex characterization of dynamically constrained anti windup controllers based on a recent description of deadzone nonlinearities via local sector conditions a new lmi characterization is proposed to compute full order continuous time anti windup controllers with pole constraints more precisely an upper bound is introduced on the real part of the controller poles to avoid slow dynamics which often leads to poor time domain performance as is demonstrated in a short applicative part the introduction of such a bound allows us to efficiently handle the trade off between stability domain enlargement and time domain response relevance

the generalized h 2 control problem abstract in this paper we consider the problem of finding an internally stabilizing controller such that the controlled or regulated signals have a guaranteed maximum peak value in response to arbitrary but bounded energy exogenous inputs more specifically we give a complete solution to the problem of finding a stabilizing controller such that the closed loop gain from l 2 0 to l 0 is below a specified level we consider both state feedback and output feedback problems in the state feedback case it is shown that if this synthesis problem is solvable then a solution can be chosen to be a constant state feedback gain necessary and sufficient conditions for the existence of solutions as well as a formula for a state feedback gain that solves this control problem are obtained in terms of a finite dimensional convex feasibility program after showing the separation properties of this synthesis problem the output feedback case is reduced to a state feedback problem it is shown that in the output feedback case generalized h 2 controllers can be chosen to be observer based controllers the theory is demonstrated with a numerical example

stability and performance for saturated systems via quadratic and nonquadratic lyapunov functions in this paper we develop a systematic lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration the only assumptions we make about the system are well posedness of the algebraic loop and local stability problems to be considered include the estimation of the domain of attraction the reachable set under a class of bounded energy disturbances and the nonlinear l2 gain the regional analysis is established through an effective treatment of the algebraic loop and the saturation deadzone function this treatment yields two forms of differential inclusions a polytopic differential inclusion pdi and a norm bounded differential inclusion ndi that contain the original system adjustable parameters are incorporated into the differential inclusions to reflect the regional property the main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain lyapunov function where the pdi or the ndi is valid with quadratic lyapunov functions conditions for stability and performances are derived as linear matrix inequalities lmis to obtain less conservative conditions we use a pair of conjugate non quadratic lyapunov functions the convex hull quadratic function and the max quadratic function these functions yield bilinear matrix inequalities bmis as conditions for stability and guaranteed performance level the bmi conditions cover the corresponding lmi conditions as special cases hence the bmi results are guaranteed to be as good as the lmi results in most examples the bmi results are significantly better than the lmi results

kinetic equations governing smoluchowski dynamics in equilibrium we continue our study of the statistical properties of particles in equilibrium obeying smoluchowski dynamics we show that the system is governed by a kinetic equation of the memory function form and that the memory function is given by one of the self energies available via perturbation theory as introduced in previous work we determine the memory function explicitly to second order in an expansion in a pseudopotential the method we use allows for a straightforward computation of corrections via a formal expansion and we therefore view it as an improvement over the conventional mode coupling theory mct formalism where it is not clear how to make systematic corrections in addition the formalism we have introduced is flexible enough to allow for a wide array of different approximation schemes including density expansions the convergence criteria for our formal series are not worked out here but the second order equation that we derive is promising in the sense that it leads to analytic and numerical results consistent with expectations from computer simulations of the hard sphere system in addition to replicating the desired features from conventional mct e g a two step decay these particular solutions will be discussed in forthcoming work

absolute stability criteria for multiple slope restricted monotonic nonlinearities absolute stability criteria such as the classical popov criterion guarantee stability for a class of sector bounded nonlinearities although the sector restriction bounds the admissible class of the nonlinearities the local slope of the nonlinearity may be arbitrarily large in this paper the authors derive absolute stability criteria for multiple slope restricted time invariant monotonic nonlinearities like the popov criterion in the single input single output case the authors results provide a simple graphical interpretation involving a straight line in a modified popov plane

