Global Adaptive Output Feedback Research Articles

Global adaptive event-triggered output feedback control for p-normal feedforward nonlinear systems with uncertain output function

This paper concentrates on the global adaptive event-triggered output feedback controller design for a class of p-normal feedforward nonlinear systems with uncertain output function. Due to the existence of unknown growth rate and uncertain output function, the considered uncertain nonlinear systems contain more uncertainties. To overcome this difficulty, a dynamic gain technique is introduced and an elaborate adaptive law of the gain is designed. Then, a completely time-varying event-based strategy is presented, which can effectively eliminate the effects caused by event-triggered errors. Since the presented event-triggered controller is not differentiable, a new analysis manner is developed to prove that the system is Zeno-free. Meanwhile, the closed-loop system(CLS) states are asymptotically convergent with the proposed strategy. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

Global adaptive event-triggered output feedback controller design for high-order nonlinear systems

This article focuses on the adaptive event-triggered output feedback stabilization problem for a class of high-order systems with uncertain output function. Firstly, an adaptive event-triggered mechanism with a dynamic gain is designed for the nominal system. Then the gain is employed into the observer and event-triggered controller to dominate the nonlinearities. Thirdly, it is proved that all system states converge to zero and the Zeno-behavior is excluded. Finally, a numerical example reveals the effectiveness of the proposed event-triggered control strategy.

Adaptive output feedback control for [formula omitted]-normal nonlinear time-varying delay systems with unknown output function

This paper tackles the global adaptive output feedback control issue for a family of p-normal nonlinear time-delay systems with output function unknown. Firstly, an output feedback controller (OFC) is designed through adding a power integrator technique to stabilize the nominal system (without nonlinear terms) globally. Based on the above OFC, two novelly-designed dynamic gains and a Lyapunov-Krasovskii functional are constructed to deal with the uncertainties and time-varying delays, respectively. It can be proved that the p-normal nonlinear lower-triangular time-delay system is globally asymptotically stable (GAS) with bounded dynamic gains. Finally, a numerical example demonstrates the feasibility of the control strategy.

Global adaptive output feedback control for a class of stochastic nonlinear systems with unknown homogeneous growth rates

AbstractThis article focuses on the adaptive output feedback stabilization for a class of stochastic nonlinear systems whose drift and diffusion terms satisfy homogeneous growth conditions. Since the homogeneous growth rates are unknown, two dynamic gains are coupled into the full‐order homogeneous observer. By virtue of adding a power integrator technique and the homogeneity theory, two adaptive laws and a homogeneous output feedback controller are designed. Based on the celebrated nonnegative semimartingale convergence theorem and the general stochastic Barbˇlat's lemma, it is indicated that all the signals of the closed‐loop system are bounded almost surely, and all the system states of the closed‐loop system converge to origin almost surely. Finally, the effectiveness of the proposed control scheme is verified by means of both numerical and practical examples.

Adaptive output feedback tracking for time-delay nonlinear systems with unknown control coefficient and application to chemical reactors

In this paper, the problem of global adaptive output feedback tracking is considered for a class of highly nonlinear time-delay systems with unknown control coefficient and relaxed lower-triangular growth constraints. Based on the non-separation principle, a non-identifier-based adaptive output feedback controller is proposed by designing a novel update law of the dynamic gain in observer and controller. The novel gain can simultaneously compensate the uncertain parameters, the output-polynomial growth rate and the unknown time-varying delay. The proposed controller is well universal attributed to using the non-identification adaptive mechanism, and all design parameters are easy to get by simple calculation. With the help of Lyapunov–Krasovskii functionals and Barbalat’s lemma, it is shown that the solutions of the resulting closed-loop system are globally uniformly ultimately bounded by improving the backstepping design and dynamic high-gain scaling approach; the adaptive tracking is achieved under any small pre-given tracking error. Finally, the effectiveness of the proposed controller is illustrated by two examples.

Global adaptive output feedback stabilization for nonlinear time‐delay systems with unknown measurement sensitivity

AbstractIn this article, a global output feedback stabilization scheme is proposed for a class of time‐delay uncertain nonlinear systems with unknown measurement sensitivity. A new high gain observer is designed with which the sensitivity function can be tackled by only one dynamic gain and the coupled linear‐like controller is fairly simple. By introducing some transformations of the state estimation errors and observer states, and appropriately choosing Lyapunov–Krasovskii functionals, it is proved that the proposed controller can globally stabilize the system.

