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In this paper, we propose and solve the problem of feedback linearization of single-input control affine time-varying nonlinear systems. Feedback linearizability of time-varying is shown to be equivalent to the orbital feedback linearizability (or feedback linearization by state-dependent time scaling) of an extended version of the time-varying system. Necessary and sufficient conditions for feedback...
The present research work aims at the development of a systematic method to arbitrarily assign the zero dynamics of a nonlinear system by constructing the requisite synthetic output maps. The minimum-phase synthetic output maps constructed can be made statically equivalent to the original output maps, and therefore, they could be directly used for nonminimum-phase compensation purposes. Specifically,...
This paper describes the effects of input saturation in model-based fault diagnosis. A linear model has been used for the residual generator, in order to show its lack of robustness. The experiments have been developed on a simple simulation case: a liquid tank. The aim of the paper is to show the relation between the degree of nonlinearity and the performance of a diagnosis method based on linear...
In this paper, a sensor fault diagnosis and accommodation method is developed in nonlinear case. This method makes possible the sensor faults compensation. Its principle is based on the on-line detection, localization and estimation of a faulty element when a fault occurs on a nonlinear system. Then, a new control law is computed in order to compensate the fault effect on the system. The performances...
The problem of observer design for robust residual generation in nonlinear discrete-time systems is considered. The method is proposed to solve this problem involving nonlinear time-dependent transformation of state-space system model into strict feedback form. To make this transformation practicable, algebra of time-dependent functions is developed.
In this paper, we introduce the notions of state-space symmetry for nonlinear systems and of the cross operator as a nontrivial natural extension of the linear symmetric case, in terms of the controllability and observability operators associated to it. We give a characterization of a symmetric nonlinear system in terms of the cross operator and a coordinate transformation. Then we analyze the use...
This paper deals with computer simulation of nonlinear control systems specified in the form of so-called generalized transfer functions. It briefly summarizes the underlying theoretical concepts, discusses the basics of their software implementation in Maple computer algebra system and presents special-purpose tools developed for simulation of generalized transfer functions in the MATLAB/Simulink...
This report presents a study on the problem of residual evaluation and threshold computation for detection of faults in continuous time nonlinear systems. A generalized framework for designing norm-based residual evaluation scheme is proposed. The problem of threshold computation is formulated as an optimization problem and its solution is developed using the well known LMI technique. Three commonly...
An approach for the identification of single-input single-output dynamic errors-in-variables bilinear system models for the case of white input noise and coloured output noise is proposed. The algorithm is based on the extension of the bias compensation technique for bilinear systems that is applied to a set of overdetermined normal equations. The separable nonlinear least squares method is used,...
This paper presents a method to identify the parameters of continuous and discrete MIMO Takagi-Sugeno (TS) fuzzy models. The proposed method combines the Levenberg/Marquadt (LM) optimisation algorithm and least squares (LS) method. The LM algorithm is used to estimate the Gaussian membership function parameters whereas the parameters of linear local models is determined using a LS algorithm. To illustrate...
A new model class is proposed to use for identification purposes, which is able to approximate many nonlinear systems quite accurately. Conditions are given for the system to be representable by a linear-in-parameters equation, which allows to use effective linear methods to solve the identification problem. Finally an example is provided to illustrate the use of the proposed model class for identification...
A new method to design asymptotically stabilizing control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the construction used in nonlinear regulator theory to derive the (invariant) output zeroing manifold...
In this note we extend the design tool presented in [6] for robust stabilization of nonminimum-phase nonlinear systems to the case of output regulation problems. As in [6] we take advantage from a design tool known in the linear literature as “vibrational feedback” to handle the presence of unstable zero dynamics in output regulation problems in presence of uncertainties. This work frames in a research...
Previously, a nonlinear passivity control has been proposed for a discrete-time (neutrally) stable bilinear system. However, the decay rate of the closed-loop system is not exponential. In this paper, a new nonlinear control is suggested to achieve exponential decay rate. It is also shown that the new control is robust against small parametric uncertainties.
In this paper the computation of linear time-varying tracking controllers on the basis of a Jacobian linearization of a nonlinear system about a reference trajectory is considered. An exponentially stabilizing controller is determined by approximately solving a Sylvester matrix differential equation using a Galerkin approach. The solution is obtained in parametric form so that conditions for the free...
The problem of observer-based fault diagnosis in certain class of nonlinear dynamic systems is studied. To solve this problem, the following approach is suggested: replacing the initial nonlinear system by certain linear logic-dynamic system, obtaining the bank of linear logic-dynamic observers, and transforming these observes into the nonlinear ones. The procedure of the linear logic-dynamic observers...
An optimal control problem for nonlinear ODEs, subject to mixed control-state and pure state constraints is considered. Sufficient conditions are formulated, under which there exist unique normal Lagrange multipliers and they are given by regular functions. These conditions include pointwise linear independence of gradients of α-active constraints and controllability of the linearized state equation.
In this note we present a method for globally asymptotically stabilizing a MIMO nonlinear system by output feedback. The result relies on the use of filtered transformations and backstepping, and can be viewed as a direct extension of an existing method. The method is demonstrated via simulation on an example.
This paper presents a new adaptive nonlinear control for trajectory tracking of non-affine nonlinear systems. The referred proposed controller which is based on a L2 norm prescribed to minimize a trajectory tracking error has adaptive and optimal characters. Moreover with the systems output feedback, the proposed controller which dose not require any knowledge of nonlinear internal dynamics can be...
This paper considers the global robust output regulation problem of nonlinear output feedback systems in the case that both exosystem and high-frequency gain sign are unknown. The unavailability of these information poses challenges in the control law design. To solve the output regulation problem, a feedback controller is proposed by integrating the internal model principle, certainty equivalence...
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