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In this article, an adaptive conditional servocompensator is proposed to achieve precise tracking control of systems with hysteresis without requiring explicit inversion of the hysteresis. Motivated by a range of applications, such as the piezoelectric-actuated nanopositioning, the system considered in this work consists of a chain of integrators preceded by a hysteresis nonlinearity modeled by a modified Prandtl–Ishlinskii (MPI) operator with uncertainty. To facilitate the proposed control design, the MPI operator is rearranged into a form comprised of three parts: a linear term, a nominal hysteretic term represented by a classical Prandtl–Ishlinskii (PI) operator, and a hysteretic perturbation. The bound on the hysteretic perturbation is further derived based on the parameter uncertainty of the MPI operator. The controller consists of two major elements. The first is a continuously implemented sliding mode controller (SMC), which exploits the bound on hysteretic perturbation and drives the system states to a bounded set in finite time. To properly “cancel” the nominal hysteresis effect without inversion, a technique involving a low-pass filter is introduced. The second element of the proposed controller is an adaptive conditional servocompensator that aims to eliminate periodic components in the tracking error. We show that, with persistent excitation, the closed-loop variables are ultimately bounded and the tracking error approaches a neighborhood of zero, where the neighborhood can be made arbitrarily small via the choice of the SMC boundary-layer width parameter and the servocompensator order. The proposed approach is implemented experimentally on a commercial nanopositioner under different types of periodic references, and it shows superior tracking performance over the traditional proportional–integral control, as well as several hysteresis inversion-based approaches reported in the literature.

In this article, we consider the synchronization problem in a network of nonlinear multiagent systems having the same relative degree $r$ . The agents do not have access to their state or output and only have relative output information from their neighbors. The controller structure is decentralized in nature and, therefore, depends only on the relative information available to it. The agent dynamics are transformed into relative dynamics by a change of coordinates where the agent dynamics are coupled. Extended high-gain observers are used to estimate the nonlinear coupling at each agent and then cancel them using feedback control. Therefore, the problem changes to a stabilization problem of $N$ nonlinear systems in the relative coordinates. It is shown that the agents achieve practical synchronization and the synchronization error can be made arbitrarily small by tuning the high-gain observer parameter. Finally, simulations are done with a network of power systems to show the efficacy of the proposed controller.

We propose a new algorithm for controlling the transient behavior of the tracking error for nonlinear systems with arbitrary relative degree. In tracking problems, the transient behavior of the error is more important than the behavior of its derivatives. We introduce a concept of virtual output, which converts an arbitrary relative degree system into a relative degree one system. The virtual output is chosen in such a way that the difference between the virtual output and the tracking error can be made arbitrarily small all the time. Assuming that the state derivatives are not available for feedback we use a high-gain observer to estimate the derivatives and construct the virtual output.

This paper presents an output feedback model predictive control for a class of nonlinear systems in a multirate scheme, where the control sampling period is larger than the estimation sampling period. With a small sampling period, the observer is designed to be faster than the dynamics of the closed-loop system under state feedback. Stabilization is achieved by a separation approach in which the control is designed first using state feedback and practical stabilization is achieved by output feedback.

High-gain observers proved to be a useful tool in the design of output feedback control of nonlinear systems. However, the observer faces a numerical challenge when its dimension is high. For an observer of dimension ρ and a high-gain parameter k , the observer gain is of the order of k ρ and the observer variables could be of the order of k ρ − 1 during the transient period. This paper presents a new high-gain observer that is based on cascading lower-dimensional observers with saturation functions in between them. The observer gain in the new observer is of the order of k and its variables are limited to be of the order of k during the transient period. It is shown that the cascade observer has properties similar to the standard one. In particular, a nonlinear separation principle is proved.

High-gain observers play an important role in the design of feedback control for nonlinear systems. This article overviews the essentials of this technique, starting with motivating examples that illustrate the main features of highgain observers, with emphasis on the peaking phenomenon and the role of control saturation in dealing with it. The observer design for single-output and multi-output systems is presented along with the use of the observer in feedback control. A nonlinear separation principle is discussed, and the use of an extended high-gain observer as a disturbance estimator is covered. The most serious challenge in implementing high-gain observers is the effect of measurement noise, which is covered next. The article ends by presenting an experimental application of the extended high-gain observer to speed control of a permanent magnet synchronous motor (PMSM).

