Output Feedback For Nonlinear Systems Research Articles

Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystems

This paper deals with global output regulation with nonlinear exosystems for a class of uncertain nonlinear output feedback systems. The circle criterion is exploited for the internal model design to accommodate the nonlinearities in the exosystems, and the explicit conditions are given for the exosystems such that the proposed internal model design can be applied. The uncertainties of the output feedback systems are in the form of unknown constant parameters, and adaptive control techniques are used to ensure the global stability of the proposed control design for output regulation.

Adaptive output feedback control for nonlinear time-delay systems using neural network

This paper extends the adaptive neural network (NN) control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay. Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov-Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved. The feasibility is investigated by two illustrative simulation examples.

Asymptotic stabilization via output feedback for nonlinear systems with delayed output

We propose a novel and simple design scheme of output feedback controller for a class of nonlinear systems with delayed output. The nonlinear systems considered here are more general than feedforward systems (upper triangular systems). By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and solving linear matrix inequalities (LMIs), the delay-dependent controller making the closed-loop system globally asymptotically stable (GAS) is explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

Asymptotic Rejection of General Periodic Disturbances in Output-Feedback Nonlinear Systems

This note deals with asymptotic rejection of general periodic disturbances in nonlinear systems. A novel approach based on integrations over the half of disturbance period is proposed to estimate disturbances which may not be harmonic or even smooth. The proposed algorithm uses the period and the knowledge of the basic disturbance patterns, while the amplitude and phase of the disturbances are unknown, and they are estimated. Based on the estimated disturbance, the disturbance rejection algorithm is then proposed for linear systems and nonlinear systems in the output feedback format, which asymptotically rejects the periodical disturbances. The proposed algorithm extends asymptotic rejection of unknown disturbances from sinusoidal disturbances to a more general class of periodical disturbances which includes zero-mean square waves, symmetric triangular waves etc.

Semi-global stabilisation of a class of non-minimum phase non-linear output-feedback systems

The stabilisation of non-linear systems with unstable zero-dynamics is considered. The non-linear systems are assumed to be transformable to the non-linear output feedback form. The control design starts from the state feedback, and the state variables associated with the zero-dynamics are stabilised first. The state feedback control design is then carried out using backstepping. An observer with linear error dynamics is constructed with a design parameter which can be set at any positive value. The dynamic output feedback control is then designed, by substituting the state in state feedback control with the observed one and imposing a saturation on the control input. The saturation level depends on the domain of the initial state. The proposed control design asymptotically stabilises the system for any prescribed domain of the initial state.

A Unifying Framework for Global Regulation Via Nonlinear Output Feedback: From ISS to iISS

This paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input-to-state stable inverse dynamics, subject to possibly unknown control direction. The contribution of the paper is two-fold. Firstly, we consider the problem of global regulation, instead of global asymptotic stabilization (GAS), for systems with generalized dynamic uncertainties. It is shown by an elementary example that GAS is not solvable using conventional smooth output feedback. Secondly, we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system. Using our framework, most of the known classes of output feedback form systems are broadened in several directions: unmeasured states and unknown parameters can appear nonlinearly, restrictive matching and growth assumptions are removed, the dynamic uncertainty satisfies the weaker condition of Sontag's integral input-to-state stability, and the sign of high-frequency gain may be unknown. A constructive strategy is proposed to design a dynamic output feedback control law, that drives the state to the origin while keeping all other closed-loop signals bounded.

Adaptive stabilization of a class of nonlinear systems with unstable internal dynamics

This note considers global stabilization of a class of uncertain nonlinear output feedback systems with unstable internal dynamics. The coefficients which characterize the internal dynamics are allowed to be functions of system output, and the uncertainty of the system is characterized by an unknown constant parameter vector. The key step in the proposed control design is to estimate the internal state variables and impose control over them. The control design is presented first for systems without unknown parameters, and then for the systems with unknown parameters using adaptive control techniques.

