non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

remarks on linearization of discrete time autonomous systems and nonlinear observer design abstract this paper presents necessary and sufficient conditions under which a discrete time autonomous system with outputs is locally state equivalent to an observable linear system or a system in the nonlinear observer form krener and isidori 1983 in particular an open problem raised in lee and nam 1991 namely the observer linearization problem is solved for a nonlinear system which may not be invertible i e the mapping f may not be a local diffeomorphism as a consequence the nonlinear observer design problem is solved by means of exact linearization techniques

discrete time certainty equivalence output feedback allowing discontinuous control laws including those from model predictive control we present certainty equivalence output feedback results for discrete time nonlinear systems that employ possibly discontinuous control laws in the feedback loop coupling assumptions of nominal robustness with uniform observability or detectability assumptions we assert nominally robust stability for output feedback closed loops we further show that model predictive control mpc can be used to generate a feedback control law that is robustly globally asymptotically stabilizing when used in a certainty equivalence output feedback closed loop allowing for discontinuous feedback control laws is important for systems employing mpc since the method can and sometimes necessarily does result in discontinuous control laws

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

finite time observers application to secure communication in this paper control theory is used to formalize finite time chaos synchronization as a nonlinear finite time observer design issue this paper introduces a finite time observer for nonlinear systems that can be put into a linear canonical form up to an output injection the finite time convergence relies on the homogeneity properties of nonlinear systems the observer is then applied to the problem of secure data transmission based on the finite time chaos synchronization and the two channel transmission method

further results on nonlinear receding horizon observers further results are proposed that concern the design and the convergence of receding horizon nonlinear observers the key feature is the definition of observability radius in relation with a prespecified compact set of initial configurations this enables a semiglobal convergence result to be derived that turns out to be a global convergence result when appropriate regularity assumptions are made a simple example is proposed to illustrate the basic features of the note

an immersion based observer design for rank observable nonlinear systems in this note an observer design for a wide class of nonlinear systems is proposed it is based on some high gain design for the particular case of state affine systems up to triangular nonlinearity on the one hand and immersion of nonlinear systems into such a form on the other hand conditions for the observer convergence are given in terms of appropriate excitation and a constructive procedure for the immersion is presented the methodology is illustrated by examples of application

state equivalence of discrete time nonlinear control systems to state affine form up to input output injection in this paper the problem of transformation of a discrete time nonlinear control system into a state affine form up to input output injection is addressed a set of coordinate free necessary and sufficient conditions for such a transformation to be possible is first proposed and a more constructive procedure is then presented no restriction of invertibility of the state transition map is required

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

on the uniform observability of discrete time nonlinear systems in constructing an observer for a discrete time nonlinear system the system is commonly required to satisfy a certain kind of uniform observability condition that is the state should always be reconstructible from observation windows of a specific length irrespective of the values of the state and inputs in this technical note it is proved that this uniform requirement is unnecessary in the sense that if the initial state and inputs are on a compact set then the uniform observability is derived from its non uniform counterpart

the extended luenberger observer for nonlinear systems abstract for nonlinear single input single output systems dot x f x u y h x u the relationships for a state transformation into the nonlinear observer canonical form are developed it is possible to dimension a nonlinear observer by an eigenvalue assignment without solving the nonlinear partial differential equations for the transformation if the transformed nonlinearities are linearized about the reconstructed state with reference to the extended kalman filter algorithm this nonlinear observer design is called the extended luenberger observer

length of state cycles of random boolean networks an analytic study in this paper we consider the mean length of transients and the length of state cycles in random boolean networks we present an approximate calculation of these quantities as a function of the size and connectivity of the network where using an annealed approximation we derive a recursive formula for the length of steps of the system using the mean step length and an effective momentary state space we calculate an approximate formula for the probability distribution function pdf of the length of state cycles and transients we compare this pdf with analytical results in special cases and with simulations by the monte carlo procedure

brief paper on the observability of discrete time dynamic systems a geometric approach a coordinate free description for dynamic systems described by explicit nonlinear difference equations in one independent variable via a differential geometric framework is presented based on this covariant approach suitable geometric objects for discrete time dynamics are introduced especially the observability along a trajectory is discussed and transformations to normal forms are derived in addition the obtained local observability criteria can be checked by computer algebra algorithms some examples illustrate the proposed approach

