Global decentralised stabilisation for a class of uncertain large-scale feedforward nonlinear systems

In this paper, the problem of global decentralised stabilisation for a class of uncertain large-scale feedforward nonlinear systems is investigated. The system under consideration is allowed to contain unknown non-Lipschitz continuous nonlinear terms. The design of the global decentralised controllers takes a two steps procedure. First of all, based on the adding a power integrator technique and the homogeneous domination approach a local homogeneous decentralised controller is proposed for each subsystem of the large-scale feedforward nonlinear system. Then, we integrate a series of nested saturation functions with the homogeneous decentralised controllers and adjust the saturation levels to ensure globally asymptotic stability of the closed-loop system. Simulation studies are conducted to illustrate the effectiveness of the proposed control method.     

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.     

Decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems

Under the weaker conditions on the drift and diffusion terms, this paper focuses on the global decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems. By introducing an appropriate coordinate transformation, the original system is transformed into an equivalent one with tunable gain. After that, by reasonably combing the homogeneous domination approach with stochastic nonlinear systems stability criterion, and skillfully choosing the low gain scale, the decentralised output-feedback controller is constructed for each subsystem to ensure that the closed-loop system is globally asymptotically stable in probability. The simulation example is given to demonstrate the effectiveness of the proposed design scheme.     

Homogeneity with incremental degrees and global stabilisation of a class of high-order upper-triangular systems

The problem of global asymptotic stabilisation is investigated for a class of upper-triangular systems with uncontrollable linearisation. A notion of generalised homogeneity is introduced in this article, providing a new insight and a deeper perspective on how to categorise nonlinear terms into the higher-order and equal-order terms in a non-traditional way. The delicate analysis and new categorisation of the vector field make it possible to encompass more general nonlinearities. A globally stabilising controller is recursively constructed by a bottom-up, step-by-step procedure, containing the equal-order terms as its indispensable components. It is illustrated that the results obtained in this article incorporate and extend existing results for the global stabilisation of upper-triangular systems.     

Global stabilisation of a class of generalised cascaded systems by homogeneous method

This paper considers the problem of global stabilisation of a class of generalised cascaded systems. By using the extended adding a power integrator technique, a global controller is first constructed for the driving subsystem. Then based on the homogeneous properties and polynomial assumption, it is shown that the stabilisation of the driving subsystem implies the stabilisation of the overall cascaded system. Meanwhile, by properly choosing some control parameters, the global finite-time stability of the closed-loop cascaded system is also established. The proposed control method has several new features. First, the nonlinear cascaded systems considered in the paper are more general than the conventional ones, since the powers in the nominal part of the driving subsystem are not required to be restricted to ratios of positive odd numbers. Second, the proposed method has some flexible parameters which provide the possibility for designing continuously differentiable controllers for cascaded systems, while the existing designed controllers for such kind of cascaded systems are only continuous. Third, the homogenous and polynomial conditions adopted for the driven subsystem are easier to verify when compared with the matching conditions that are widely used previously. Furthermore, the efficiency of the proposed control method is validated by its application to finite-time tracking control of non-holonomic wheeled mobile robot.     

一类上三角随机非线性系统的输出反馈控制

针对一类上三角随机非线性系统的输出反馈控制问题,首先利用反推技术,为其对应的标称系统设计稳定的输出反馈控制器;然后利用低增益齐次占优技术,为整个系统设计输出反馈控制器.所设计的控制器能保证闭环系统的平衡点为依概率全局渐近稳定的,并将低增益齐次占优技术推广到了随机系统,首次解决了一类上三角随机系统的镇定问题.最后通过数值仿真验证了所提出控制方案的有效性.     

Reduced-order observer-based decentralised control of non-linear interconnected systems

The output feedback-based asymptotic stabilisation problem for a class of non-linear interconnected systems is considered, where the non-linear interconnections between subsystems satisfy quadratic constraints. A novel decentralised dynamic output feedback control strategy involving local projection operator-based reduced-order observers is proposed. This decentralised controller is characterised by the separation property. Two easily verifiable conditions that guarantee the asymptotic stability of the closed-loop system driven by the proposed decentralised controller are given. The effectiveness of the developed decentralised control strategy is illustrated with a numerical example and simulations.     

Global sliding mode with fractional operators and application to control robot manipulators

In this paper, a novel fractional-order global sliding-mode control scheme is presented. It is first used to stabilise a coupled second-order nonlinear system, and then it is generalised to control a class of multi-input and multi-output nonlinear systems with the model uncertainties and external disturbances. The proposed sliding manifold, which will converge to the origin in finite time by utilising a classical quadratic Lyapunov function, ensures global stabilisation of the system and the reduction of the chattering phenomenon during the control processes. Based on input-to-state stability and Lyapunov's stability theorem, the closed-loop system can be globally uniformly asymptotically stabilised to the origin in the future time. Some results about the control and stabilisation of integer-order nonlinear systems, when the fractional-order sliding-mode controller is used, are illustrated in this paper. Finally, an application to two-degree of freedom polar robot manipulator is provided to show the validity and feasibility of the proposed method.     