We show, in this paper, how a classical method for feedback linearization of a multivariable invertible nonlinear system, via dynamic extension and state feedback, can be robustified. The synthesis of the controller is achieved by means of a recursive procedure that, at each stage, consists in the augmentation of the system state space, to the purpose of rendering feedback-linearization possible, and in the design of a high-gain extended observer, to the purpose of estimating the state of the plant as well as the perturbations due to model uncertainties. As a result, a closed-loop system is obtained that, for any bounded set of initial conditions and any bounded input, recovers the performance that would have been obtained by means of the classical technique of feedback linearization via dynamic state feedback.

Smart material-based systems, such as piezoelectric nanopositioning stages, exhibit pronounced hysteresis nonlinearity that poses significant control challenges. Much of the existing work employs an inverse hysteresis operator to approximately cancel out the hysteresis nonlinearity. In this paper we propose an inversion-free approach to the control of systems with hysteresis, removing the computational complexity in constructing an inverse compensator. The hysteresis nonlinearity is modeled as a Modified Prandtl-Ishlinskii (MPI) operator. We utilize the properties of the MPI hysteresis model to transform the system into a semi-affine form, where one term has the control input appearing linearly and the other term represents the hysteretic perturbation. The proposed controller is designed based on an adaptive conditional servocompensator approach, which is a continuously-implemented sliding mode control law powered with an adaptive servocompensator. An analytical bound on the hysteretic perturbation is derived and used in the design of the sliding mode control law. A low-pass filter is augmented with the control law, to avoid solving a complicated equation involved. Our stability analysis shows that, under reasonable assumptions, the boundedness of the closed-loop system trajectories is ensured. Experiments conducted on a commercially available nanopositioner confirms the effectiveness of the proposed method as compared to the case when an inverse model is implemented; indeed, the tracking error is reduced by approximately 50% for sinusoidal references under the proposed controller.

This note addresses the problem of feedback linearization for nonlinear systems with time-varying input and output delays. To solve the realization issue of future states, a high-gain-observer is constructed as a predictor. Then, the output feedback predictive control is presented. The stability of the closed-loop system is analyzed by using a Lyapunov-Krasovskii functional. It is demonstrated that by designing the observer gain high enough, the closed-loop system recovers the performance of state feedback control with no time delay. However, the gain of the observer is limited by the time delay. Finally, numerical simulations are given to illustrate the effectiveness of the proposed control.

We propose an output-feedback tracking controller for uncertain, nonaffine, nonlinear systems. The output feedback controller results in a closed-loop system with a three-time-scale structure; an extended high-gain observer estimates unmeasured states and uncertainties in the fastest time scale and dynamic inversion is used to deal with nonaffine inputs and input uncertainties in the intermediate time scale while the plant dynamics evolves in the slowest time scale. The dynamic inversion algorithm is based on sector conditions and results in exponential convergence of the inputs. Together with the extended high-gain observer, dynamic inversion results in performance recovery of a target system. The singular perturbation method is used to analyze the stability and performance of the system and numerical simulations are used to demonstrate the effectiveness of the control design.

This paper focuses on the regulation problem for non-minimum-phase nonlinear systems with slow integrators, high-gain feedback and high-gain observer. The developed methodology involves four steps: At first, we design a full-information feedback controller for an auxiliary system, which parallels the stabilization of the original system, as pioneered in [11]. Then we use high-gain feedback to stabilize the original system, which is able to recover the performance of the auxiliary system by choosing the gain high enough. In the third step, with a condition on the dc steady-state input-output map, a slow integrator is added that enforces the objective of regulation. At last, we extend the methodology into the output feedback case by utilizing the extended high-gain observer to estimate the derivatives of the output as well as one unknown term including system uncertainties. The use of the observer recovers the performance under full-information feedback. The effectiveness of such methodology is demonstrated on the linearized inverted pendulum on a cart model (LIPC-model).

High-gain observers play an important role in the design of feedback control for nonlinear systems. One challenge in the use of high-gain observers is the effect of measurement noise. It is shown in the literature that the presence of measurement noise puts a constraint on how high the observer gain could be, which forces a trade-off between the fast convergence of state estimates and the error due to measurement noise. A number of techniques have been proposed in the literature to attenuate the effects of measurement noise on systems utilizing a high-gain observer. In experimental applications of high-gain observers, it is quite common to use a low-pass filter to filter out the high-frequency components of the noise before feeding the measurement into the observer. In this paper we analyze effect of measurement noise on high-gain observers when low pass filters are used.