dynamic anti windup scheme for feedback linearizable nonlinear control systems with saturating inputs this paper proposes a dynamic compensation scheme for input constrained feedback linearizable nonlinear systems to cope with the windup phenomenon given a dynamic feedback linearizing controller designed without considering its input constraint an additional dynamic compensator is proposed to account for the constraint this dynamic anti windup is based on the minimization of a reasonable performance index the proposed strategy is a nonlinear extended version of park j k choi c h 1995 dynamic compensation method for multivariable control systems with saturating actuators ieee transactions on automatic control 40 9 1635 1640 with simplified derivation of an optimization solution under relaxed assumptions the parameter matrices and structure of the solution are explicitly decided by mathematical optimization for infinite horizon without tuning of design parameters unlike previous schemes during input saturation the role of the anti windup scheme with the proposed dynamic feedback compensator is to maintain the controller states to be exactly the same as those without input saturation the local asymptotic stability and the total stability of the resulting systems are proved the usefulness of the proposed design method is illustrated by comparative simulations for a constrained control system

output feedback robust stabilization of uncertain linear systems with saturating controls an lmi approach the problem of robust controller design is addressed for an uncertain linear system subject to control saturation no assumption is made concerning open loop stability and no a priori information is available regarding the domain of stability a saturating linear output feedback law and a safe set of initial conditions are determined using a heuristic based on iterative lmi relaxation procedures a readily implementable algorithm based on standard numerical techniques is described and illustrated on two numerical examples

inherent observer property in a class of anti windup compensators owing to the types of non linearities involved the analysis and the comparison of different anti windup compensators that are available in the literature become difficult towards achieving a better understanding of the mechanisms of these anti windup compensators we here expose the observer property inherent in a class of anti windup compensators this observer property allows us to unify these anti windup compensators as special cases of the generalized anti windup compensator due to astrom and wittenmark 1984 and provides a general framework to investigate their performance

a novel approach for static anti windup compensation of one sided lipschitz systems under input saturation abstract this paper illustrates a new strategy for designing the local static anti windup aw compensator for nonlinear systems with one sided lipschitz osl nonlinearities under saturating actuators and exogenous disturbances the static aw strategy is designed such that the resulting closed loop system with osl nonlinearity actuator saturation and exogenous disturbance is stable and the region of attraction can be maximized inequalities based conditions are formulated for the static aw gain design by using lyapunov stability theory sector condition l2 gain reduction osl inequality and quadratic inner bounded qib condition the proposed aw technique is simpler to design straightforward to implement and deals with a broader class of systems in contrast to conventional methods an application example demonstrates that the proposed static aw can successfully mitigate the saturation consequences in osl nonlinear systems

robust stabilizing controller design for takagi sugeno fuzzy descriptor systems under state constraints and actuator saturation abstract the aim of this paper is to present a new framework for designing robust controllers for uncertain nonlinear systems described by takagi sugeno fuzzy descriptor systems and subject to input and state constraints for this a novel structure of modified parallel distributed compensation control laws is proposed the controller parameters can be obtained through the numerical resolution of an optimization problem with linear matrix inequality constraints derived from lyapunov s stability theory and the choice of an original lyapunov function this ensures the stabilization of the closed loop system and the respect of the state and input constraints regionally the technique is illustrated through three numerical examples

stability analysis for a class of nonlinear discrete time control systems subject to disturbances and to actuator saturation this paper addresses the stability characterisation problem for a class of nonlinear discrete time control systems subject to actuator saturation and energy bounded disturbance inputs the considered class of systems covers all nonlinear discrete time systems that can be modelled by rational difference equations based on quadratic and piecewise quadratic lyapunov functions conditions based on linear matrix inequalities are proposed to analyse the asymptotic stability internal stability and the l2 input to state stability external stability of the closed loop system the proposed conditions are then incorporated into convex optimisation problems to either maximise an estimate of the region of attraction or a bound on the admissible l2 disturbances and also to obtain an estimate of the system l2 gain for an admissible set of disturbances

brief stability analysis of discrete time systems with actuator saturation by a saturation dependent lyapunov function in this paper stability of discrete time linear systems subject to actuator saturation is analyzed using a saturation dependent lyapunov function this saturation dependent lyapunov function captures the real time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction which is based on the solution of an lmi optimization problem numerical examples are presented to show the effectiveness of the proposed method

the l2 anti windup problem for discrete time linear systems definition and solutions abstract the anti windup problem for discrete time linear systems is formalized in terms of the l 2 norm of the deviation of the actual response of the system with saturation and anti windup compensation from the ideal unconstrained response we show that paralleling continuous time results a r teel n kapoor the l 2 anti windup problem its definition and solution in proceedings of the 4th ecc brussels belgium july 1997 the problem is globally solvable if and only if the plant is non exponentially unstable and it is robustly globally solvable if and only if the plant is exponentially stable we provide a constructive solution whenever the problem is solvable also offered is a high performance global solution for exponentially stable plants based on receding horizon control illustrative simulations are included

