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In this article a global method for master-slave synchronization of nonlinear systems is provided. Based on a diffeomorphic transformation of the original dynamics, a reduced observer is designed such that the nonlinear state feedback law is independent of the inertial frame. Generally, the method requires non trivial computations but leads to global convergence results for the invariant tracking error. We illustrate the design procedure in detail for a master-slave synchronization of a bacterial growth model, which may escape to infinity in finite time.

This work addresses the lateral stabilisation problem of four-wheels ground vehicles. The objective is to estimate the largest state-space region such that the closed-loop vehicle lateral stability...

The generation of high-energy laser pulses by so-called regenerative (optical) amplifiers is limited by the occurrence of period-doubling bifurcations induced by an inherently unstable pulse-to-pulse dynamics. Recently, the application of linear feedback methods to stabilize this pulse-to-pulse dynamics by modifying the supplied seed pulses was suggested as an alternative to the quite expensive current state of the art involving dedicated pre-amplifiers. To address some shortcomings inherent to the linear feedback, this paper investigates the design of nonlinear state feedback laws and in particular the possibility to stabilize the pulse-to-pulse dynamics globally subject to the given input constraints.

This paper presents a nonlinear equivalent-input-disturbance (NEID) approach to rejecting an unknown exogenous disturbance in a nonlinear system. An NEID compensator has two parts: a conventional equivalent-input-disturbance estimator and a nonlinear state feedback term. This design ensures that only the exogenous disturbance is rejected and the useful nonlinearity of the system is retained. Unlike other active disturbance-rejection methods, a Lipschitz condition is not necessary to guarantee the convergence of the observation error. Analysis of control performance provides upper bounds for the evaluation of disturbance rejection and the degree of nonlinearity retention. Numerical examples show the validity and superiority of this method.

In this paper, we consider consensus problem for a class of nonlinear multi-agents system. The interaction topology among the agents is assumed to be fixed and directed topology. To achieve the consensus problem, a neighbor-based nonlinear state feedback controller is designed for each agent, based on algebraic graph and the positive polynomial theories. A sufficient condition is established to solve consensus problem of the considered nonlinear multi-agents systems. Then, the state feedback gain matrix can be obtained from the feasible solution to the sum of squares programs. Finally, a simulation example is given to illustrate our approach.

This letter proposes a new method for robust state-feedback control design for nonlinear systems. We introduce robust control contraction metrics (RCCM), extending the method of control contraction metrics from stabilization to disturbance attenuation and robust control. An RCCM is a Riemannian metric that verifies differential $L^{2}$ -gain bounds in closed-loop, and guarantees robust stability of arbitrary trajectories via small gain arguments. Numerical search for such a metric can be transformed to a convex optimization problem. We also show that the associated Riemannian energy can be used as a robust control Lyapaunov function. A simple computational example based on jet-engine surge illustrates the approach.

This paper treats robust controller design for affine fuzzy large-scale systems (AFLSS) composed of Takagi-Sugeno-Kang type fuzzy subsystems with offset terms, disturbances, uncertainties, and interconnections. A decentralized nonlinear state feedback controllers are developed for stabilization of the overall AFLSS in terms of some sufficient conditions with low computational effort and free gains. A numerical example is given to illustrate the feasibility of the proposed approach.

Assume that when the number of pests reaches the certain threshold, pest management strategy will be taken to control pests. Based on this assumption, in this paper, we propose a pest management model with nonlinear state feedback control. We then analyze the dynamic behavior of the model. More precisely, we first investigate the singularity of the model by using method of qualitative analysis; secondly the existence of periodic solution of the model is studied by using successor functions and Poincare-Bendixson theorem; and then it is followed by the study of the stability of periodic solution; finally, an example with numerical simulations is given to illustrate our conclusions.

This paper is concerned with nonlinear control with integral compensation for the output voltage of boost converters through the use of their discretized bilinear model. We first derive a nonlinear state feedback control law through Lyapunov stability theory, where we introduce a Lyapunov function candidate and maximize its decrement at each switching instant under a penalty on the control input. This approach is then modified to incorporate an integral action in the control law, and a method is provided for confirming the closed-loop stability under the modified control law. We next apply the design method of the control law with integral compensation to the identified discretized bilinear model of a boost converter. Finally, we carry out control experiments with the designed control law, through which the effectiveness of the overall scheme of the present study is demonstrated.

International audience; A solution to the problem of global fixed-time output stabilization of a chain of integrators is proposed. A nonlinear state feedback and a dynamic observer are designed in order to guarantee both fixed-time estimation and fixed-time control. Robustness with respect to exogenous disturbances and measurement noises is established. The performance of the obtained control and estimation algorithms are illustrated by numeric experiments.