moving horizon observers and observer based control in this paper two topics are explored a new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed the moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing or approximately minimizing a cost function over the preceding interval horizon t t t as t advances so does the horizon convergence of the estimator is established under the assumption that the corresponding global optimization problem can be approximately solved and a uniform reconstructability condition is satisfied the latter condition is automatically satisfied for linear observable systems the utility of the estimator for receding horizon control is explored in particular stability of a composite moving horizon system comprising a moving horizon regulator and a moving horizon observer is established

on the observer problem for discrete time control systems this paper studies the construction of observers for nonlinear time varying discrete time systems in a general context where a certain function of the states must be estimated appropriate notions of robust complete observability are proposed under which a constructive proof of existence of an observer is developed moreover a transitive observer property is proven according to which a state observer can be generated as the series connection of two observers the analysis and the results are developed in general normed linear spaces to cover both finite dimensional and infinite dimensional systems

on the observer design in discrete time abstract the paper deals with the equivalence under coordinates change and output transformation of a discrete time nonlinear system to observer canonical forms necessary and sufficient conditions for local equivalence to these forms are given

constrained state estimation for nonlinear discrete time systems stability and moving horizon approximations state estimator design for a nonlinear discrete time system is a challenging problem further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances one strategy for constrained state estimation is to employ online optimization using a moving horizon approximation we propose a general theory for constrained moving horizon estimation sufficient conditions for asymptotic and bounded stability are established we apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation examples are used to illustrate the benefits of constrained state estimation our framework is deterministic

nonlinear observers for autonomous lipschitz continuous systems this paper considers the state observation problem for autonomous nonlinear systems an observation mapping is introduced which is defined by applying a linear integral operator rather than a differential operator to the output of the system it is shown that this observation mapping is well suited to capture the observability nature of smooth as well as nonsmooth systems and to construct observers of a remarkably simple structure a linear state variable filter followed by a nonlinearity the observer is established by showing that observability and finite complexity of the system are sufficient conditions for the observer to exist and by giving an explicit expression for its nonlinearity it is demonstrated that the existence conditions are satisfied and hence our results include a new observer which is not high gain for the wide class of smooth systems it is shown that the observer can as well be designed to realize an arbitrary finite accuracy rather than ultimate exactness on a compact region of the state space this requires only observability of the system a corresponding numerical design procedure is described which is easy to implement and computationally feasible for low order systems

further results on the uniform observability of discrete time nonlinear systems in this technical note the relation between notions of uniform observability of discrete time nonlinear systems based on injectivity of an observation map window the full rankness of its jacobian and a k function is investigated it is proven that a system is uniformly observable in the sense of injectivity of the observation map together with the full rankness of its jacobian if and only if it is so in some k function senses

moving horizon state estimation for nonlinear discrete time systems new stability results and approximation schemes a moving horizon state estimation problem is addressed for a class of nonlinear discrete time systems with bounded noises acting on the system and measurement equations as the statistics of such disturbances and of the initial state are assumed to be unknown we use a generalized least squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding window strategy for the resulting estimator the existence of bounding sequences on the estimation error is proved in the absence of noises exponential convergence to zero is obtained moreover suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value the approximate solution can be determined either on line by directly minimizing the cost function or off line by using a nonlinear parameterized function simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended kalman filter

bundle methods for sum functions with easy components applications to multicommodity network design we propose a version of the bundle scheme for convex nondifferentiable optimization suitable for the case of a sum function where some of the components are easy that is they are lagrangian functions of explicitly known compact convex programs this corresponds to a stabilized partial dantzig wolfe decomposition where suitably modified representations of the easy convex subproblems are inserted in the master problem as an alternative to iteratively inner approximating them by extreme points thus providing the algorithm with exact information about a part of the dual objective function the resulting master problems are potentially larger and less well structured than the standard ones ruling out the available specialized techniques and requiring the use of general purpose solvers for their solution this strongly favors piecewise linear stabilizing terms as opposed to the more usual quadratic ones which in turn may have an adverse effect on the convergence speed of the algorithm so that the overall performance may depend on appropriate tuning of all these aspects yet very good computational results are obtained in at least one relevant application the computation of tight lower bounds for fixed charge multicommodity min cost flow problems