Adaptive tracking with complete compensation of unknown disturbances for nonlinear output feedback systems

The complete adaptive compensation of unknown disturbances for uncertain nonlinear output feedback systems is studied. The unknown disturbances are generated from an unknown linear exosystem whose order is assumed known and the eigenvalues are distinct. The uncertainty of the system is characterised by unknown constant parameters contained in a vector. The uncertainties in the nonlinear system and the uncertainties in the exosystem are tackled concurrently. The proposed control design is able to completely adaptively compensate for the disturbances without knowing their amplitudes, frequencies and phases, as long as the number of different frequency components in the disturbances is known. A new control strategy, different from the current ones for output regulation with adaptive internal models, is proposed, which results in the direct estimation of all original unknown parameters in the system and the removal of the restriction imposed by the current methods that all the nonlinear functions must be polynomials of the system output. The completely new design of additional filters makes it possible to adaptively tackle the concurrent uncertainties in the system and the exosystem.

Recursive Back‐Stepping Design of An Adaptive Fuzzy Controller for Strict Output Feedback Nonlinear Systems

ABSTRACTIn this paper, a back‐stepping adaptive fuzzy controller is proposed for strict output feedback nonlinear systems. The unknown nonlinearity and external disturbances of such systems are considered. We assume that only the output of the system is available for measurement. As a result, two filters are constructed to estimate the states of strict output feedback systems. Since fuzzy systems can uniformly approximate nonlinear continuous functions to arbitrary accuracy, the adaptive fuzzy control theory combined with a tuning function scheme is developed to derive the control laws of strict output feedback systems that possess unknown functions. Moreover, the H∞ performance condition is introduced to attenuate the effect of the modeling error and external disturbances. Finally, an example is simulated in order to confirm the applicability of the proposed method.

Adaptive control for output feedback nonlinear systems in the presence of modeling errors

The paper is extending output feedback nonlinear control and backstepping approaches to a class of systems approximately diffeomorphic to output feedback systems that include unknown functions. The unknown functions are addressed via online function approximation, which results in two types of uncertainty. Parametric uncertainty due to online function approximation and non-parametric uncertainty. The non-parametric uncertainty results from the inability of any function approximator to perfectly model an unknown function and from terms unmodeled by the output feedback form. The non-parametric terms are assumed to be bounded by unknown constants. The backstepping procedure is applied to adapt with respect to both parametric uncertainties and the upper bound on the non-parametric uncertainties.

A flat-zone modification for robust adaptive control of nonlinear output feedback systems with unknown high-frequency gains

This note deals with adaptive control of perturbed nonlinear output feedback systems with unknown high-frequency gains. The disturbances in the systems are assumed to be bounded, but the bounds are unknown. A flat-zone modification is proposed to incorporate both the bound estimation and Nussbaum gain design in the nonlinear adaptive control. To ensure the differentiability of stabilizing functions needed for backstepping design, high order terms are introduced in the Lyapunov function candidate with a flat zone around the neighborhood of the origin. The output tracking error converges to an arbitrarily small interval around zero.

REDUCED ORDER ADAPTIVE OBSERVER BACKSTEPPING

It is the intent of this paper to add to, and improve the existing design tools for nonlinear output feedback systems. Considered here are systems, exhibiting parametric uncertainty, and containing nonlinearities dependent on the output alone. A lower triangular state transformation is utilised, equivalent to that obtained via the traditional and recursive back stepping algorithm. Extra damping is introduced to counter the uncertainty and observer error effects. The benefits of this approach lie in the significant reduction in total controller dynamic order, as well as the simplicity and clarity provided by implementing back stepping from a purely structural perspective.

Adaptive observer backstepping control using neural networks

This paper extends the application of neurocontrol approaches to a new class of nonlinear systems diffeomorphic to output feedback nonlinear systems with unmeasured states. A neural-based adaptive observer is introduced for state estimation as well as system identification using only output measurements during online operation. System identification is achieved via the online approximation of a priori unknown functions. The controller is designed using the backstepping control design procedure. Leakage terms in the adaptive laws and nonlinear damping terms in the backstepping controller are introduced to prevent instability from arising due to the inherent approximation error. A primary benefit of the online function approximation is the reduction of approximation errors, which allows reduction of both the observer and controller gains. A semi-global stability analysis for the proposed approach is provided and the feasibility is investigated by an illustrative simulation example.

