Global regulation for a class of stochastic high-order nonlinear systems with multiple unknown control directions

This paper concerns the global regulation for a class of stochastic high-order nonlinear systems which admit more general system form than the existing works. For details, except for the serious system nonlinearities which show that the considered systems are the generalisations of the strict-feedback systems, the most distinct feature of the systems is exhibited by the multiple unknown control directions, that is, all control coefficients of the virtual and actual control have unknown signs. By skillfully employing the Nussbaum function, and applying the method of adding a power integrator, an effective regulation control scheme is successfully provided for the considered systems. In particular, the presented controller can guarantee that all the closed-loop system states are bounded, and especially the original system states converge to the origin, both in the sense of probability one.     

Global stabilisation for a class of switched high-order stochastic nonlinear systems

This paper is devoted to the problem of global stabili sation for a class of switched high-order stochastic nonlinear systems under arbitrary switchings. By extending the adding -a -power -integrator technique and choosing an appropriate common Lyapunov function, a common state-feedback controller is explicitly constructed to render the closed-loop system globally asymptotically stable in probability. The effectiveness of the proposed approach is demonstrated by a simulation example.     

Global output regulation of a class of lower triangular nonlinear systems with unknown control direction via output feedback

In this paper, we study the global output regulation problem of a class of lower triangular systems under measurement output feedback. A novel high-gain filter is proposed to estimate the unmeasured states of the systems. Furthermore, we integrate the robust stabilisation technique and Nussbaumgain technique to achieve asymptotic regulation when the control direction is unknown. The simulation results illustrate the effectiveness of the proposed method.     

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.     

Global finite-time stabilisation for a class of stochastic high-order time-varying nonlinear systems

In this paper, the problem of global finite-time stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with time-varying nonlinearities. Based on the generalised stochastic Lyapunov theorem on finite-time stability, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed to guarantee that the closed-loop system is globally finite-time stable in probability. Finally, several simulation examples are provided to illustrate the effectiveness of the proposed method.     

Global finite-time output feedback stabilisation for a class of switched high-order nonlinear systems

This paper studies the problem of global finite-time output feedback stabilisation for a class of switched high-order nonlinear systems under arbitrary switchings. Based on adding one power integrator technique, we design a common homogeneous controller to guarantee finite-time stability of the closed-loop switched nonlinear system. An example is given to illustrate the effectiveness of the proposed control scheme.     

Global robust output regulation for a class of nonlinear systems

The problem of global robust output regulation is solved for a class of nonlinear systems driven by a linear neutrally stable exosystem. The proposed scheme makes use of a dynamic controller which processes information from the regulated error only. Robust regulation is achieved for every initial condition in the state space, and for all possible values of the uncertain parameter vector and the exogenous signal ranging over arbitrary compact sets. The regulator synthesis is based upon a recursive procedure, and takes advantage of both the special normal form of the plant equations and the passivity property of the internal model.     

Global finite-time stabilization for a class of high-order nonlinear systems with multiple unknown control directions

This paper considers the problem of the global finite-time stabilization for the high-order nonlinear systems with unknown control directions. Due to the uncertainty of control directions, the paper analyzes all possible conditions of the directions. The Lyapunov-based logic switching rule ensures that we can find the correct control directions. The adaptive switching controller with a switching parameter which is to be tuned online guarantees that the derivative of Lyapunov function is less than a negative definite function and the closed-loop system is globally finite-time stable. The effectiveness of the proposed method is illustrated by an example.     

Global decentralised stabilisation for a class of uncertain large-scale high-order upper-triangular nonlinear systems

This paper considers the global decentralised stabilisation problem for a class of uncertain large-scale high-order upper-triangular nonlinear systems. First, a local linear decentralised controller is recursively constructed based on the generalised homogeneous system theory and the adding a power integrator method. Second, aiming for global stabilisation, a series of nested saturation functions are integrated with the proposed local linear decentralised controller. Then, it is proved that the obtained decentralised saturated controller will render the whole closed-loop system globally asymptotically stable. Due to the flexibility of the generalised homogeneous method, the proposed control approach not only weakens the existing restrictions imposed on the interconnected nonlinearities, but also can be applied to a more general class of upper-triangular nonlinear systems. Furthermore, two simulations examples are conducted to show the effectiveness of the proposed control scheme.     

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.     

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.     

