Output‐feedback control strategies of lower‐triangular nonlinear nonholonomic systems in any prescribed finite time

In this paper, output‐feedback control strategies are proposed for lower‐triangular nonlinear nonholonomic systems in any prescribed finite time. Specifically, by employing the input‐state–scaling technique, the controlled systems are firstly converted into lower‐triangular nonlinear systems, which makes it possible to study such systems using the high‐gain technique. Then, by introducing a scaling of the state by a function that grows unbounded toward the terminal time and proposing a high‐gain observer–prescribed finite time recovering the system states, the output‐feedback regulation control problem in any prescribed finite time is firstly achieved for nonlinear nonholonomic systems with unknown constant incremental rate. Moreover, by designing another time‐varying high gain, the output‐feedback stabilization control problem in any prescribed finite time is then achieved for nonlinear nonholonomic systems with a time‐varying incremental rate. Finally, a numerical example is introduced to show the effectiveness of proposed control strategies.     

GLOBAL ROBUST SERVOMECHANISM OF A CLASS OF NONLINEAR SYSTEMS USING OUTPUT FEEDBACK

The robust servomechanism problem (alternatively, output regulation problem) of the class of nonlinear systems in lower triangular form has been extensively studied in recent years. The semi‐global solution was first given by either state feedback or output feedback. The global solution by state feedback was given very recently. However, the global solution by output feedback has long been an open problem. In this paper, we present a set of solvability conditions of the global robust servomechanism problem for this class of nonlinear systems by output feedback.     

Global output‐feedback stabilization for a class of stochastic nonlinear systems via sampled‐data control

In this paper, the global sampled‐data output‐feedback stabilization problem is considered for a class of stochastic nonlinear systems. First, based on output‐feedback domination technique and emulation approach, a systematic design procedure for sampled‐data output‐feedback controller is proposed for a class of stochastic lower‐triangular nonlinear systems. It is proved that the proposed sampled‐data output‐feedback controller will stabilize the given stochastic nonlinear system in the sense of mean square exponential stability. Because of the domination nature of the proposed control approach, it is shown that the proposed control approach can also be used to handle the global sampled‐data output‐feedback stabilization problems for a more general class of stochastic non‐triangular nonlinear systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

Global output feedback stabilisation of nonlinear systems with a unifying linear controller structure

We investigate the problem of global stabilisation by linear output feedback for a class of uncertain nonlinear systems with zero-dynamics. Compared with the previous works, new dilation-based assumptions are introduced that allow the system nonlinearities and its bounding functions to be coupled with all the states. The nonlinear systems of this paper can be considered as an extended form of some low triangular and feedforward systems. Dynamic gain scaling technique is applied to the controller design and stability analysis. It is proved that with a unifying linear controller structure and flexible adaptive laws for the observer gain, global stabilisation of the nonlinear systems can be achieved.     

Semiglobal stabilization of linearly uncontrollable and unobservable nonlinear systems via sampled‐data control

This article investigates the problem of using sampled‐data state/output feedback to semiglobally stabilize a class of uncertain nonlinear systems whose linearization around the origin is neither controllable nor observable. For any arbitrarily large bound of initial states, by employing homogeneous domination approach and a homogeneous version of Gronwall‐Bellman inequality, a sampled‐data state feedback controller with appropriate sampling period and scaling gain is constructed to semiglobally stabilize the system. In the case when not all states are available, a reduced‐order sampled‐data observer is constructed to provide estimates for the control law, which can guarantee semiglobal stability of the closed‐loop system with carefully selected sampling period and scaling gain.     

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.     

Global output feedback stabilization of upper‐triangular nonlinear systems using a homogeneous domination approach

This paper addresses the problem of global output feedback stabilization for a class of upper‐triangular systems with perturbing nonlinearities that are higher‐order in the unmeasurable states. A new design method based on the homogeneous domination approach and finite‐time stabilization technique is developed, which leads to global output feedback stabilizers for the upper‐triangular nonlinear systems under a homogeneous growth condition. A new perspective shown in this paper is that the finite‐time stabilization, in addition to its faster convergence rate, can also be utilized to handle control problems that were previously unresolved under asymptotic stabilization. Copyright © 2006 John Wiley & Sons, Ltd.     

Global output feedback sampled‐data stabilization for upper‐triangular nonlinear systems with improved maximum allowable transmission delay

This paper addresses the problem of output feedback sampled‐data stabilization for upper‐triangular nonlinear systems with improved maximum allowable transmission delay. A class of hybrid systems are firstly introduced. The transmission delay may be larger than the sampling period. Then, sufficient conditions are proposed to guarantee global exponential stability of the hybrid systems. Based on these sufficient conditions and a linear continuous‐discrete observer, an output feedback control law is presented to globally exponentially stabilize the feedforward nonlinear system. The improved maximum allowable transmission delay is also given. The results are also extended to output feedback sampled‐data stabilization for lower‐triangular nonlinear systems. Finally, illustrative examples are used to verify the effectiveness of the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Finite-time output feedback stabilisation for a class of feedforward nonlinear systems with input saturation

This paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.     