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

a parametric periodic lyapunov equation with application in semi global stabilization of discrete time periodic systems subject to actuator saturation this paper is concerned with semi global stabilization of discrete time linear periodic systems subject to actuator saturation provided that the open loop characteristic multipliers are within the closed unit circle a low gain feedback design approach is proposed to solve the problem by state feedback our approach is based on the solution to a parametric discrete time periodic lyapunov equation the proposed approaches not only generalize the corresponding results for time invariant systems to periodic systems but also reveal some important intrinsic properties of this class of periodic matrix equations a numerical example is worked out to illustrate the effectiveness of the proposed approaches

field theoretic formulation of kinetic theory basic development we show how kinetic theory the statistics of classical particles obeying newtonian dynamics can be formulated as a field theory the field theory can be organized to produce a self consistent perturbation theory expansion in an effective interaction potential the need for a self consistent approach is suggested by our interest in investigating ergodic nonergodic transitions in dense fluids the formal structure we develop has been implemented in detail for the simpler case of smoluchowski dynamics one aspect of the approach is the identification of a core problem spanned by the variables the number density and b a response density in this paper we set up the perturbation theory expansion with explicit development at zeroth and first order we also determine all of the cumulants in the noninteracting limit among the core variables and b

siso linear system control via saturating actuator l2 tracking performance in the presence of arbitrary shaped inputs most studies on linear system control in the presence of actuator saturation have focused on closed loop asymptotic stabilisation available tracking results are generally limited to constraint compatible inputs references disturbances with known exogenous input models the problem of output reference tracking in the presence of arbitrary shaped not necessarily constraint compatible inputs has yet to be investigated in this study we show that an tracking performance is achievable for siso linear systems using a given class of saturated controllers accordingly the tracking error energy resp power is bounded by the energy resp power of a well defined mismatch input depending on the disturbance and reference compatibility in the disturbance free case this entails perfect asymptotic tracking of arbitrary shaped constraint compatible reference signals otherwise the average tracking quality is proportional to the mismatch input power in the case of periodic inputs constraint compatible or not

technical communique lmi relaxations for robust stability of linear systems with saturating controls a method is proposed for studying robust stability of uncertain linear systems subject to actuator saturation it hinges upon successive lmi relaxations and therefore can readily be implemented using widely available numerical tools the technique is illustrated on two examples and is shown to significantly improve previously published results

an anti windup design for linear systems with input saturation abstract an anti windup design problem is posed and it is shown that all observer based anti windup modifications solve this problem at least locally sufficient conditions for an observer based anti windup modification to solve the global version of this problem are presented a novel observer based anti windup design is then proposed such that the anti windup problem can be interpreted in terms of a reduced order system in particular the proposed anti windup design induces an invariant subspace for the dynamic behavior of the mismatch between the constrained and unconstrained closed loops the dynamics in this invariant subspace are identical to the behavior of the plant with input saturation starting at the origin stabilized by linear state feedback and driven by the mismatch between the unconstrained input and this input passed through a saturation function the second part of the paper shows how the original dynamic compensator can be modified while retaining those dynamic features that produce a desirable closed loop steady state response to ensure that the requisite invariant subspace exists and it is reasonably tuned for input saturation two case studies are carried out on systems that have been investigated in the literature

brief multiplier theory for stability analysis of anti windup control systems we apply the passivity theorem with appropriate choice of multipliers to develop a general framework for analyzing stability of anti windup bumpless transfer awbt schemes for appropriate choices of the multipliers we reduce the resulting sufficient conditions for stability to equivalent linear matrix inequalities lmis we show that a number of previously reported attempts to analyze awbt stability using seemingly diverse techniques such as the popov circle and off axis circle criteria the optimally scaled small gain theorem generalized m upper bound and describing functions can all be generalized within the framework of this paper

analysis and design for discrete time linear systems subject to actuator saturation we present a method to estimate the domain of attraction for a discrete time linear system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis the following surprising result is revealed for systems with single input suppose that an ellipsoid is made invariant with a linear feedback then it is invariant under the saturated linear feedback if and only if there exists a saturated nonlinear feedback which makes the ellipsoid invariant finally the set invariance condition is extended to determine invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements

augmented lyapunov function approach to l2 gain analysis for discrete time systems with saturation nonlinearities abstract this paper presents a method for l 2 gain analysis of discrete time systems with saturation nonlinearity by using an augmented lyapunov functional by using sector and slope properties of the saturation nonlinearity the l 2 gain performance criterion is obtained via lmi formulation the proposed lyapunov function have augmented quadratic form with states as well as the sector bounded nonlinear function numerical examples show that the proposed method is less conservative than the existing ones

stationary processes whose filtrations are standard we study the standard property of the natural filtration associated to a 0 1 valued stationary process in our main result we show that if the process has summable memory decay then the associated filtration is standard we prove it by coupling techniques for a process whose associated filtration is standard we construct a product type filtration extending it based upon the usual couplings and the vershik s criterion for standardness

anti windup based dynamic controller synthesis for nonlinear systems under input saturation this paper describes the design of dynamic controller and static anti windup compensator awc for lipschitz nonlinear systems under input saturation global and local awc based control schemes for stabilization of the nonlinear systems are proposed and necessary conditions for feasibility of the control approaches are investigated a one step approach for simultaneous design of h controller and awc by means of linear matrix inequalities lmis is presented herein which supports multi objective synthesis to attain stabilization or tracking robustness against disturbance and noise and penalization of large and high frequency control signals this multi objective synthesis can be accomplished by incorporating design weights as commonly used in the standard h control theory to design a performance oriented anti windup based control scheme lmis for the global control of the nonlinear systems subject to input saturation are derived by application of a quadratic lyapunov function the lipschitz condition the global sector condition l 2 gain reduction substantial matrix algebra and variable transformation in order to cope with unstable and oscillatory nonlinear systems lmi based local results are established using a local sector condition additional conditions are derived by incorporating properties of the saturation function to ensure well posedness of the controller two simulation examples are provided to show the effectiveness of the proposed control schemes for control of stable and chaotic nonlinear systems under input saturation

fundamental theory of statistical particle dynamics we present a fundamental theory for the kinetics of systems of classical particles the theory represents a unification of kinetic theory brownian motion and field theory it is self consistent and is the dynamic generalization of the functional theory of fluids in equilibrium this gives one a powerful tool for investigating the existence of ergodic nonergodic transitions near the liquid glass transition

scheduled controllers for linear systems with bounded actuators state and output feedback controllers are designed for disturbance attenuation in linear systems with bounded actuators the controller is scheduled according to the proximity to the origin of the state of the plant in the state feedback case and the compensator state in the case of output feedback this procedure yields a linear parameter varying structure for the controller that allows higher gain and hence higher performance controllers as the states move closer to the origin the main results give sufficient conditions for the satisfaction of a parameter dependent performance measure without violating the saturation bounds linear splines are used to obtain solutions that can be obtained by standard lmi software examples including an open loop unstable system highlight the application of the results

optimal directionality compensation in processes with input saturation non linearities a notion of process directionality in input constrained processes is defined and the class of processes that do not exhibit the process directionality is characterized an optimal directionality compensator for non linear processes with actuator saturation non linearities is presented given an unconstrained controller output and the characteristic decoupling matrix of the process under consideration the compensator calculates an optimal constrained feasible process input that results in a process response as close as possible to the response of the same process to the unconstrained controller output the compensator can be used for both linear and non linear processes irrespective of the type of controller being used for processes whose non singular characteristic matrix can be made diagonal by row or column rearrangements the optimal directionality compensator is identical to a series of limiters clippers this class of processes does not exhibit the process directionality over a short time

simultaneous quadratic stabilization for a class of non linear systems with input saturation using dynamic surface control in this paper a new method to estimate the initial condition set which guarantees the quadratic stability for a class of non linear systems via dynamic surface control dsc in the presence of input saturation has been proposed the estimated set is enlarged to allow some degree of input saturation while achieving the simultaneous quadratic stability of the system in the domain a convex optimization problem to obtain ellipsoidal initial condition sets via a linear matrix inequality lmi approach as well as an illustrative example will be presented

sufficient conditions of standardness for filtrations of stationary processes taking values in a finite space let x be a stationary process with finite state space a bressaud et al ann probab 34 2006 1589 1600 recently provided a sufficient condition for the natural filtration of x to be standard when a has size 2 their condition involves the conditional laws p x of x0 conditionally on the whole past xk k 1 x and controls the strength of the influence of the old past of the process on its present x0 it involves the maximal gaps between p x and p y for infinite sequences x and y which coincide on their n last terms in this paper we first show that a slightly stronger result holds for any finite state space then we provide sufficient conditions for standardness based on average gaps instead of maximal gaps