Adaptive event‐triggered output feedback control for a class of p‐normal nonlinear systems with sensor failure

SummaryThis article investigates the problem of global adaptive output feedback control for a class of p‐normal nonlinear systems with time‐varying sensor failure and unknown growth rate via an event‐triggered strategy. Due to the existence of time‐varying sensor failure, only the system output with sensor failure is available for feedback control design. To overcome this obstacle, an adaptive reduced‐dimensional observer using only failure output is constructed. Subsequently, a novel adaptive event‐triggered controller is designed by virtual of a dynamic gain technique, under which all the states of the considered closed‐loop systems are bounded as well as the proposed event‐triggered mechanism is Zeno‐free. Finally, two examples are provided to demonstrate the validity of the presented control method.

Global adaptive output feedback tracking for a class of nonlinear systems with quantized input

In this paper, we consider the quantized control of a class of nonlinear systems whose nonlinear functions satisfy more general growth conditions. Based on a reduced-order observer and a dynamic gain, an adaptive output feedback tracking controller is designed. It is proved that by suitably choosing design parameters and functions, the tracking error can converge to an arbitrarily small residual set while all the other signals of the closed-loop system are bounded.

Constrained global adaptive controller for a plug-flow tubular reactor with partial temperature measurements

Abstract In this work, a global constrained adaptive output feedback is presented for a class of plug-flow tubular reactors models described by non-linear partial differential equations. The output of the system is the measured temperature in a fixed zone of the reactor. It is then used to regulate the temperature throughout the reactor to a ball with radius $\lambda $ (arbitrarily small) centred at the fixed temperature profile.

Adaptive output feedback control of feedforward nonlinear distributed delay systems with unknown delay kernel

ABSTRACTThis paper considers the problem of global adaptive output feedback regulation for a class of uncertain feedforward nonlinear distributed delay systems. Compared with the existing results, we reduce the conservatism of the restrictive conditions by combining the dynamic scaling technique and the backstepping method, in particular, uncertain control coefficients and unknown delay kernels are admitted. With the help of the Lyapunov–Krasovskii theorem, a delay-independent output feedback controller is proposed by constructing an input-driven observer with a novel dynamic gain, which guarantees that all the closed-loop signals are globally bounded while rendering the states of original system and the estimate states globally asymptotically to converge to zero as time goes to infinity. Finally, a numerical example is given to illustrate the usefulness of our results.

Global adaptive output feedback tracking for a class of non‐linear systems with unknown backlash‐like hysteresis

The authors consider a class of non-linear systems preceded by unknown backlash-like hysteresis. Unlike other schemes dealing with hysteresis, the non-linear systems of this study not only involve unknown parameters but also take non-linear terms linear in the unmeasured states into account. An adaptive output feedback controller by utilising a modified high-gain observer and backstepping approach is proposed, which is able to mitigate the effects of the hysteresis, and guarantee the global stability of the closed-loop system and the arbitrarily small steady-state tracking error. Moreover, it is proved that by introducing an initialisation technique, the ℒ∞ tracking performance can be achieved.

Global adaptive output feedback tracking for a class of multivariable nonlinear systems

In this paper, global adaptive output feedback tracking problem is considered for a class of multivariable nonlinear systems with unknown parameters and nonlinear terms linear in unmeasured states. Based on a modified high-gain observer and symmetric positive diagonal unity upper triangular factorisation of high-frequency gain matrix, an adaptive backstepping design is proposed, which is able to guarantee global stability of the closed-loop system and circumvent the over-parameterisation problem raised by using conventional backstepping method. Moreover, with the introduction of an error modification and an initialisation technique, it is proved that the tracking performance can be achieved.

Adaptive Output Feedback Control of Multivariable Nonlinear Systems Based on Hurwitz Assumption

In this paper, global adaptive output feedback tracking problem is considered for a class of multivariable nonlinear systems with unknown parameters and nonlinear terms linear in unmeasured states. Based on a modified high-gain observer and Hurwitz assumption of high frequency gain matrix, an adaptive backstepping design is proposed, which is able to guarantee global stability of the closed-loop system and circumvent the over-parameterization problem raised by using conventional back stepping method.

Global adaptive output feedback control for a class of nonlinear time-delay systems

This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.