Unlike previous work in the area of high-gain observers, the focus of this paper is the effect measurement noise has on the tracking error, not the estimation error. Although a tradeoff exists between the speed of state reconstruction and the bound on the steady-state estimation error, such a compromise is not evident in the tracking error of the first state. The purpose of this work is to provide the reader with the relationship between the high-gain observer parameter and the tracking error and its subsequent derivatives. Copyright © 2015 John Wiley & Sons, Ltd.

A sliding mode controller (SMC) is proposed for a class of systems comprising a hysteresis operator preceding a linear system with an all-pole transfer function. The hysteresis operator is modeled with uncertain piecewise linear characteristics, and a nominal inverse operator is included to mitigate the hysteresis effect. A classical SMC design typically uses a constant coefficient in the switching component, which is tuned via trial-and-error. In this paper, a state- and time-dependent coefficient is proposed based on the derived inversion error, which eliminates the need for parameter tuning and ensures the convergence of the sliding surface to the boundary layer without compactness assumptions. In addition, singular perturbation is used to analyze the system behavior within the sliding-surface boundary layer for the case of a constant coefficient in the classical SMC design. In particular, analytical insight is gained on the frequency-scaling behavior of the tracking error under a periodic reference. Simulation and experimental results based on a piezoelectric actuator-based nanopositioner are presented to illustrate the design and analysis, where the hysteresis nonlinearity is represented by a Prandtal-Ishlinskii operator.

The theory of high-gain observers has been developed for about twenty years. This talk is a brief introduction to high-gain observers in nonlinear feedback control, with emphasis on the peaking phenomenon and the role of control saturation in dealing with it. The talk surveys recent results on the nonlinear separation principle, extended high-gain observers, performance in the presence of measurement noise, sampled-data control, and experimental testbeds.

Trajectory reversing is a method commonly used for estimating the region of attraction of stabilized equilibria. Using a discrete set of points obtained by trajectory reversing, this paper presents an algorithm for estimation and mathematical representation of the region of attraction using convex hulls. Several two-dimensional examples are presented to illustrate the usefulness of the algorithm. The method provides larger estimates compared to that obtained by existing algorithms but its main advantage lies in its applicability to higher-order systems. The mathematical representation of the region of attraction is useful in applying the Impulse Manifold Method, which was developed for stabilization of equilibria of underacuated systems from configurations lying outside their region of attraction. The region of attraction of the pendubot upright equilibrium is estimated to demonstrate the applicability of our algorithm to higher-order systems and illustrate the usefulness of the Impulse Manifold Method through simulations.

The paper addresses the high-gain observer design for nonlinear systems in the presence of sensor nonlinearities. It is shown that the properties of high-gain observers with linear outputs will hold with nonlinear outputs, provided the nonlinear output function is incrementally inside the sector [β, ∞] for some β > 0 and the observer eigenvalues are chosen to be real.

A full order observer is designed for a class of nonlinear systems that can potentially admit unstable zero dynamics. The structure of the observer is composed of an Extended High Gain Observer (EHGO), for the estimation of the derivatives of the output, augmented with an Extended Kalman Filter (EKF) for the estimation of the states of the internal dynamics. The EHGO is also utilized to estimate a signal that is used as a virtual output to an auxiliary system comprised of the internal dynamics. In the special case of the system being linear in the states of the internal dynamics, we achieve semi-global asymptotic convergence of the estimation error. We demonstrate the efficacy of the observer in two examples; namely, a synchronous generator connected to an infinite bus and a Translating Oscillator with a Rotating Actuator (TORA) system.

