Output-feedback Canonical Form Research Articles

Distributed Output-Feedback Asymptotic Consensus Tracking for High-Order Multiagent Systems With Quantized Input.

This article is devoted to distributed adaptive asymptotic consensus tracking control based on output feedback for the uncertain high-order multiagent systems with input quantization. Compared with the output-feedback canonical form, the system takes unmeasured states-dependent nonlinearities into account and also includes unknown parameters and quantized input. The improved K -filters with one dynamic gain are constructed to dispose the unmeasured states-dependent nonlinearities and estimate the unknown states. Then, the novel recursive control strategy with the aid of new first-order dynamic parameter filters is proposed, which is able to effectively counteract the filter errors and steer the consensus tracking errors to zero asymptotically with low design complexity. Moreover, the new funnel variable combined with prespecified time performance function is first introduced, which can predefine practical transition time and maximum overshoot of consensus error. Finally, simulation results are presented to illustrate the validity and superiority of the proposed scheme.

Model Identification and Adaptive State Observation for a Class of Nonlinear Systems

In this article, we consider the joint problems of state estimation and model identification for a class of continuous-time nonlinear systems in the output-feedback canonical form. An adaptive observer is proposed that combines an extended high-gain observer and a discrete-time identifier. The extended observer provides the identifier with a dataset permitting the identification of the system model and the identifier adapts the extended observer according to the new estimated model. The design of the identifier is approached as a system identification problem and sufficient conditions are presented that, if satisfied, allow different identification algorithms to be used for the adaptation phase. The cases of recursive least-squares and multiresolution black-box identification via wavelet-based identifiers are specifically addressed. Stability results are provided relating the asymptotic estimation error to the prediction capabilities of the identifier. Robustness with respect to additive disturbances affecting the system equations and measurements is also established in terms of an input-to-state stability property relative to the noiseless estimates.

Extended backstepping approach for a class of non-linear systems in generalised output feedback canonical form

In this study, an extended backstepping approach is developed for tracking control of a class of systems that are globally diffeomorphic into systems in generalised output feedback canonical form. Output-dependent non-linearities are allowed to enter such a system both additively and multiplicatively. The system contains unknown parameters multiplied by output-dependent non-linearities. This method relies on a parameter estimator and state observer design and standard backstepping construction. Compared with the traditional parameter estimation and state observation, the approach in this study has three distinct features due to adopting the new adaptive mechanism recently developed in literature. First, the parameter estimator and state observer does not follow the classical certainty equivalent principle. Second, the design treats the unknown parameter estimation and unmeasured state observation in a united way. Third, unlike the conventional observer-based backstepping, the design does not require the construction of Lyapunov function for every augmented sub-system. Furthermore, the method is applied to the stabilisation of single-machine-infinite-bus power systems with steam valve control using only measurements of the power angle as an illustrative example. A typical example is also given to show that the proposed method can be applied to more general systems which violate the cascading upper diagonal dominance conditions.

Robust stabilization of a class of non‐minimum‐phase nonlinear systems in a generalized output feedback canonical form

AbstractIn this paper, a globally robust stabilizer for a class of uncertain non‐minimum‐phase nonlinear systems in generalized output feedback canonical form is designed. The system contains unknown parameters multiplied by output‐dependent nonlinearities and output‐dependent nonlinearities enter such a system both additively and multiplicatively. The proposed method relies on a recently developed novel parameter estimator and state observer design methodology together with a combination of backstepping and small‐gain approach. Our design has three distinct features. First, the parameter estimator and state observer do not necessarily follow the classical certainty‐equivalent principle any more. Second, the design treats unknown parameters and unmeasured states in a unified way. Third, the technique by combining standard backstepping and small‐gain theorem ensures robustness with respect to dynamic uncertainties. Finally, two numerical examples are given to show that the proposed method is effective, and that it can be applied to more general systems that do not satisfy the cascading upper diagonal dominance conditions developed in recent papers, respectively. Copyright © 2008 John Wiley & Sons, Ltd.