Global robust and adaptive output feedback dynamic positioning of surface ships

A constructive method was presented to design a global robust and adaptive output feedback controller for dynamic positioning of surface ships under environmental disturbances induced by waves, wind, and ocean currents. The ship’s parameters were not required to be known. An adaptive observer was first designed to estimate the ship’s velocities and parameters. The ship position measurements were also passed through the adaptive observer to reduce high frequency measurement noise from entering the control system. Using these estimate signals, the control was then designed based on Lyapunov’s direct method to force the ship’s position and orientation to globally asymptotically converge to desired values. Simulation results illustrate the effectiveness of the proposed control system. In conclusion, the paper presented a new method to design an effective control system for dynamic positioning of surface ships.

Theory and experiments of global adaptive output feedback tracking control of manipulators

A new adaptive controller for robot manipulators is proposed. The new approach uses only position measurements. The main conclusions derived from the closed-loop system analysis are in two main results. In the first one, the global convergence of the position and velocity tracking errors is stated by using a condition that relates the viscous friction damping and the desired joint speed. In the second one, such a condition is dropped out but the local exponential stability of the closed-loop system is shown. To confirm the theoretical conclusions, a detailed experimental study in a two degrees-of-freedom direct-drive manipulator is provided, where the performance of the new controller is compared with respect to a known output feedback adaptive controller.

Adaptive output feedback asymptotic stabilization of nonholonomic systems with uncertainties

A global adaptive output feedback control strategy is presented for a class of nonholonomic systems in generalized chained form with drift nonlinearity and unknown virtual control parameters. The purpose is to design a nonlinear output feedback switching controller such that the closed-loop system is globally asymptotically stable. By using the input-state scaling technique and an integrator back-stepping approach, an output feedback controller is given. A filter of observer gain is introduced for state and parameter estimates. Meanwhile, in order to avoid the over-parameters, a tuning function technique is utilized. A novel switching control strategy based on the output measurement of the first subsystem rather than time is used to overcome the uncontrollability of the x 0 -subsystem in the origin. The proposed controller can guarantee that all the system states globally converge to the origin, while other signals maintain bounded. The numerical simulation testifies the effectiveness.

Global adaptive output feedback controllers with application to non‐linear friction compensation

AbstractIn this paper, we consider a class of non‐linear systems in which a set of constant parameters is unknown and some state variables are not available for measurement. For such systems we provide a constructive procedure for the solution of the global adaptive tracking problem with dynamic partial state feedback. We illustrate an application of the control strategy to the adaptive non‐linear friction compensation of a DC motor servomechanism. We improve previous results in tow directions: we allow for a subset of the unmeasurable states to enter in a system non‐linearly; we consider systems which are linearly parametrized with respect to a set of unknown constant parameters. Copyright © 2002 John Wiley & Sons, Ltd.

A NONLINEAR TRANSFORMATION APPROACH TO GLOBAL ADAPTIVE OUTPUT FEEDBACK CONTROL OF 3RD-ORDER UNCERTAIN NONLINEAR SYSTEMS

In this paper, we present a global adaptive output feedback control scheme for a class of 3rd-order uncertain nonlinear systems to which adaptive observer backstepping method may not be applicable directly. In contrast to the existing output feedback form, the allowed extended output feedback structure includes quadratic and multiplicative dependency of unmeasured states. Our novel design technique employs a change of coordinates and adaptive backstepping. With these proposed tools, we can remove linear and quadratic dependence on the unmeasured states in the state equation. Also, the multiplication of the two unmeasured states can be eliminated. From the transformed systems, a state observer can be constructed in a very easy way. The overall scheme achieves globally exponential convergence of the tracking error to zero while maintaining global boundedness of all the signals and states.

A combined backstepping and small-gain approach to adaptive output feedback control

In this brief article, a novel combined backstepping and small-gain approach is presented to the global adaptive output feedback control of a class of uncertain nonlinear systems with unmodeled dynamics. The use of small-gain techniques permits removal of a common restriction, i.e. that the nonlinearities in the system are only dependent on the measured output. The design procedure is divided into two parts. In the first part, based on a partial-state observer, integrator backstepping is used to design an adaptive output-feedback controller which ensures robustness with respect to unknown parameters and uncertain nonlinearities. In the second part, it is shown that the adaptive controller can be made robust against dynamic uncertainties by means of recent nonlinear small-gain results.