We propose an adaptive servocompensator utilizing frequency estimation and slow adaptation for systems subject to inputs of unknown frequencies. We show that the proposed controller can achieve zero tracking error for a class of periodic references and disturbances, including scenarios specifically relevant to piezo-actuated nanopositioning systems. In particular, for the case of a sinusoidal reference input, we establish the exponential stability of the closed-loop system in the presence of harmonic disturbances, under certain conditions on the amplitudes of the reference and disturbances. We also prove exponential stability in the case of sinusoidal reference and disturbance with two distinct frequencies. Additionally, we show that the proposed method, in conjunction with approximate hysteresis inversion, can attenuate the effect of hysteresis nonlinearity preceding linear dynamics and ensure the boundedness of the closed-loop system. Experiments conducted on a commercially available nanopositioner confirm our theoretical analysis and demonstrate the effectiveness of the proposed method as compared to Iterative Learning Control, a competitive technique in nanopositioning for tracking periodic references.

We address the problem of state estimation for a class of nonlinear systems with measurement noise in the context of feedback control. It is well-known that high-gain observers are robust against model uncertainty and disturbances, but sensitive to measurement noise when implemented in a feedback loop. This work presents the benefits of a nonlinear-gain structure in the innovation process of the high-gain observer, in order to overcome the tradeoff between fast state reconstruction and measurement noise attenuation. The goal is to generate a larger observer gain during the transient response than in the steady-state response. Thus, by reducing the observer gain after achieving satisfactory state estimates, the effect of noise on the steady-state performance is reduced. Moreover, the nonlinear-gain observer presented in this paper is shown to surpass the system performance achieved when using comparable linear-gain observers. The proof argues boundedness and ultimate boundedness of the closed-loop system under the proposed output feedback.

Guidance law of a homing missile is implemented using an extended high gain observer without the model assumptions on target maneuvers. First, for a class of multi-input–multi-output nonlinear systems, extended high-gain observers are used for output feedback control with partial practical stabilization. Then the method is applied to the guidance law implementation of a homing missile with bearing only measurement. Simulation results show satisfactory performance.

High-gain observers proved to be a useful tool in the design of output feedback control of nonlinear systems. However, the observer faces a numerical challenge when its dimension is high. For an observer of dimension ρ and a high-gain parameter k, the observer gain is of the order of kρ and the observer variables could be of the order of kρ−1 during the transient period. This paper presents a new high-gain observer that is based on cascading lower-dimensional observers with saturation functions in between them. In the new observer, the gains and variables are of the order of k. It is shown that the cascade observer has properties similar to the standard one.

We solve the problem of output feedback stabilization of a class of nonlinear systems, which may have unstable zero dynamics. We allow for any globally stabilizing full state feedback control scheme to be used as long as it satisfies a particular ISS condition. We show semi-global stability of the origin of the closed-loop system and also the recovery of the performance of an auxiliary system using a full-order observer. This observer is based on the use of an extended high-gain observer to provide estimates of the output and its derivatives plus a signal used by an extended Kalman filter to provide estimates of the remaining states. Finally, we provide a simulation example that illustrates the design procedure., 9 pages, 1 figure

It is shown that a nonlinear output feedback stabilizing controller, which combines a globally bounded state feedback controller with a high-gain observer, is robust with respect to input and output time-delays in the plant. The time delay needs to be sufficiently small, but the upper bound on the delay is independent of how fast the observer is.

An output feedback controller with adaptive conditional servocompensator is developed for robust output regulation of a class of nonlinear minimum-phase systems. It is shown that the controller achieves asymptotic regulation and can be tuned to recover the transient performance of a state feedback sliding-mode-controller.

A robust, stabilizing output feedback controller for systems in the normal form, which could potentially include unstable zero dynamics, is presented. The control scheme adopted herein incorporates continuously-implemented sliding mode control-chosen for its robustness properties as well as its ability to prescribe or constrain the motion of trajectories in the sliding phase-and an extended high gain observer to estimate the derivatives of the output and one of the unknown functions. Stabilization in the case of an unknown control coefficient and uncertain constant parameters is shown.

This paper studies the output regulation of nonlinear systems using conditional servocompensators. Previous work introduced the conditional servocompensator, which acts as a traditional servocompensator in the neighborhood of a zero-error manifold while acting as a stable system otherwise, leading to improvement in the transient response while achieving zero steady-state regulation error. The conditional servocompensator tool was introduced for sliding-mode feedback controllers. This paper extends the technique to more general feedback controllers by using Lyapunov redesign and saturated high-gain feedback.

