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International audience; In this paper it is proposed to extend the result described in Khalil and Praly (2014) and the references therein, regarding the high-gain observer-based nonlinear control to the case of systems with diffusion sensor dynamic. Based on some usual hypotheses, we provide sufficient conditions involving the high-gain parameter and the length on the PDE sensor. In fact it is brought into light an explicit trade off between them: the larger the observer gain, the smaller the length of the PDE sensor needs to be. The stability analysis of the closed loop is based on a Lyapunov functional.

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.

In this paper, we consider the frequency synchronization problem in a network of lossless, connected, and network-reduced power system. Frequency synchronization is an important problem in power systems as frequency deviation can lead to degraded power quality, tripping of generators, etc. We present a load-estimator-based consensus algorithm in a network of fourth-order generator models that achieves practical frequency synchronization in the presence of unknown time-varying power demand. We do not assume that the demand is generated by a known model. We follow a multiple time-scale approach for the stability analysis. It is shown that synchronization is achieved for the case of constant power demand, by showing that the system is exponentially stable. For the case of time-varying power demand, we show the error trajectories are ultimately bounded, and the synchronization error is proportional to an upper bound on the derivative of the time-varying power demand. We simulate the controller performance on a four area network which is equivalent to the IEEE New England 39-Bus system.

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.

An output feedback controller is proposed for stabilization of the inverted pendulum on a cart in the presence of uncertainties. The output feedback controller has a multi-time-scale structure in which Extended High-Gain Observers are used to estimate system states and uncertainties in the first and fastest time scale; dynamic inversion is used to deal with uncertain input coefficients in the second time scale; the pendulum converges to a reference trajectory in the third time scale; and finally, the reference trajectory is designed such that both the pendulum and the cart converge to the desired equilibrium in the fourth and slowest time scale. The multi-time-scale structure allows independent analysis of the dynamics in each time scale and singular perturbation methods are effectively utilized to establish exponential stability of the equilibrium. Simulation results indicate that the output feedback controller provides a large region of attraction and experimental results establish the feasibility of practical implementation.

In this paper, we present conditions for the stabilization and regulation of the tracking error for an n -dimensional minimum-phase system preceded by a Prandtl–Ishlinskii hysteresis operator. A general controller structure is considered; however, we assume that an integral action is present. The common Lyapunov function theorem is utilized together with a Linear Matrix Inequality (LMI) condition to show that, under suitable conditions, the tracking error of the system goes to zero exponentially fast when a constant reference is considered. A key feature of this LMI condition is that it does not require the hysteresis effect to be small, meaning that hysteresis inversion is not required. We use this condition together with a periodicity assumption to prove that a servocompensator-based controller can stabilize the system without using hysteresis inversion. Additionally, we draw parallels between our LMI condition and passivity-based results achieved in the literature. We then verify our LMI results in simulation, where we show that the LMI condition can accurately predict the stability margins of a system with hysteresis. Finally, we conduct experiments using a servocompensator-based controller, where we verify the stability of the system and achieve a mean tracking error of 0.5 % for a 200 Hz sinusoidal reference.

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.

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.

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 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 is on the design of robust output feedback integral control for minimum-phase nonlinear systems with a well-defined relative degree. Previous work has shown how to design such controllers to achieve asymptotic regulation by a two-step process. First, robust control is designed to bring the trajectories to a small neighborhood of an equilibrium point. Within this neighborhood, the control then acts as a high-gain feedback that stabilizes the equilibrium point. The asymptotic regulation achieved by integral action happens at the expense of degrading the transient performance. In this paper, we present an approach to improve the transient performance. The control design is a continuous sliding mode control with integral action. However, the integrator is introduced in such a way that it provides integral action only ''conditionally'', effectively eliminating the performance degradation. There are two main results in the paper: the first is asymptotic regulation and the second confirms the transient performance improvement by showing that the output feedback continuous sliding-mode control with integral action can be tuned to recover the performance of a state feedback ideal sliding mode control without integral action.

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 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.

We consider a single-input-single-output nonlinear system which can be represented by an input-output model. The system, which can be transformed into the normal form, is required to be minimum phase. The model contains unknown bounded disturbances. We assume that the reference signal and its derivatives are bounded. A high-gain observer is used to estimate derivatives of the tracking error while rejecting the effect of the disturbances. We design a globally bounded output-feedback variable structure controller that ensures tracking of the reference signal in the presence of unknown time-varying disturbances and modeling errors. We give regional as well as semiglobal results. We do not require exponential stability of the zero dynamics nor global growth conditions. © 1997 Elsevier Science Ltd.

The effect of unmodeled fast actuator dynamics on the output feedback stabilization of feedback-linearizable systems is studied. It is shown that if the actuator dynamics are sufficiently fast, the output feedback controller will stabilize the origin of the actual system. Moreover, it is shown that the actuator dynamics need not be faster than the observer dynamics.

We consider a single-input-single-output nonlinear system which has a uniform relative degree equal to the dimension of the state vector. The system can be transformed into a normal form with no zero dynamics. We allow the system's equation to depend on bounded uncertain parameters which do not change the relative degree. Disturbances are assumed to satisfy a strict-feedback condition which allows us to use a time-varying, disturbance-dependent transformation to transform the system into an error space where disturbances and uncertainties satisfy the matching condition. The nonlinear functions in the error space are used to choose an internal model which is augmented with the system, and a robust state feedback control is designed to drive the error to a positively invariant set that contains the origin. We then show the existence of a zero-error manifold inside this set which attracts all trajectories inside the set. To implement this control using output feedback, we saturate the state feedback control outside a compact set of interest and estimate the state using a high-gain observer. The output feedback controller recovers the robustness and asymptotic tracking properties of the state feedback controller.

The singular perturbation theory is extended to systems with several small parameters which can change the system order. Difficulties arising in testing the boundary layer stability in multiparameter linear problems are discussed. The theory is applied to linear quadratic optimal control and Nash game problems.

This paper presents a composite control approach to the problem of steering the state of a singularly perturbed system from a given initial state to a given final state, while minimizing a cost functional. The problem is treated for a class of nonlinear systems whose fast dynamics are weakly nonlinear in the fast variables and control inputs. The composite control comprises three components: a reduced control, a feedback boundary-layer stabilizing control and an open-loop right boundary-layer control. It is shown that application of the composite control results in a final state that is O(ϵ) close to the desired state, and a value of the cost that is O(ϵ) close to the optimal cost of the reduced problem.

Sufficient conditions are derived to guarantee the asymptotic stability of a class of nonlinear singularly perturbed systems with several perturbation parameters of the same order. Estimates of the region of attraction and bounds on the small parameters are obtained.

This paper considers the stochastic control of linear-quadratic problems for singularly perturbed systems when the input noise is colored. A near optimal linear output feedback control is obtained by optimizing a slow subsystem only.

Multimodel strategies in which control agents use different simplified models of the same system are studied for interconnected systems with slow and fast dynamics. The well-posedness of multimodel strategies in the presence of random disturbances and imperfect partial observations is established by studying an LQG control problem. The study reveals that for the well-posedness of multimodel strategies control agents need to communicate their observations and decisions. The need to communicate decisions does not arise when all agents use the same overall model to compute the optimal control.