Iterative learning of model reference adaptive controller for uncertain nonlinear systems with only output measurement

In this paper, a model reference adaptive control strategy is used to design an iterative learning controller for a class of repeatable nonlinear systems with uncertain parameters, high relative degree, initial output resetting error, input disturbance and output noise. The class of nonlinear systems should satisfy some differential geometric conditions such that the plant can be transformed via a state transformation into an output feedback canonical form. A suitable error model is derived based on signals filtered from plant input and output. The learning controller compensates for the unknown parameters, uncertainties and nonlinearity via projection type adaptation laws which update control parameters along the iteration domain. It is shown that the internal signals remain bounded for all iterations. The output tracking error will converge to a profile which can be tuned by design parameters and the learning speed is improved if the learning gain is large.

Global high-gain-based observer and backstepping controller for generalized output-feedback canonical form

We provide results and extensions for global output feedback design for systems in the generalized output-feedback canonical form. Our investigations reveal several conceptual and structural connections between high-gain design and two recent results on the generalized output-feedback canonical form. The recognition of these links provides new insight into the stabilization mechanisms of these designs, particularly in the observer design. Furthermore, we have extended the results to include output dependent upper diagonal terms and also shown that the additional scaling proposed in a recent paper can be removed through a simultaneous stabilization result (i.e., solving a special pair of coupled matrix Lyapunov equations). We provide necessary and sufficient conditions for solvability of these coupled Lyapunov equations. The removal of the additional scaling makes the connection between the obtained results and proofs and our earlier results assuming cascading upper diagonal dominance (CUDD) more transparent. Moreover, removing the additional scaling (and possibly introducing a negative scaling) provides a better guaranteed convergence of the observer errors and allows smaller controller gains. It is shown that the high gain scaling induces the CUDD structure on the observer error dynamics. Finally, the design utilizes a reduced-order observer.

Decentralized control and disturbance attenuation for large-scale nonlinear systems in generalized output-feedback canonical form

A global decentralized robust adaptive output-feedback dynamic compensator is proposed for stabilization, tracking, and disturbance attenuation of the decentralized generalized output-feedback canonical form. This represents the largest class for which decentralized robust adaptive output-feedback tracking and disturbance attenuation results are currently available. The system is allowed to contain unknown parameters multiplying output-dependent nonlinearities, and, also, unknown nonlinearities satisfying certain bounds. Under the assumption that a constant matrix can be found for each subsystem to achieve a certain property, it is shown that reduced-order observers and backstepping controllers can be designed to achieve practical stabilization of the tracking error in each subsystem in the presence of bounded disturbance inputs. Sufficient conditions under which asymptotic tracking and stabilization can be achieved are also obtained. Signal gains from disturbance inputs to tracking errors are presented in the input-to-output-practical-stability and integral-input-to-output-practical-stability frameworks. A particular case in which the standard L 2 -gain disturbance attenuation is achieved is also provided.

Robust adaptive control for non‐linear systems in generalized output‐feedback canonical form

AbstractDesign of global robust adaptive output‐feedback dynamic compensators for stabilization and tracking of a class of systems that are globally diffeomorphic into systems in generalized output‐feedback canonical form is investigated. This form includes as special cases the standard output‐feedback canonical form and various other forms considered previously in the literature. Output‐dependent non‐linearities are allowed to enter both additively and multiplicatively. The system is allowed to contain unknown parameters multiplying output‐dependent non‐linearities and, also, unknown non‐linearities satisfying certain bounds. Under the assumption that a constant matrix can be found to achieve a certain property, it is shown that a reduced‐order observer and a backstepping controller can be designed to achieve practical stabilization of the tracking error. If this assumption is not satisfied, it is shown that the control objective can be achieved by introducing additional dynamics in the observer. Sufficient conditions under which asymptotic tracking and stabilization can be achieved are also given. This represents the first robust adaptive output‐feedback tracking results for this class of systems. Copyright © 2003 John Wiley & Sons, Ltd.