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

antiwindup for stable linear systems with input saturation an lmi based synthesis this paper considers closed loop quadratic stability and l sub 2 performance properties of linear control systems subject to input saturation more specifically these properties are examined within the context of the popular linear antiwindup augmentation paradigm linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification called the unconstrained closed loop behavior building on known results on h sub spl infin and lpv synthesis the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem which has an attractive system theoretic interpretation the lower bound on the achievable l sub 2 performance is the maximum of the open and unconstrained closed loop l sub 2 gains in the special cases of zero order static and plant order antiwindup compensation the feasibility conditions become convex linear matrix inequalities it is shown that if and only if the plant is asymptotically stable plant order linear antiwindup compensation is always feasible for large enough l sub 2 gain and that static antiwindup compensation is feasible provided a quasi common lyapunov function between the open loop and unconstrained closed loop exists using the solutions to the matrix feasibility problems the synthesis of the antiwindup augmentation achieving the desired level of l sub 2 performance is then accomplished by solving an additional lmi

a switching anti windup design based on partitioning of the input space abstract this paper revisits the problem of enlarging the domain of attraction of a linear system with multiple inputs subject to actuator saturation by designing a switching anti windup compensator the closed loop system consisting of the plant the controller and the anti windup compensator is first equivalently formulated as a linear system with input deadzone we then partition the input space into several regions in one of these regions all inputs saturate with the time derivative of the saturated input being zero in each of the remaining regions there is a unique input that does not saturate the time derivative of the deadzone function associated with the unsaturating input is zero by utilizing these special properties of the inputs on an existing piecewise lyapunov function of the augmented state vector containing the deadzone function of inputs we design a separate anti windup gain for each region of the input space the switching from one anti windup gain to another is activated when the input signals leave one region for another which can be implemented online since only the measurement of the input signals is required simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction than the existing approaches

saturated linear quadratic regulation of uncertain linear systems stability region estimation and controller design this paper considers the problems of estimating the stability region domain of attraction and controller design for uncertain linear continuous time systems with input saturation when linear quadratic lq optimal controller is used by exploiting the structure of the lq controller and the property of saturation functions it is established that the estimation of stability region can be obtained by solving linear matrix inequality lmi problems moreover an iterative lmi ilmi algorithm is presented to design an lq controller such that the largest estimated stability region can be obtained two examples are given to compare our results with existing ones

feedback linearizing control of discrete time nonlinear systems with input constraints a feedback linearizing control strategy for discrete time nonlinear systems subject to input constraints is proposed the control system comprises i a feedback linearizing controller ii a constraint mapping algorithm that transforms the actual input constraints into constraints on the feedback linearized system and iii a linear model predictive controller that regulates the resulting constrained linear system closed loop stability analysis is a challenging problem because the transformed constraints are state dependent sufficient conditions for asymptotic stability are presented for fully and partially feedback linearizable systems as part of the analysis a new stability result for unconstrained discrete time nonlinear systems which parallels a well known continuous time result is derived

piecewise quadratic lyapunov functions for systems with deadzones or saturations a piecewise quadratic lyapunov function is developed for the analysis of the global and regional performances for systems with saturation deadzone in a general feedback configuration with an algebraic loop this piecewise quadratic lyapunov function effectively incorporates the structure of the saturation deadzone nonlinearity several sector like conditions are derived to describe the complex nonlinear algebraic loop these conditions transform several performance analysis problems into optimization problems with linear or bilinear matrix inequalities the effectiveness of the results is demonstrated with numerical examples

stability criteria of sector and slope restricted lur e systems presents stability criteria of sector and slope restricted lur e systems in terms of linear matrix inequalities by fully exploiting inherent properties of sector and slope restrictions in the time domain interpreting the time domain criteria in the frequency domain furthermore supplies simpler expressions several examples show excellent performances of these criteria