Global finite-time stabilization for a class of switched nonlinear systems via output feedback

This paper addresses the problem of global finite-time stabilization for a class of uncertain switched nonlinear systems via output feedback under arbitrary switchings. Based on the adding a power integrator approach, we design a homogeneous observer and controller for the nominal switched system without the perturbing nonlinearities. Then, a scaling gain is introduced into the proposed output feedback stabilizer to implement global finite-time stability of the closed-loop system. In addition, the proposed approach can be also extended to a class of switched nonlinear systems with upper-triangular growth condition. Two examples are given to illustrate the effectiveness of the proposed method.     

Global output feedback stabilisation for a class of upper triangular stochastic nonlinear systems

This paper investigates the problem of global output feedback stabilisation for a class of upper triangular stochastic nonlinear systems which are neither necessarily feedback linearisable nor affine in the control input. Based on the adding of a power integrator technique and homogeneous domination approach, an output feedback controller is explicitly constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability. A simulation example is provided to demonstrate the effectiveness of the design scheme.     

Global finite‐time stabilization for a class of high‐order switched nonlinear systems via sampled‐data control

This paper investigates the global finite‐time stabilization for a class of high‐order switched nonlinear systems via the sampled‐data output feedback control. Firstly, we design a continuous‐time output feedback controller for the nominal part via adding a power integrator technique. Based on the homogeneous theory, together with the Gronwall‐Bellman inequality, a sampled‐data output feedback controller is designed with suitable sampling periods to ensure that the closed‐loop system can be globally stabilized in finite time. In the meantime, the proposed control method can be extended to the switched nonlinear systems with an upper‐triangular growth condition. Finally, two examples are presented to illustrate the validity of the proposed control scheme.     

Global sampled-data output feedback control for a class of feedforward nonlinear systems

This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Output feedback control of large-scale nonlinear time-delay systems in lower triangular form

This paper is concerned with the stabilization problem for a class of large-scale nonlinear time-delay systems in lower triangular form. The uncertain nonlinearities are assumed to be bounded by continuous functions of the outputs or delayed outputs multiplied by unmeasured states or delayed states. An observer based output feedback control scheme is proposed using the dynamic gain control design approach. Based on Lyapunov stability theory, global asymptotic stability of the closed-loop control system is proved. Contrary to many existing control designs for lower triangular nonlinear systems, the celebrated backstepping method is not utilized here. An example is finally given to demonstrate the effectiveness of the proposed design procedure.     

Finite‐time output feedback stabilization of nonlinear high‐order feedforward systems

This paper considers the global finite‐time output feedback stabilization of a class of nonlinear high‐order feedforward systems. By using the homogeneous domination method together with adding a power integrator method and overcoming several troublesome obstacles in the design and analysis, a global finite‐time output feedback controller with reduced‐order observer is recursively designed to globally finite‐time stabilize nonlinear high‐order feedforward systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Semi‐Global Robust Output Regulation for A Class of Singular Nonlinear Systems with Unknown Algebraic Equations

This paper considers semi‐global robust output regulation problem for a class of singular nonlinear systems whose algebraic equations are not precisely known. Since the algebraic equations are not known, the output regulation problem of singular nonlinear systems cannot be solved by directly reducing the singular nonlinear system into a normal nonlinear system. Based on internal model principle, we convert the robust output regulation problem of singular nonlinear systems into a robust stabilization problem of an augmented singular nonlinear system. The augmented singular nonlinear system is also with unknown algebraic equations. However, without transforming the singular nonlinear system into a normal nonlinear system, it is shown that the augmented singular nonlinear system can be semi‐globally stabilized by a high gain output feedback control law under some reasonable assumptions. Moreover, the semi‐global stabilization control law of the augmented singular nonlinear systems also solves the semi‐global robust output regulation problem of the original singular nonlinear system.     

Semi‐Global Output Feedback Stabilization for a Class of Uncertain Nonlinear Systems

This paper addresses the problem of semi‐global stabilization by output feedback for a class of nonlinear systems whose output gains are unknown. For each subsystem, we first design a state compensator and use the compensator states to construct a control law to stabilize the nominal linear system without the perturbing nonlinearities. Then, combining the output feedback domination approach with block‐backstepping scheme, a series of homogeneous output feedback controllers are constructed recursively for each subsystem and the closed‐loop system is rendered semi‐globally asymptotically stable.     

Global finite-time output feedback stabilisation for a class of uncertain nontriangular nonlinear systems

This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.     

Robust output feedback stabilization of nonlinear systems with low‐order and high‐order nonlinearities

In this paper, we consider the problem of global output feedback stabilization for a class of nonlinear systems whose nonlinearities are assumed to be bounded by both low‐order and high‐order nonlinearities multiplied by a polynomial‐type output‐dependent growth rate. Instead of the previously proposed dual observer, based on the homogeneous domination approach, a new reduced‐order observer is constructed, which greatly simplifies the closed‐loop controller and is able to cover a more general class of nonlinear systems. Copyright © 2015 John Wiley & Sons, Ltd.