We consider multirate sampled-data output feedback control of a class of nonlinear systems using high-gain observers where the measurement sampling rate is made faster than the control update rate. We show that, in the presence of bounded disturbances, given a sampled data state feedback controller that achieves stabilization with respect to a closed set, the multirate output feedback controller recovers stabilization of the same set provided the measurement sampling rate is sufficiently fast. As an application we consider the control of smart material actuated systems. This scheme combines a discrete-time high-gain observer with a hysteresis inversion controller where the hysteresis is modeled using a Preisach operator. Experimental results for the control of a shape memory alloy actuated rotary joint are provided.

This paper studies sampled-data output feedback control of nonlinear systems using high-gain observers in the presence of measurement noise. The observer is designed in continuous time, then discretized. It is shown that the sampled-data output feedback controller recovers the performance of the continuous-time state feedback controller as the observer gain is increased. However, the effect of measurement noise dominates beyond a certain point, and the gap between the performance of the two controllers widens as the observer gain is increased further. The analysis quantifies the relationship between the high-gain observer parameter and the amplitude of the noise.

This paper considers output feedback control using high-gain observers in the presence of measurement noise for a class of nonlinear systems. We study stability in the presence of measurement noise and illustrate the tradeoff when selecting the observer gain between state reconstruction speed and robustness to model uncertainty on the one hand versus amplification of noise on the other. Based on this tradeoff we propose a high-gain observer that switches between two gain values. This scheme is able to quickly recover the system states during large estimation error and reduce the effect of measurement noise in a neighborhood of the origin of the estimation error. We argue boundedness and ultimate boundedness of the closed-loop system under switched-gain output feedback.

We study the closed-loop behavior of the extended Kalman filter (EKF) for a class of deterministic nonlinear systems that are transformable to the special normal form with linear internal dynamics. We argue that the closed-loop system is asymptotically stable and the estimation error exponentially converges to zero. We compare the performance of the EKF to a high-gain observer through simulation

We consider dynamic output feedback practical stabilization of uniformly observable nonlinear systems, based on high-gain observers with saturation. We assume that uncertain parameters and initial conditions belong to known but comparably large compact sets. In this situation, designs based on traditional robust or adaptive techniques, if applicable, would lead to high controller, observer, and adaptation gains. High gains may excite unmodeled dynamics and significantly amplify measurement noise. Moreover, they could be impossible or too costly to implement. In order to reduce the control efforts and improve robustness of a continuous high-gain-observer-based sliding mode control with respect to these nonideal operational conditions, we have recently proposed a new logic-based switching design strategy. In this paper, we generalize our technique and apply it to a wider class of nonlinear systems and more general Lyapunov-function-based state and output feedback designs. It is important to notice, in particular, that we require neither the sign of the high-frequency gain to be known nor the system to he minimum-phase. The key idea is to split the set of parameters into smaller subsets, design a controller for each of them, and switch the controller if the derivative of the Lyapunov function does not satisfy a certain inequality, after a dwell-time period. We do not order the candidate controllers in advance, as in our earlier work. Instead, we use estimates of the derivatives of the states, provided by an extended order high-gain observer, to calculate instantaneous performance indices. When the controller is falsified, we switch to a new controller that corresponds to the smallest index among the controllers that have not been falsified yet. This modification is important when the number of candidate controllers is high and pre-routed search may lead to an unacceptable transient performance.

It is shown that a nonlinear output feedback stabilizing controller, which combines a globally bounded state feedback controller with a high-gain observer, is robust with respect to unmodeled fast actuator and sensor dynamics. The actuator and sensor dynamics need to be sufficiently fast relative to the dynamics of the nominal closed-loop system under state feedback, but they need not be faster than the observer dynamics.

This paper studies the regulation of nonlinear systems using conditional integrators. Previous work introduced the tool of conditional integrators that provide integral action inside a boundary layer while acting as stable systems outside, leading to improvement in transient response while achieving asymptotic regulation in the presence of unknown constant disturbances or parameter uncertainties. The approach, however, is restricted to a sliding mode control framework. This paper extends this tool to a fairly general class of state feedback control laws, with the stipulation that we know a Lyapunov function for the closed-loop system. Asymptotic regulation with improvement in transient response is done by using the Lyapunov redesign technique to implement the state feedback control as a saturated high-gain feedback and introducing a conditional integrator to provide integral action inside a boundary layer. Improvement in the transient response using conditional integrators is demonstrated with an experimental application to the pendubot. Copyright © 2005 John Wiley & Sons, Ltd.