a magnitude and rate saturation model and its use in the solution of a static anti windup problem in this paper we address the anti windup design problem for linear control systems with strictly proper controllers in the presence of input magnitude and rate saturation using generalized sector condition we provide an lmi based procedure for the construction of a linear anti windup gain acting on the controller state equation such that regional closed loop stability is guaranteed and suitable performance measures are optimized the approach is successfully illustrated on a simulation example

robust control of uncertain multi inventory systems via linear matrix inequality we consider a continuous time linear multi inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes we address the problem of e stabilising the inventory since this implies some reduction of the inventory costs the main results are certain conditions under which e stabilisability is possible through a saturated linear state feedback control all the results are based on a linear matrix inequalities approach and on some recent techniques for the modelling and analysis of polytopic systems with saturations numerical simulations are provided

antiwindup design with guaranteed regions of stability an lmi based approach this note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs considering that a linear dynamic output feedback has been designed to stabilize the linear system without saturation a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed loop system it is shown that the closed loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity a modified sector condition is then used to obtain stability conditions based on quadratic lyapunov functions differently from previous works these conditions are directly in linear matrix inequality form some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones

simultaneous l p stabilization and internal stabilization of linear systems subject to input saturation state feedback case abstract we consider the problem of simultaneous finite gain l p stabilization and internal stabilization of linear systems subject to input saturation via linear static state feedback we show that bounded input finite gain l p stabilization and local asymptotic stabilization can always be achieved simultaneously no matter where the poles of the open loop system are and the locations of these poles play a role only when bounded input finite gain l p stabilization and global or semi global stabilization are required simultaneously

brief paper simultaneous linear and anti windup controller synthesis using multiobjective convex optimization we present a method for the synthesis of a control law for input constrained linear systems that incorporates both a traditional linear output feedback controller as well as a static anti windup compensator unlike traditional two step anti windup controller designs in which the linear controller and anti windup compensator are designed sequentially our method synthesizes all controller parameters simultaneously this one step design retains the anti windup structure thus providing structurally a priori compensation for saturation we derive sufficient conditions for guaranteeing global quadratic stability and for satisfying multiple possibly conflicting performance objectives on the constrained and unconstrained closed loop dynamics the resulting synthesis problem is recast as an optimization over linear matrix inequalities lmis we demonstrate the proposed method on a benchmark problem

piecewise fuzzy anti windup dynamic output feedback control of nonlinear processes with amplitude and rate actuator saturations in this paper a novel anti windup dynamic output compensator is developed to deal with the robust h infin output feedback control problem of nonlinear processes with amplitude and rate actuator saturations and external disturbances via fuzzy modeling of nonlinear systems the proposed piecewise fuzzy anti windup dynamic output feedback controller is designed based on piecewise quadratic lyapunov functions it is shown that with sector conditions robust output feedback stabilization of an input constrained nonlinear process can be formulated as a convex optimization problem subject to linear matrix inequalities simulation study on a strongly nonlinear continuously stirred tank reactor cstr benchmark plant is given to show the performance of the proposed anti windup dynamic compensator

gain scheduled output control design for a class of discrete time nonlinear systems with saturating actuators this paper deals with the stabilization of a class of nonlinear discrete time systems under control saturations including time varying parameter dependency the control law studied consists of the gain scheduled feedback of the measured output and of the nonlinearity present in the dynamics of the controlled system furthermore the saturations are taken into account by modeling the nonlinear saturated system through a dead zone nonlinearity satisfying a modified sector condition thus as for precisely known systems linear matrix inequality lmi stabilization conditions are proposed for such a generic system these conditions can be cast into convex programming problems for design purposes an illustrative example stresses the efficiency of the main result

anti windup synthesis for systems with rate limits using riccati equations this article develops an anti windup aw scheme for systems with rate limited actuators the main results show how a full order aw compensator can be synthesised using an algebraic riccati equation and several free parameters a further result then shows how the free parameters may be chosen to influence in an intuitive way the local gain of the system and the size of the region of attraction the results are of interest due to their low computational burden and hence their applicability to the systems of large state dimension

