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

linearization of discrete time systems abstract we characterize the equivalence of single input single output discrete time nonlinear systems to linear ones via a state coordinate change and with or without feedback four cases are distinguished by allowing or disallowing feedback as well as by including the output map or not the interdependence of these problems is analyzed an important feature that distinguishes these discrete time problems from the corresponding problem in continuous time is that the state coordinate transformation is here directly computable as a higher composition of the system and output maps finally certain connections are made with the continuous time case

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

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

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

spectral properties of some jacobi matrices with double weights abstract we study the spectral properties of jacobi matrices with the weights satisfying 2n 1 2n na or 2n 2n 1 na a 0 we show that for a 1 these are cases of spectral phase transitions in a we use a new method of estimating transfer matrix products to describe the absolutely continuous part of these operators for a 1 the existence of a spectral gap is proved we also show how the results for double weights can be used for the spectral analysis of the jacobi matrices related to some birth and death processes previously studied by janas and naboko

on subordinacy and analysis of the spectrum of one dimensional schrodinger operators abstract by considering the behaviour as n of the ratio of l2 0 n norms of solutions of d 2 dr 2 v r u xu 0 r x r a characterisation of the absolutely continuous and singular spectra of one dimensional schrodinger operators is deduced the analysis is applicable to all operators for which l d 2 dr 2 v r is regular at 0 and in the limit point case at infinity with v r locally integrable

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

receding horizon control and discontinuous state feedback stabilization this paper addresses three aspects of receding horizon control in discrete time 1 feedback stabilization of general nonlinear systems with receding horizon control 2 the generation of stabili

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

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

analytic discs attached to conormal bundles of cr manifolds abstract letmbe a cr submanifold ofx c n t m xthe conormal bundle tominx zo resp po a point ofm resp t m x def t m x 0 with po zo aa small analytic disc c1up to the boundary attached tomthroughzo a aliftofatot xthroughpoattachedt m x if the levi form ofmhas a constant number of negative eigenvalues in a neighborhood ofp0then we show that in factais contained inmanda int m x whenmis a hypersurface and it is pseudoconvex i e the number of its negative levi eigenvalues is identically 0 then the inclusiona mis classical and follows from the hopf lemma applied to a plurisubharmonic exhaustion function as in d f note that in this case the existence of a lifta t m xis automatic according to b f 1980 math subject classification 1985 revision 32 f

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

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

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

exact linearization of nonlinear systems trajectory tracking with bounded controls and state constraints the exact linearization of nonlinear control systems provides a useful method for designing feedback controllers based on the linear model in which the nonlinear plant is transformed this paper deals with two drawbacks involved in this method when applied to trajectory tracking problems the control must be bounded and the evolution of the state variables must lie within a determined region of the state space conditions for fulfilling both constraints are given and an application to a robot manipulator is shown

spectral theory for a class of periodically perturbed unbounded jacobi matrices elementary methods we use elementary methods to give a full characterization of the spectral properties of unbounded jacobi matrices with zero diagonal and off diagonal entries of the type n n c n where n is a real periodic sequence the spectral properties depend strongly on the parity of the minimal period of c n the methods used are asymptotic diagonalization techniques including the finite difference version of levinson s theorem subordinacy theory and the variational principle

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

feedback linearization of sampled data systems it is shown that feedback linearizability of a continuous time system can be destroyed through the introduction of the usual sample and hold devices a method whereby a feedback linearizable discrete time model can be recovered is given

jacobi matrices with rapidly growing weights having only discrete spectrum we establish sufficient conditions for self adjointness on a class of unbounded jacobi operators defined by matrices with main diagonal sequence of very slow growth and rapidly growing off diagonal entries with some additional assumptions we also prove that these operators have only discrete spectrum

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

jacobi matrices with power like weights grouping in blocks approach the paper deals with jacobi matrices with weights k given by k k 1 k where 12 1 and limk k 0 the main question studied here concerns when the spectrum of the operator j defined by the jacobi matrix has absolutely continuous component covering the real line a sufficient condition is given for a positive answer to the above question the method used in the paper is based on a detailed analysis of generalized eigenvectors of j in turn this analysis relies on the so called grouping in blocks approach to a large product of the transfer matrices associated to j