Robust Adaptive Output Feedback Control Research Articles

Output Feedback Adaptive Robust Control of Uncertain Linear Systems With Disturbances

Abstract In this paper, a discontinuous projection based output feedback adaptive robust control (ARC) scheme is constructed for a class of linear systems subjected to both parametric uncertainties and disturbances that might be output dependent. An observer is first designed to provide exponentially convergent estimates of the unmeasured states. This observer has an extended filter structure so that on-line parameter adaptation can be utilized to reduce the effect of possible large disturbances that have known shapes but unknown amplitudes. Estimation errors that come from initial state estimates and uncompensated disturbances are dealt with via certain robust feedback at each step of the backstepping design. Compared to other existing output feedback robust adaptive control schemes, the proposed method explicitly takes into account the effect of disturbances and uses both parameter adaptation and robust feedback to attenuate their effects for an improved tracking performance. Experimental results on the control of an iron core linear motor are presented to illustrate the effectiveness and achievable performance of the proposed scheme.

Robust adaptive output-feedback control for a class of nonlinear systems with general uncertainties

This paper investigates the robust adaptive output-feedback control for a class of nonlinear systems with general uncertainties and unknown parameters. First, a stable state observer is constructed and the system state is observed, and then the adaptive output-feedback controller is constructively designed for tracking the given reference signal. It is proven that the constructed controller is robust to the uncertainties of both the unknown parameters and the system states. These results show that the global stability of the resulting closed-loop systems has been guaranteed and the ε-tracking problem has been solved. Meanwhile, it is also proven that the tracking error tends to a ‘steady state’ at the negative exponential attenuating rate. Simulation examples show that the tracking effects of the designed adaptive control systems are good, and the control quantities used in the simulation examples are always within the range of the admissible control.

ADAPTIVE ROBUST CONTROL FOR A CLASS OF UNCERTAIN TIME–DELAY SYSTEMS VIA OUTPUT FEEDBACK

The problem of robust stabilization is considered for a class of systems with the delayed state perturbations, uncertainties, and external disturbances. It is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances, are unknown. An improved adaptation law with s–modification is first introduced to estimate these unknown bounds. Then, by making use of the updated values of the unknown bounds, a class of adaptive robust output feedback controllers is proposed. On the basis of the strictly positive realness of the nominal system, it is also shown from the Kalman–Yakubovitch lemma that the solutions of the resulting adaptive closed–loop time-delay system can be guaranteed to be uniformly bounded, and the states decreases uniformly asymptotically to zero. Finally, a numerical example is given to demonstrate the validity of the results.

ADAPTIVE OUTPUT FEEDBACK CONTROL OF UNCERTAIN MIMO NONLINEAR SYSTEMS WITH UNKNOWN ORDERS

In this paper, we propose a design method for a robust adaptive output feedback control system for uncertain MIMO nonlinear systems with a higher order relative degree and an uncertain controlled system order. By using a virtual input filter method, this method allows an adaptive output feedback control of MIMO nonlinear systems without constructing a state observer in the controller.

Robust adaptive control of nonlinear systems with unmodelled dynamics

A robust adaptive output feedback controller is proposed for a class of nonlinear systems represented by input–output models. In the design of the adaptive controller, a signal is used to characterise the unmodelled dynamics and a nonlinear damping term is introduced to counteract the effects of the unmodelled dynamics and bounded disturbances. With the proposed controller, all the variables in the closed-loop system are bounded in the presence of unmodelled dynamics and bounded disturbances. Moreover, the mean-square tracking error can be made arbitrarily small by choosing appropriate design parameters.

Robust Adaptive Output Feedback Control for a Class of Nonlinear Systems

In this paper, we consider a class of single input-single output nonlinear systems whose nominal model is feedback linearizable and satisfies a minimum-phase condition. The system model depends linearly on unknown parameters which belong to a known compact convex set, and includes asymptotically stable, nonlinear actuators. A semi-global adaptive output feedback controller is developed; this scheme guarantees that the output of the system tracks any bounded reference signal which possesses bounded derivatives and satisfies a persistence of excitation condition. The controller scheme consists of an adaptive state-feedback controller and a high-gain observer. It is established that when the speeds of the observer and actuator are sufficiently high, the adaptive output feedback controller recovers the performance achieved under state feedback. In addition, the special case of robust adaptive regulation is presented. Finally an example is given to illustrate the developed theory.

Decentralized robust adaptive control of nonlinear systems with unmodeled dynamics

The authors present a decentralized robust adaptive output feedback control scheme for a class of large-scale nonlinear systems of the output feedback canonical form with unmodeled dynamics. A modified dynamic signal is introduced for each subsystem to dominate the unmodeled dynamics and an adaptive nonlinear damping is used to counter the effects of the interconnections. It is shown that under certain assumptions, the proposed decentralized adaptive control scheme guarantees that all the signals in the closed-loop system are bounded in the presence of unmodeled dynamics, high-order interconnections and bounded disturbances. Furthermore, by choosing the design constants appropriately, the tracking error can be made arbitrarily small regardless of the interconnections, disturbances, and unmodeled dynamics in the system. An illustration example demonstrates the effectiveness of the proposed scheme.

Robust Adaptive Output Feedback Control for a Class of Nonlinear Systems

Robust Adaptive Output Feedback Control for a Class of Nonlinear Systems

Adaptive output feedback tracking with almost disturbance decoupling for a class of nonlinear systems

For a class of single-input, single-output uncertain nonlinear systems affected both by uncertain constant parameters (with known bounds) and unknown time-varying bounded disturbances, a new robust adaptive output-feedback tracking control is presented. It is based on a reduced-order observer and guarantees input-to-state stability of the error system and almost disturbance decoupling of the tracking error with respect to disturbances and parameter estimation errors; asymptotic output tracking with arbitrary transient performance when disturbances are L 2 ∩ L ∞ signals.

Adaptive output feedback tracking with almost disturbance decoupling for a class of nonlinear systems

For a class of single-input, single-output uncertain nonlinear systems affected both by uncertain constant parameters (with known bounds) and unknown time-varying bounded disturbances, a new robust adaptive output-feedback tracking control is presented. It is based on a reduced-order observer and guarantees input-to-state stability of the error system and almost disturbance decoupling of the tracking error with respect to disturbances and parameter estimation errors; asymptotic output tracking with arbitrary transient performance when disturbances are L 2∩ L ∞ signals.

Robust adaptive output-feedback control of a class of uncertain nonlinear systems

With an attempt to simplify the controller design and to reduce the control effort, a new robust output-feedback controller is designed to solve the tracking problem of a class of nonlinear uncertain systems by using observer plus backstepping. In the controller design, a simple observer is constructed, by which only a coarse estimate of the unknown states is provided, and a positive function used to generate a new normalization signal and the positive nonlinear functions used in nonlinear damping terms are all left to be chosen freely. Thanks to these techniques, the new controller can be designed with a simpler structure and reduced control effort under weaker assumptions on both the uncertainties and the reference signal. The global boundness of all closed-loop signals can be guaranteed, and the output tracking error can be made as small as possible

Robust adaptive output feedback control of nonlinear systems without persistence of excitation

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 nth-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.