Global state feedback stabilisation for a class of high-order nonlinear systems with quantised input and state

In this paper, we aim at addressing the problem of global state feedback stabilisation for a class of high-order nonlinear systems with quantised input and state. The nonlinear functions of the system are bounded by both low-order and high-order terms multiplied by a polynomial-type incremental rate. With the combination of homogeneous domination approach and sector bound approach, a quantised controller computed from quantised state is constructed and a guideline is derived for selecting the parameters of the quantisers. Further, it is proved that, with the proposed scheme, the closed-loop system is globally asymptotically stable.     

Global robust output regulation of lower triangular systems with nonlinear exosystems and its application

This paper studies the global robust output regulation problem for lower triangular systems subject to nonlinear exosystems. By employing the internal model approach, this problem can be boiled down to a global robust stabilization problem of a time-varying nonlinear system in the cascade-connected form. Then, a set of sufficient conditions for the solvability of the problem is derived, and thus, leading to the solution to the global robust output regulation problem. An application of the main result of this paper is also proposed.     

Global stabilisation for a class of more general high-order time-delay nonlinear systems by output feedback

This paper addresses the problem of global stabilisation by output feedback for a class of high-order time-delay nonlinear systems with more general uncertainties, which cover both high-order and low-order nonlinearities. By introducing sign function and necessarily modifying the homogeneous domination approach, an output feedback controller is successfully constructed to guarantee the global asymptotic stability of the resulting closed-loop system. Due to the versatility of the homogeneous domination approach and homogeneous properties, the proposed method is also utilised to the control design of upper-triangular systems.     

Global output feedback stabilisation of high-order nonlinear systems with low-order and high-order nonlinearities

In this paper, we study the global output feedback stabilisation of a class of high-order nonlinear systems with more general low-order and high-order nonlinearities. By constructing the novel Lyapunov function and observer, based on the homogeneous domination theory together with adding a power integrator method, an output feedback controller is developed to guarantee the equilibrium of the closed-loop system globally uniformly asymptotically stable.     

Global stabilisation of high-order nonlinear systems with multiple time delays

This paper focuses on the stabilisation for a class of high-order nonlinear systems with multiple time delays. Growth restriction on system nonlinearities is further relaxed. Design procedures of a continuous controller are provided by the method of adding a power integrator, and the stability of the resulting closed-loop system is rigorously proven with the help of the elegant choice of a Lyapunov–Krasovskii functional. Finally, a simulation example is provided to demonstrate the validness of the proposed approach.     

一类高阶次随机非线性系统的输出反馈镇定

针对一类高阶次随机非线性系统,研究其输出反馈镇定问题．通过选择有效的观测器和李雅普诺夫函数,所设计的光滑输出反馈控制器保证了闭环系统的平衡点是依概率全局渐近稳定的,输出几乎处处调节到零．数值仿真验证了控制方案的有效性．     

Output-feedback control of a class of high-order stochastic nonlinear systems

This article investigates the problem of output-feedback stabilisation for a class of high-order stochastic non-linear systems in which the diffusion terms depend on unmeasurable states besides the output. By introducing a new rescaling transformation, adopting an effective observer and choosing the appropriate Lyapunov function, an output-feedback controller is constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, the output can be regulated to the origin almost surely, and the problem of inverse optimal stabilisation in probability is solved. The efficiency of the output-feedback controller is demonstrated by several simulation examples.     

Global state feedback stabilisation of stochastic high-order nonlinear systems with high-order and low-order nonlinearities

In this paper, the problem of global stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with both high-order and low-order nonlinearities, to which the existing control methods are inapplicable. Based on the generalised stochastic Lyapunov theorem, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed, which can guarantee the global asymptotic stability in probability of the resulting closed-loop system in the sense of weak solution, and also is able to lead to an interesting result of finite-time stabilisation under appropriate conditions. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.     

Robust output regulation for nonlinear systems with nonpolynomial nonlinearity under nonlinear exosystems

This paper studies a robust output regulation problem with nonlinear exosystems without the assumption that the solution to the regulator equations along the trajectory of the exosystems should be polynomial. Based on the extended concepts of steady-state generator and internal model, a set of sufficient conditions for the solvability of the problem are given. Thus, the result developed in this paper can allow the robust output regulation problem with nonlinear exosystems to accommodate much more general nonlinear given plants including those which contain nonpolynomial nonlinearity.