Global output feedback tracking for nonlinear systems in generalized output-feedback canonical form

A global output feedback dynamic compensator is proposed for stabilization and tracking of a class of systems that are globally diffeomorphic into systems which are in generalized output-feedback canonical form. This form includes as special cases the standard output-feedback canonical form and various other forms considered previously in the literature. Output-dependent nonlinearities are allowed to enter both additively and multiplicatively. Under the assumption that a constant matrix can be found to achieve a certain property, it is shown that a reduced-order observer and a backstepping controller can be designed to achieve asymptotic tracking. For the special case of linear systems, the designed dynamic controller reduces to the standard reduced-order observer and linear controller. This is the first global output-feedback tracking results for this class of systems.

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.

Active identification for discrete-time nonlinear control. I. Output-feedback systems

The problem of controlling nonlinear systems with unknown parameters has received a great deal of attention in the continuous-time case. In contrast, its discrete-time counterpart remains largely unexplored, primarily due to the difficulties associated with utilizing Lyapunov design techniques in a discrete-time framework. Existing results impose restrictive growth conditions on the nonlinearities to yield global stability. In this paper, we propose a novel approach, which removes this obstacle and yields global stability and tracking for systems that can be transformed into an output-feedback canonical form, in which the nonlinearities depend only on the measured output, but are otherwise arbitrary. The main novelties of our design are: (i) the temporal and algorithmic separation of the parameter estimation task from the control task, and (ii) the development of an active identification procedure, which uses the control input to actively drive the system state to points in the state space that allow the orthogonalized projection estimator to acquire all the necessary information about the unknown parameters. We prove that our algorithm guarantees complete (for control purposes) identification in a finite time interval, whose maximum length we compute. Thus, the traditional structure of concurrent online estimation and control is replaced by a two-phase control strategy: first use active identification, and then utilize the acquired parameter information to implement any control strategy as if the parameters were known.

Decentralized adaptive output feedback design for large-scale nonlinear systems

In this paper, we present a global, decentralized adaptive design procedure for a class of large-scale nonlinear systems, which utilizes only local output feedback. The advocated scheme guarantees robustness to parametric and dynamic uncertainties in the interconnections and also rejects any bounded disturbances entering the system. The systems belonging to this class are those which can be transformed using a global diffeomorphism to the output feedback canonical form, where the interconnections are a function of subsystem outputs only. The uncertainties are assumed to be bounded by an unknown pth-order polynomial in the outputs. The resulting controller maintains global robustness and disturbance rejection properties. The output tracking error is shown to be bounded within a compact set, the size of which can be made arbitrarily small by appropriate choice of the control gains. For the case where the objective is regulation, global asymptotic regulation of all the states of the closed-loop system is achieved.

Adaptive dead-zone compensation for output-feedback canonical systems

An adaptive output feedback dead-zone compensation scheme is designed for systems with an unknown dead-zone at the input of an n th-order smooth nonlinear dynamics in the output-feedback canonical form. The proposed adaptive controller employs an adaptive dead-zone inverse to cancel the dead-zone and uses a backstepping design for adaptive output feedback control. It has a new state observer parametrization that is needed to handle the dead-zone uncertainty and a new robust control law that is suitable for the parameter projection needed to implement an adaptive dead-zone inverse. The adaptive dead-zone compensation design ensures closed-loop signal boundedness and improves system tracking performance.

Adaptive output-feedback design for a class of nonlinear discrete-time systems

We present adaptive output-feedback schemes for a class of discrete-time systems whose continuous-time counterparts are the output-feedback canonical form. We first develop a systematic design procedure for the deterministic case. Global boundedness and convergence are achieved with no restriction imposed on the nonlinearities. Then we proceed to develop an analogous design procedure for the adaptive case. Depending on the characteristics of the nonlinearities, global boundedness and convergence can be achieved with various update laws. A rank condition is required to ensure such properties for nonlinearities which are not globally Lipschitz.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>