Output feedback regulation of a class of triangular structural nonlinear systems with unknown measurement sensitivity

ABSTRACT

This paper investigates the problem of global regulation via output feedback for a class of triangular structural nonlinear systems with unknown measurement sensitivity. Two kinds of triangular structure nonlinear systems, namely upper triangular systems and lower triangular systems, are considered here, and the key features of our considered systems are that there are uncertain linear growth condition in the nonlinear terms. Firstly, for a class of upper triangular nonlinear systems with unknown measurement sensitivity, an output feedback controller is designed such that global regulation of the system is achieved. Then, for a class of lower triangular nonlinear systems with unknown measurement sensitivity, global regulation is realised in a unifying framework. Finally, two simulation examples are respectively given to demonstrate the effectiveness of the theoretical results.     

Output feedback control of a class of nonminimum‐phase nonlinear systems

The problem of global stabilization by output feedback is investigated in this paper for a class of nonminimum‐phase nonlinear systems. The system under consideration has a cascade configuration that consists of a driven system known as the inverse dynamics and a driving system. It is proved that although the zero dynamics may be unstable, there is an output feedback controller, globally stabilizing the nonminimum‐phase system if both driven and driving systems have a lower‐triangular form and satisfy a Lipschitz‐like condition, and the inverse dynamics satisfy a stronger version of input‐to‐state stabilizability condition. A design procedure is provided for the construction of an n‐dimensional dynamic output feedback compensator. Examples and simulations are also given to validate the effectiveness of the proposed output feedback controller. Copyright © 2016 John Wiley & Sons, Ltd.     

A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback

In this paper, we introduce a generalized framework for global output feedback stabilization of a class of uncertain, inherently nonlinear systems of a particularly complex nature since their linearization around the equilibrium is not guaranteed to be either controllable or observable. Based on a new observer/controller construction and a homogeneous domination design, this framework not only unifies the existing output feedback stabilization results, but also leads to more general results which have been never achieved before, establishing this methodology as a universal tool for the global output feedback stabilization of inherently nonlinear systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Global adaptive regulation of feedforward nonlinear time‐delay systems by output feedback

The problem of global adaptive state regulation is investigated via output feedback for uncertain feedforward nonlinear time‐delay systems. Compared with existing results, our control schemes can be applicable to more general nonlinear time‐delay systems because of combining the low‐gain scaling approach with the backstepping method. In particular, we allow that there exist uncertain output function and uncertain growth rate imposed on nonlinear terms. Also, one considers a class of nonlinear systems with main‐axis delay. By the Lyapunov–Krasovskii theorem, delay‐independent controllers are proposed by constructing novel low‐gain observers driven by system input, to regulate the states of original system while all the closed‐loop signals are globally bounded. Furthermore, two examples are given to illustrate the usefulness of our results. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive output feedback regulation for a class of uncertain nonlinear systems

In this paper, the problem of global state regulation by output feedback is investigated for a class of uncertain nonlinear systems satisfying some relaxed upper‐triangular‐type condition. Using a linear dynamic gain observer with two dynamic gains and introducing two appropriate change of coordinates, we give a constructive design procedure for the linear‐like output feedback stabilizing controller. It is proved that the proposed controller globally regulates all the states of the uncertain system and maintains global boundedness of the closed‐loop system. An example is provided to demonstrate the effectiveness of the proposed design scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Recursive scaling design for robust global nonlinear stabilization via output feedback

This paper proposes a novel approach to robust backstepping for global stabilization of uncertain nonlinear systems via output feedback. The design procedure developed in this paper is based on the concept of state‐dependent scaling, which handles output‐feedback stabilization problems of strict‐feedback systems with various structures of uncertainties in a unified way. The proposed method is suitable for numerical computation. The theory of the method employs the Schur complements formula instead of Young's inequality and completing the squares. This paper shows a condition of allowable uncertainty size under which an uncertain system is globally stabilized by output feedback. A class of systems is shown to be always globally stabilizable for arbitrarily large nonlinear size of uncertainties. A recursive procedure of robust observer design for such a class of uncertain systems is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Global stabilization by output feedback: examples and counterexamples

We show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback. We show that a main obstruction is related to ‘unboundedness unobservability’. This is that some unmeasured state components may escape in finite time whereas the measurements remain bounded.     

A note on reduced order stabilizing output feedback controllers

In this paper we show that if a certain class of nonlinear systems is globally asymptotically stabilizable through an n-dimensional output feedback controller then it can be always stabilized through an (n − p)-dimensional output feedback controller, where p is the number of outputs and n is the dimension of the state space. This result gives an alternative construction of reduced order controllers for linear systems, and recovers in a more general framework the concept of dirty derivative, used in the framework of rigid and elastic joint robots, and gives an alternative procedure for designing reduced-order controllers for nonlinear systems considered in the existing literature.     