We consider a single-input single-output minimum-phase non-linear system which has a normal form. In previous work, integral control and high-gain observers were used to achieve robust regulation under output feedback. To improve the transient performance, we propose the use of integrators with non-linear gains. We prove that the controller achieves regional and semiglobal regulation. Simulation results are presented showing the improved overshoot and settling time.

This paper studies sampled-data output feedback control of a class of nonlinear systems. It is shown that the performance of a stabilizing continuous-time state feedback controller can be recovered by a sampled-data output feedback controller when the sampling period is sufficiently small. The output feedback controller uses a deadbeat discrete-time observer to estimate the unmeasured states. Two schemes are proposed to overcome large initial transients when the controller is switched on.

SUMMARY We consider the design of a robust continuous sliding mode controller for the output regulation of a class of minimum-phase nonlinear systems. Previous work has shown how to do this by incorporating a linear servocompensator in the sliding mode design, but the transient performance is degraded when compared to ideal sliding mode control. Extending previous ideas from the design of ‘conditional integrators’ for the case of asymptotically constant references and disturbances, we design the servocompensator as a conditional one that provides servocompensation only inside the boundary layer; achieving asymptotic output regulation, but with improved transient performance. We give both regional as well as semi-global results for error convergence, and show that the controller can be tuned to recover the performance of an ideal sliding mode control. Copyright # 2005 John Wiley & Sons, Ltd.

This paper investigates the regulation problem for nonminimum-phase nonlinear systems via slow integrators and high-gain feedback. The developed methodology involves four steps: in the first step, we design a full-information feedback controller for an auxiliary system, which parallels the stabilization of the original system, as pioneered in [18] . In the second step, we use high-gain feedback to stabilize the original system, which is able to recover the performance of the auxiliary system by choosing the gain high enough. In the third step, with a condition on the dc steady-state input–output map, a slow integrator is added that enforces the objective of regulation. In the last step, we extend the methodology into the output feedback case by utilizing the extended high-gain observer to estimate the derivatives of the output as well as one unknown term including system uncertainties. The use of the observer recovers the performance under full-information feedback. The design procedure is first presented for the linear model for the clarity of the proposed methodology. The effectiveness of such methodology is demonstrated on the nontrivial translational oscillator rotating actuator example. At last, the design for minimum-phase nonlinear systems is also provided. In this case, the performance recovery of the closed-loop auxiliary system by output feedback is verified.

The paper is concerned with the design of an integral control for minimum-phase nonlinear systems that have a well-defined relative degree. Earlier work by the author and coworkers has shown how integral control can be combined with robust control techniques to achieve nonlocal and semiglobal regulation results. The results are applicable to output feedback control problems through the use of high-gain observers and saturation nonlinearities. When used with sliding-mode control, the technique produces universal integral regulators that have been shown to coincide with PI and PID controllers, followed by limiters, for relative-degree-one systems and relative-degree-two systems. The use of integral action improves the steady-state response at the expense of degrading the transient response. The present paper summarizes two recent techniques to modify the universal integral regulator so as to improve its transient performance. One technique uses antiwindup integration, while the other uses nonlinear integrators.

We investigate the robust stabilization of a class of nonlinear systems in the presence of unmodeled actuator and sensor dynamics. We show that, given any globally bounded stabilizing state-feedback control, the closed-loop system performance can be recovered by a sufficiently fast high-gain observer in the presence of sufficiently fast actuator and sensor dynamics. The performance recovery includes recovery of exponential stability of the origin, the region of attraction and state trajectories. Moreover, it is shown that the sensor dynamics should be sufficiently faster than the observer dynamics; a restriction that does not apply to the actuator dynamics.

We consider a single-input single-output nonlinear system which has a well defined normal form with asymptotically stable zero dynamics. We study the design of a robust output feedback controller, that incorporates a linear servo compensator, to achieve asymptotic tracking and disturbance rejection. We determine the least amount of precise information about the plant that is needed to design the controller. Such design will be robust to plant parameters and uncertainties which are not used in the design calculations. We also study the robustness of the design to errors in determining the linear servo compensator. Such errors could arise from approximating a general continuous nonlinear function by a polynomial one, or from errors in determining the frequencies of the exogenous signals. We give regional as well as semiglobal results.