Global output regulation of uncertain nonlinear systems with exogenous signals

The paper addresses the global output tracking of a class of uncertain output feedback systems affected by disturbances which are generated from a known exosystem. The system uncertainty is parametrized by a unknown parameter vector, which is absorbed in the parametrization of disturbances. A controller based on the estimation of states and disturbances from the output is designed using backstepping to asymptotically track arbitrary trajectories and to guarantee the boundedness of all other variables. The proposed control algorithm provides an alternative with global tracking to structurally stable regulation of nonlinear output feedback systems. It can also be viewed as a generalization to adaptive control algorithms.

Analysis and design of robust adaptive control for nonlinear output feedback systems under disturbances with unknown bounds

Robust adaptive control of nonlinear output feedback systems under bounded disturbances whose bounds are unknown is considered. A new algorithm is proposed for estimation of unknown bounds and adaptive control of the uncertain nonlinear system. To carry out the backstepping design with the estimation of unknown bounds, a new Lyapunov function is introduced with a flat zone in the pre-specified neighbourhood of the origin. The adaptive law based on the Lyapunov function has a dead zone, whose size depends on the flat zone. The design procedure follows the standard backstepping with variations in dealing with the cross terms between different stages and the bound estimation. The stability analysis shows that all the variables of the closed-loop control system are bounded, and the output tracking error converges to the flat zone which can be arbitrarily small. The proposed method does not need any bound of uncertain parameters or unknown disturbances, and it prevents the bursting phenomena.

Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance

We address the class of stochastic output-feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori. This problem is analogous to deterministic disturbance attenuation problems. We first design a controller which guarantees that the solutions converge (in probability) to a residual set proportional to the unknown bound on the covariance. Then, for the case of a vanishing noise vector field, we design an adaptive controller which, besides global stability in probability, guarantees regulation of the state of the plant to zero with probability one.

Output-feedback disturbance attenuation and adaptive control for stochastic nonlinear systems

We address the class of stochastic output-feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori. This problem is analogous to deterministic disturbance attenuation problems. We first design a controller which guarantees that the solutions converge (in probability) to a residual set proportional to the unknown bound on the covariance. Then, for the case of a vanishing noise vector field, we design an adaptive controller which, besides global stability in probability, guarantees regulation of the state of the plant to zero with probability one.

Almost disturbance decoupling of uncertain nonlinear output feedback systems

The paper addresses the output tracking of a class of uncertain nonlinear output feedback systems affected by disturbances that are known to be bounded but are otherwise unknown. The system uncertainty is parametrised by a parameter vector of which a normed upper bound is known. An adaptive controller is designed to guarantee arbitrary disturbance attenuation on the output tracking error for smooth reference signals under the minimum phase assumption. The paper represents an extension of disturbance decoupling results to uncertain systems as well as an extension of adaptive control results to the disturbance decoupling problem.

Nonlinearities enhance parameter convergence in strict feedback systems

Following the development of a parameter convergence analysis procedure for output-feedback nonlinear systems (1995, 1998), the authors shift their attention to strict feedback nonlinear systems in this paper. They develop an analytic procedure which allows us, given a specific nonlinear system and a specific reference signal, to determine a priori whether or not the parameter estimates will converge to their true values, simply by checking the linear independence of the rows of a constant real matrix. Moreover, the authors show that this convergence is exponential. Finally, they prove that even if the rows of this constant matrix are not linearly independent, partial parameter convergence is still achieved, in the sense that the parameter error vector converges asymptotically to the left nullspace of this matrix.

Robust adaptive control of nonlinear output-feedback systems under bounded disturbances

The paper presents a robust adaptive control algorithm for uncertain nonlinear output-feedback systems under bounded disturbances based on a dead-zone modification. The algorithm guarantees the boundedness of all the variables of systems with arbitrary relative degrees under the minimum phase assumption. An example is included to demonstrate the proposed algorithm.