Output feedback model predictive control of uncertain norm‐bounded linear systems

A constrained output feedback model predictive control (MPC) scheme for uncertain Norm‐Bounded discrete‐time linear systems is presented. This scheme extends recent results achieved by the authors under full‐state availability to the more interesting case of incomplete and noisy state information. The design procedure consists of an off‐line step where a state feedback and an asymptotic observer (dynamic primal controller) are designed via bilinear matrix inequalities and used to robustly stabilize a suitably augmented state plant. The on‐line moving horizon procedure adds N free control moves to the action of the primal controller which are computed by solving a linear matrix inequality optimization problem whose numerical complexity grows up only linearly with the control horizon N. The effectiveness of the proposed MPC strategy is illustrated by a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

Output feedback control for a class of nonlinear systems

This paper studies the global stabilization problem by an output controller for a family of uncertain nonlinear systems satisfying some relaxed triangular-type conditions and with dynamics which may not be exactly known. Using a feedback domination design method, we explicitly construct a dynamic output compensator which globally stabilizes such an uncertain nonlinear system. The usefulness of our result is illustrated with an example.     

Global output feedback regulation of nonlinear time delay systems subject to sensor measurement faults

This article studied the global output feedback regulation problem for a class of uncertain nonlinear time delay systems subject to unknown measurement faults on sensors. Different from the existing works, we consider the unknown time‐varying delays on the system states and relax their conservative condition on nonlinear functions. By introducing two novel time‐varying gains, a new global output feedback regulation algorithm is proposed, which ensures control parameters can be chosen flexibly. The proposed linear‐like controller is independent of the unknown time‐varying delays. Moreover, it has a simple structure, which is convenient for the implementation in practice. Based on the Lyapunov stability theory, it is strictly proved that all signals of the resulting closed‐loop system are globally bounded with the designed controller. Finally, a simulation example is presented to illustrate the effectiveness of the proposed output feedback regulation algorithm.     

Output‐feedback stabilization for planar output‐constrained switched nonlinear systems

In this paper, globally asymptotical stabilization problem for a class of planar switched nonlinear systems with an output constraint via smooth output feedback is investigated. To prevent output constraint violation, a common tangent‐type barrier Lyapunov function (tan‐BLF) is developed. Adding a power integrator approach (APIA) is revamped to systematically design state‐feedback stabilizing control laws incorporating the common tan‐BLF. Then, based on the designed state‐feedback controllers and a constructed common nonlinear observer, smooth output‐feedback controllers, which can make the system output meet the predefined constraint during operation, are proposed to deal with the globally asymptotical stabilization problem of planar switched nonlinear systems under arbitrary switchings. A numerical example is employed to verify the proposed method.     

Robust output feedback stabilization via a small gain theorem

In this paper, we give sufficient conditions for designing robust globally stabilizing controllers for a class of uncertain systems, consisting of ‘nominal’ nonlinear minimum phase systems perturbed by uncertainties which may affect the equilibrium point of the nominal system (‘biased’ systems). The constructive proof combines a systematic step-by-step procedure, based on H_∞ arguments, with a small gain theorem, recently proved for nonliner systems. At each step, one finds two Lyapunov functions, one for a state-feedback problem and the other one for an output injection problem. Combining these two functions, one derives at each step a Lyapunov function candidate for solving an ouptut feedback stabilization problem. This approach allows one to put into a unified framework many existing results on robust output feedback stabilization. © 1998 John Wiley & Sons, Ltd.     

Global output regulation for output feedback systems with an uncertain exosystem and its application

This paper presents the solvability conditions for the global robust output regulation problem for a class of output feedback systems with an uncertain exosystem by using output feedback control. An adaptive control technique is used to handle the unknown parameter vector in the exosystem. It is shown that this unknown parameter vector can be exactly estimated asymptotically if a controller containing a minimal internal model is employed. The effectiveness of our approach has been illustrated by an asymptotic tracking problem of a generalized fourth‐order Lorenz system. Copyright © 2009 John Wiley & Sons, Ltd.     