brief multivariable anti windup controller synthesis using linear matrix inequalities we present a general formulation of the problem of multi variable anti windup bumpless transfer awbt controller synthesis which provides sufficient conditions for stability covering a large class of typical input nonlinearities such as saturation deadzone and switching override nonlinearities the resulting synthesis method demonstrates graceful performance degradation whenever input nonlinearities are active through minimization of a weighted l 2 gain the main contribution of the paper is that the awbt controller synthesis using static compensation is cast as a convex optimization over linear matrix inequalities

predictive control for sector bounded nonlinear model and its application to solid oxide fuel cell systems in this paper a nonlinear model predictive control method is presented for solid oxide fuel cell systems for realistic modeling a sector bounded nonlinear model with input constraint is considered as a performance index we consider one horizon cost function that is represented by the weighted sum of state control input and nonlinear function by minimizing the upper bound of the cost function the optimized control input sequences are obtained for cost monotonicity a terminal inequality condition is derived in terms of a finite number of linear matrix inequalities lmis by using augmented vector feedback law which consists of state and sector bounded nonlinear function in order to show the effectiveness of the proposed method the sector bounded nonlinear model is derived for the solid oxide fuel cell systems and the system performance is verified by applying the proposed mpc algorithm to the systems

l2 anti windup for linear dead time systems in this paper we address and solve the problem of antiwindup augmentation for linear systems with input and output delay in particular we give a formal definition of the anti windup construction problem in the global local robust and nominal cases for each of these cases we show that a specific anti windup compensation structure which is a generalization of the approach in 131 is capable of solving the anti windup problem whenever this is solvable the effectiveness of the proposed scheme is shown on a simple example taken from the literature in which the plant is a marginally stable linear system the anti windup design problem has been qualitatively stated already from the 1950 s both in the analog and in the digital control framework however the arisin solutions were at that time mainly application oriente and not applicable to large classes of control systems it was only in the 1980 s that some design techniques ap plicable to large classes of control systems were formalized although the issue of performance characterization and improvement was still mostly unsolved an interestin survey of these techniques can be found in 141 anotier dhenomenon that is often found in coninnction

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

a stability inequality for nonlinear feedback systems with slope restricted nonlinearity using lyapunov s direct method a stability inequality in frequency domain is derived for nonlinear feedback systems with slope restricted nonlinearity in the present approach a transformed system that involves the slope of the nonlinearity is considered thus leading to a stability inequality that incorporates the slope information but not the sector information of the nonlinearity the approach is essentially an extension of a recent idea of the author

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

smoluchowski dynamics and the ergodic nonergodic transition we use the recently introduced theory for the kinetics of systems of classical particles to investigate systems driven by smoluchowski dynamics we investigate the existence of ergodic nonergodic ene transitions near the liquid glass transition we develop a self consistent perturbation theory in terms of an effective two body potential and work to second order in this potential at second order we have an explicit relationship between the static structure factor and the effective potential and choose the static structure factor in the case of hard spheres to be given by the solution of the percus yevick approximation for hard spheres then using the analytically determined ene equation for the ergodicity function we find an ene transition for packing fraction greater than a critical value 0 76 which is physically unaccessible the existence of a linear fluctuation dissipation theorem in the problem is shown and used to great advantage

commuting matrices equilibrium points for control systems with single saturated input in this paper commutative matrices of multiple input multiple output mimo linear systems are considered the existence of the feedback matrices of a commutative state matrix set in the mimo closed loops is reduced to the existence of an invariant subspace of a matrix a the existence of feedback matrices in systems in open loop is equivalent to the existence of the solution of matrix equations denoted by kronecker products by defining new equilibrium points the relationship between equilibrium points are discussed for a linear system with a single saturated input four criteria for equilibrium points are outlined for such linear systems finally four interesting examples including their corresponding simulink plots are shown to illustrate the above results

brief paper output feedback design for saturated linear plants using deadzone loops in this paper we present an lmi based synthesis approach on output feedback design for input saturated linear systems by using deadzone loops algorithms are developed for minimizing the upper bound on the regional l 2 gain for exogenous inputs with l 2 norm bounded by a given value and for minimizing this upper bound with a guaranteed reachable set or domain of attraction the proposed synthesis approach will always lead to regionally stabilizing controllers if the plant is exponentially unstable to semi global results if the plant is non exponentially unstable and to global results if the plant is already exponentially stable where the only requirement on the linear plant is detectability and stabilizability the effectiveness of the proposed techniques is illustrated with one example