5th Symposium on System Structure and Control 11th Workshop on Time-Delay Systems 6th Workshop on Fractional Differentiation and Its Applications; International audience; This paper deals with an experimental comparison between a proportional derivative (PD) controller and an adaptive nonlinear state feedback one, both applied on a tethered autonomous underwater vehicle. The aim is to show the behavior of the closed loop system in the nominal case for each of these two controllers, and then to test their robustness towards some parameters changes. The PD on one hand has a good performance for systems with an unknown model. The adaptive control law on the other hand is known to adjust the unknown parameters of the plant in order to converge to the desired trajectory. This study shows experimental results performed using each of the above mentioned control laws.

This paper investigates the active controller design for the output regulation of the Vaidyanathan 4-D hyperjerk hyperchaotic system (2015). Explicitly, nonlinear state feedback control laws have been derived to regulate the output of the 4-D Vaidyanathan hyperjerk hyperchaotic system so as to track the constant reference signals as well as to track periodic reference signals. The active control laws are derived using the Byrnes-Isidori regulator equations (1990). Numerical simulations using MATLAB are shown to illustrate the phase portraits of the Vaidyanathan hyperjerk hyperchaotic system and the output regulation results for the Vaidyanathan hyperjerk hyperchaotic system.

International audience; This paper investigates the control problem for static boost type converters using a high gain state feedback robust controller incorporating an integral action. The robust feature allows to achieve the required performance in the presence of parametric uncertainties, while the integral action provides an offset free performance with respect to the desired levels of voltage. The adopted high gain approach is motivated by both fundamental as well as practical considerations, namely the underlying fundamental potential and the design parameter specification simplicity. The stability and convergence analysis has been carried out using an adequate Lyapunov approach, and the control system calibration is achieved throughout a few design parameters which are closely related to the desired dynamical performances. The effectiveness of the proposed control approach has been corroborated by numerical simulations and probing experimental results.

In this paper a robust controller for attitude stabilization of a QuadrotorUAV is proposed. For this we design a Takagi-Sugeno (T-S) model for Quadrotor modelling , and then we use Linear Matrix Inequality (LMI), and PDC (Parallel Disturbance Compensation) techniqueto design a nonlinear state feedback controller with pole placement in a pre -specified region of the operating space .The stabilityof the whole closed-loop system is investigated using quadratic Lyapunovfunction.To demonstrateits usefulness, the proposed design methodology is applied to the problem of Quadrotor attitude stabilization. Simulation results show that the proposedLMI -based design methodology yields good transient performance.In addition, it is observed that the proposedstate feedback controller provides superior stability robustness againstparameter variationsand measurement noise.

In this paper we present a Takagi-Sugeno (T-S) model for Quadrotor modelling. This model is developed using multiple model approach, composed of three locally accurate models valid in different region of the operating space. It enables us to model the global nonlinear system with some degree of accuracy. Once the T-S model has been defined it is claimed to be relatively straightforward to design a controller with the same strategy of T-S model. A nonlinear state feedback controller based on Linear Matrix Inequality (LMI), and PDC technique with pole placement constraint is synthesized. The requirements of stability and poleplacement in LMI region are formulated based on the Lyapunov direct method. By recasting these constraints into LMIs, we formulate an LMI feasibility problem for the design of the nonlinear state feedback controller. This controller is applied to a nonlinear Quadrotor system, which is one of the most complex flying systems that exist. A comparative study between controller with stability constraints and controller with pole placement constrains is made. Simulation results show that the controller with pole placement constrains yields good tracking performance. The designed T-S model is validated using Matlab Simulink.

In order to solve the coupling of rotor current of d axis and q axis, a new kind of control scheme for double-fed induction machine (DFIM) speed regulation system is proposed based on the theory of auto disturbance rejection controller (ADRC). The ADRC is composed of three parts: tracking-differentiator (TD), extended state observer (ESO) and nonlinear state feedback controller (NSFC). In the ADRC scheme, the coupling of rotor current is regarded as the inner disturbance of DFIM, inputting this disturbance to the input port of the speed regulation system by the feedforward compensation, the speed regulation system can change to the simple integral series connection system or simple linear system. This controller can realize decoupling of rotor current of d axis and q axis, obtaining a good speed tracking performance with small overshoot and fast setting time. Simulation results indicate the rationality and validity of the ADRC.

This paper presents a control strategy for stabilization of the nonholonomic control systems with strongly nonlinear drifts and state delay. Applying a novel Lyapunov functional and backstepping recursive method, the design of robust nonlinear state feedback controllers is proposed, which can guarantee the stability of the closed-loop systems. Finally, a numerical example is provided to show the effectiveness of the method.

This paper presents a robust nonlinear state feedback linearization approach for power systems with uncertainties. The uncertainties considered here are a class of bounded perturbations to the state model of power systems. The control law is applied through the excitation system of the synchronous generators connected to the power systems to enhance the stability of the system. In this paper, uncertainties are considered for single machine infinite bus (SMIB) system. A Lyapunov-based concept is used to guarantee uniform ultimate boundedness.