Asymptotic regulation for distributed parameter systems via zero dynamics inverse design

In this paper, we introduce a new approach, zero dynamics inverse (ZDI) design, for designing a feedback compensation scheme achieving asymptotic regulation for a linear or nonlinear distributed parameter system in the case when the value w(t) at time t of the signal w to be tracked or rejected is a measured variable. Following the nonequilibrium formulation of output regulation, we formulate the problem of asymptotic regulation by requiring zero steady‐state error together with ultimate boundedness of the state of the system and the controller(s), with a bound determined by bounds on the norms of the initial data and w. Because a controller solving this problem depends only on a bound on the norm of w not on the particular choice of w, this formulation is in sharp contrast to both exact tracking, asymptotic tracking or dynamic inversion of a completely known trajectory and to output regulation with a known exosystem. The ZDI design consists of the interconnection, via a memoryless filter, of a stabilizing feedback compensator and a cascade controller, designed in a simple, universal way from the zero dynamics of the closed‐loop feedback system. This design philosophy is illustrated with a problem of asymptotic regulation for a boundary controlled viscous Burgers' equation, for which we prove that the ZDI is input‐to‐state stable. In infinite dimensions, however, input‐to‐state stable compactness arguments are supplanted by smoothing arguments to accommodate crucial technical details, including the global existence, uniqueness, and regularity of solutions to the interconnected systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Further results on global stabilization of uncertain nonlinear systems by output feedback

For a family of uncertain nonlinear systems dominated by a triangular system that satisfies linear growth condition with an output dependent growth rate, we prove that global robust stabilization can be achieved by smooth output feedback. This conclusion has incorporated and generalized the recent output feedback stabilization results, for instance, the work (IEEE Trans. Automat. Control 2002; 47 :2068–2073) where the same conclusion was already shown to be true for planar systems, and the work (Proceedings of the 42nd IEEE, CDC, 2003; 1544–1549) where the growth rate is required to be a polynomial function of the system output. There are two key ingredients in the present contribution. One of them is the introduction of a rescaling transformation with a dynamic factor that is tuned on‐line through a Riccati‐like differential equation, which turns out to be extremely effective in dealing with the system uncertainty. The other one is the development of a recursive observer design algorithm making it possible to assign the robust observer gains in a step‐by‐step fashion. Both a smooth state feedback controller and a robust observer are explicitly constructed for the rescaled system using only the knowledge of the bounding system. Copyright © 2005 John Wiley & Sons, Ltd.     

Stabilization of uncertain chained nonholonomic systems using adaptive output feedback

In this paper, adaptive output feedback control is presented to solve the stabilization problem of nonholonomic systems in chained form with strong nonlinear drifts and uncertain parameters using output signals only. The objective is to design adaptive nonlinear output feedback laws which can steer the closed‐loop systems to globally converge to the origin, while the estimated parameters remain bounded. The proposed systematic strategy combines input‐state scaling with backstepping technique. Motivated from a special case, adaptive output feedback controllers are proposed for a class of uncertain chained systems. The simulation results demonstrate the effectiveness of the proposed controllers. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Output feedback transient stabilization and voltage regulation of synchronous generators

In this brief note, we consider the transient stabilization and voltage regulation problem for a synchronous generator connected to an infinite bus. We show how a much simpler output feedback controller, compared with previous results, can be obtained if a different stability analysis is carried out: a suitable change of coordinates is performed so that advantageous triangularity properties of the regulation error dynamics are highlighted. A novel first order estimator for the uncertain mechanical input power is designed: it is the only adaptation scheme used by the controller. The innovative crucial step in the presented control design relies on relaxing the constraint imposed by the typically (previously) adopted back‐stepping techniques and constituted by the required availability of the regulation/tracking error variables: the converging estimate of the mechanical input power directly becomes the reference value for the electrical power and allows for the straightforward computation of the uncertain power angle constant value guaranteeing voltage regulation at steady state. Copyright © 2011 John Wiley & Sons, Ltd.     

Exponential passivity for output feedback stabilisation of nonlinear uncertain systems

In this article, we address the problem of stabilisation by output feedback for a class of uncertain systems. We consider uncertain systems with a nominal part which is affine in the control and an uncertain part which is norm bounded by a known function. We propose an output feedback such that the closed loop system is globally exponentially stable.     

Adaptive regulation of uncertain nonlinear systems by output feedback: A universal control approach

The problem of global state regulation via output feedback is investigated for uncertain nonlinear systems. The class of uncertain systems under consideration is assumed to be dominated by a bounding system which is linear growth in the unmeasurable states but can be a polynomial function of the system output, with unknown growth rates. To achieve global state regulation in the presence of parametric uncertainty, we propose a non-identifier based output feedback control scheme by employing the idea of universal control integrated with the design of a linear high-gain observer, whose gains are composed of two components, both of them are not constant and need to be dynamically updated. In particular, we explicitly design a universal output feedback controller which globally regulates all the states of the uncertain system while maintaining global boundedness of the closed-loop system.