High-gain observers have been used in the design of output feedback controllers due to their ability to robustly estimate the unmeasured states while asymptotically attenuating disturbances. The available techniques for the design of high-gain observers can be classified into three groups: pole-placement algorithms, Riccati equation-based algorithms, and Lyapunov equation-based algorithms. In [1], we presented separation results for globally bounded stabilizing state feedback controllers when the high-gain observer is designed using pole-placement so as to create a closed-loop system with two-time-scale structure. In this paper, we show that the separation results of [1] hold for the other observer designs.

We consider a single-input-single-output (SISO) nonlinear system that has a well-defined normal form with asymptotically stable zero dynamics. Using only knowledge of the relative degree and the sign of the high-frequency gain, we design an output feedback integral controller that asymptotically regulates the output to a bounded time-varying reference signal with a constant limit. We give regional as well as semi-global results. We also show that, for relative degree one and two systems, the proposed integral controller reduces to the classical PI and PID controllers, respectively.

This paper deals with the digital control of a particular class of non-linear singularly perturbed (NLSP) systems. Three distinct multi-rate composite control strategies are discussed. In the first case, it is assumed that measurements of the slow and fast variables are scheduled at the same fast sampling period ndelta. Then, multi-rate measurements are considered and two different strategies are presented. The paper ends with an academic example and simulations.

It is shown that the performance of a globally bounded partial state feedback control of a certain class of nonlinear systems can be recovered by a sufficiently fast high-gain observer. The performance recovery includes recovery of asymptotic stability of the origin, the region of attraction, and trajectories.

We consider a recent method for adaptive output feedback control of nonlinear systems. The method deals with a single-input-single-output minimum phase nonlinear system represented by an n th-order differential equation. A Lyapunovbased design that employs parameter projection, control saturation, and a high-gain observer has been shown to achieve semiglobal tracking. One drawback of that recent result is that tracking error convergence is shown under a persistence of excitation condition, which is uncommon in traditional adaptive control results where persistence of excitation is needed to show parameter convergence but not tracking error convergence. In this paper, we prove tracking error convergence without persistence of excitation. We then proceed to provide two other extensions. First, we show that the adaptive controller is robust with respect to sufficiently small bounded disturbance. Second, by adding a robustifying control component, we show that the controller is robust for a wide class of, not-necessarily-small, bounded disturbance, provided an upper bound on the disturbance is known.

This paper deals with the design of output feedback control to achieve asymptotic tracking and disturbance rejection for a class of nonlinear systems when the exogenous signals are generated by a known linear exosystem. The system under consideration is single-input single-output, input-output linearizable, minimum phase, and modelled by an input-output model of the form of an nth-order differential equation. We assume that, at steady state, the nonlinearities of the system can only introduce a finite number of harmonics of the original exosystem modes. This assumption enables us to identify a linear servo-compensator which is augmented with the original system. Moreover, we augment a series of m integrators at the input side, where m is the highest derivative of the input, and then represent the augmented system by a state model. The augmented system is stabilized via a separation approach in which a robust state feedback controller is designed first to ensure boundedness of all state variables and track...

A sliding mode controller is proposed for a class of systems comprising a hysteresis operator preceding an kth-order linear plant without zero dynamics. The hysteresis operator is modeled with piecewise linear characteristics with uncertainties, and a nominal inverse operator is included to mitigate the hysteresis effect. A bound on the inversion error is used in the design of the sliding mode controller. The stability of the closed-loop system is established, and singular perturbation is exploited to analyze the system behavior within the boundary layer. In particular, analytical insight is gained on the frequency-scaling behavior of the tracking error under a periodic reference. Simulation and experimental results on a piezoelectric actuator-based nanopositioner are presented to illustrate the design and analysis, where the hysteresis nonlinearity is represented by a Prandtal-Ishlinskii operator.

In this paper we utilize dynamic inversion together with high-gain observers to stabilize an inverted pendulum on a cart. Dynamic inversion is used to invert the nonlinear map involving the control input and the high-gain observers are used to estimate the states and terms related to acceleration variables. Through numerical simulations and experiments, it is shown that it is possible to stabilize the inverted pendulum on a cart and recover the performance of state feedback control.