This paper presents a control strategy for stabilization of nonholonomic control systems with strongly nonlinear uncertainties and time delay. By applying a novel Lyapunov functional, discontinuous transformation and dynamic feedback approach, robust nonlinear state feedback switching controllers are designed, which can guarantee the stabilization of closed loop systems. The proposed method proves to be effective by a simulation example.

This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model (DFHM) with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto theorem, it is proven that the chaos generated by this controller satisfies the Li-Yorke definition. An example is presented to demonstrate the effectiveness of the approach.

Stabilization in multimachine (synchronous generators) power systems is dealt with through a class of decentralized and nonlinear state feedback laws that can be separately designed in a generator-wise fashion, based on what we call the improved swing equations. Stability of the closed-loop power systems is robust with regard to perturbations in electric torques happening in the synchronous generators. The stabilization algorithm consists of decentralized control laws, and provides us with many more freedoms for accomodating various control indices.

This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.

A nonlinear state feedback control law for a stirred tank chemical reactor with recycling is studied in this paper. The system is described by nonlinear delay differential equations and the projected control law depends on the system variables at present and past times. Such feedback control law drives the output of the system, the reactor temperature, at the desired value, with exponential error decay rate. Moreover, the closed loop system is locally input-to-state stable with respect to a disturbance forcing, as the control law, the jacket temperature. Such disturbance may well describe sensor and actuator errors, as well as errors due to parameters uncertainty such as the time-delay. Copyright @ IFAC, 7th Workshop on Time-Delay Systems, Nantes, September 2007.

One of the most important problems that can arise in the development of a pharmaceutical crystallization process is the control of polymorphism, in which there exist different crystal forms for the same chemical compound. Different polymorphs can have very different properties, such as bioavailability, which motivates the design of controlled processes to ensure consistent production of the desired polymorph to produce reliable therapeutic benefits upon delivery. The optimal batch control of the polymorphic transformation of L-glutamic acid from the metastable α-form to the stable β-form is studied, with the goal of optimizing batch productivity, while providing robustness to variations in the physicochemical parameters that can occur in practice due to variations in contaminant profiles in the feedstocks. A nonlinear state feedback controller designed to follow an optimal setpoint trajectory defined in the crystallization phase diagram simultaneously provided high-batch productivity and robustness, in contrast to optimal temperature control strategies that were either nonrobust or resulted in long-batch times. The results motivate the incorporation of the proposed approach into the design of operating procedures for polymorphic batch crystallizations. © 2007 American Institute of Chemical Engineers AIChE J, 2007

In this article, a novel approach to nonlinear control of induction motors is presented. The proposed approach is used to design controllers for the rotor flux amplitude and the motor speed. The underlying design objective is to endow the closed loop system with high performance dynamics for high speed ranges while keeping the required stator voltage within the inverter ceiling limits. A comparative study between the performances of the proposed controller and field oriented control is carried out. The methods are compared in terms of their ability to handle loads on the motor shaft, their speed tracking capability and their sensitivity to operating condition variations. To estimate the rotor flux, an open loop observer is developed.

In this letter, a simple nonlinear state feedback controller is designed for generating hyperchaos from a three-dimensional autonomous chaotic system. The hyperchaotic system is not only demonstrated by computer simulations but also verified with bifurcation analysis, and is implemented experimentally via an electronic circuit.

In this paper, we present a nonlinear state feedback control using a neural network (NN). Since the NN models the nonlinear excitation controller using only measurable state variables from the synchronous generators, the proposed method can be implemented in a real system easily. The effectiveness of the proposed method is demonstrated by computer simulations for single- and multiple-machine power systems. Furthermore, the NN is implemented on the experiment system with a laboratory-size 2.2-kVA synchronous generator. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 139(3): 26–34, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.1157

An l 1 -optimal linear time-invariant (LTI) compensator may have an order significantly higher than that of the plant. In the state feedback case, there has been recent work exploring the use of nonlinear static feedback controllers which provide near optimal performance. In the case of D 12 square and invertible, we show that it is enough to have the nonlinearity on a particular substate, which can be used to significantly simplify the design problem.

In the present paper the problem of stabilization for a family of programmed motions of linear and bilinear systems using a nonlinear Luenberger observer is considered. A method for the design of the nonlinear Luenberger observer and for the synthesis of the nonlinear state feedback control is suggested. The theorem on the necessary and sufficient conditions to solve this problem is proved

This paper deals with μ synthesis for nonlinear robust control systems based on I/O linearization. By nonlinear state feedback, nonlinear systems can be linearized as controllable linear systems, such that uncertain nonlinear systems can be expressed as linear fractional transformations (LFTs) on the generalized linearized plants and uncertainty By H ∞ optimization based μ synthesis technique, controllers can be obtained for the LFTs. Then the nonlinear robust control laws can be constructed by combining the controllers and the nonlinear state feedback. An example is given to illustrate the design.