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 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.     

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 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 output feedback stabilisation of nonlinear time-delay systems with unknown output function

This paper studies the problem of global output feedback stabilisation for a class of nonlinear time-delay systems with the unknown output function. By constructing the appropriate Lyapunov–Krasovskii functional and observer, skillfully combining generalised adding a power integrator technique, sign function and homogeneous domination approach, an output feedback controller is designed to guarantee globally uniformly asymptotical stability of nonlinear time-delay systems with the unknown output function.     

Global finite-time control for a class of switched nonlinear systems with different powers via output feedback

This paper is concerned with the problem of global finite-time control for switched nonlinear systems whose nonlinear terms satisfy homogenous growth conditions. At first, we design homogenous output feedback controllers for nominal switched nonlinear systems by adding a power integrator method. Then, we employ the homogeneous domination approach to scale homogeneous observers and controllers to render switched nonlinear systems with lower-triangular homogenous growth condition globally finite-time stable. Finally, the proposed control method can be extended to switched nonlinear systems satisfying with upper-triangular homogeneous growth condition. Two examples are provided to demonstrate the effectiveness of the proposed control scheme.     

Decentralised adaptive output feedback stabilisation for stochastic time-delay systems via LaSalle-Yoshizawa-type theorem

This paper deals with the decentralised output feedback stabilisation problem for a class of large-scale stochastic time-delay nonlinear systems. A general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time-delay systems. In addition, a stochastic version of the well-known LaSalle-Yoshizawa theorem with time-varying delay is initially proposed for the controller design and stability analysis. Then, for a class of large-scale stochastic systems with time-varying delays, totally decentralised adaptive delay-dependent controllers are designed by using K-filter and backstepping approach. Via LaSalle-Yoshizawa-type theorem and constructing a general Lyapunov function, it is shown that all signals in the closed-loop system are bounded almost surely and the solution is almost surely asymptotically stable. Finally, a simulation example is given to illustrate the effectiveness of the results of this paper.     

Global adaptive exponential stabilisation for nonlinear systems with multiple unknown control directions

In this paper, we address the global generalised exponential stabilisation problem for a class of lower-triangular systems with multiple unknown directions. Instead of the well-known Nussbaum-gain adaptive rule, a Lyapunov-based adaptive logic switching rule is proposed to seek the correct control directions for such systems. The main advantage of the proposed controller is that it can guarantee the global generalised exponential stability of closed-loop systems. Simulation examples are given to verify the effectiveness of the developed control approach.     

Global sampled-data output feedback stabilisation for a class of nonlinear systems with unknown output function

This paper discusses the problem of global sampled-data output feedback stabilisation for a class of nonlinear systems whose output function is unknown. A systematic design scheme is developed to construct a linear output feedback control law in sampled-data form. An explicit formula for the maximum allowable sampling period is computed to guarantee global stability of the uncertain nonlinear systems under the proposed controller with appropriate gains. Two examples are given to demonstrate the effectiveness of the proposed design procedure.     

Continuous global stabilisation of high-order time-delay nonlinear systems++

This paper studies the global stabilisation problem for a class of high-order nonlinear systems with multiple time delays. A distinct property of the systems to be investigated is that powers on the upper bound restrictions of nonlinearities are allowed to take values on a continuous interval. By introducing the sign functions and using the generalised method of adding a power integrator, this paper successfully designs a continuous global state-feedback controller independent of time delays. Moreover, a novel Lyapunov–Krasovskii functional is constructed to prove the globally asymptotic stability of the resulting closed-loop system.     

Delay-dependent H∞ robust control for large power systems based on two-level hierarchical decentralised coordinated control structure

This article focuses on a novel two-level hierarchical decentralised coordinated control which consists of several local fuzzy power system stabilisers (LFPSSs) for each generator at the first level tuned by supervisory power system stabiliser (SPSS) at the secondary level for the transient stabilisation improvement of large power systems. First, in order to compensate the inherent nonlinear interconnections between subsystems in system dynamic model, a direct feedback linearisation compensator is proposed to act through the local excitation machine. Afterwards, the T–S fuzzy model-based decentralised LFPSS for each generator is designed. Then, for the purpose of improving dynamic performance, the SPSS is designed by using the remote signals from the wide area measurements system. However, there are unavoidable delays involved before the remote signals are received at the SPSS site or the control signals of SPSS are sent to the local systems. Taking consideration of the multiple delays, by using less conservative delay-dependent Lyapunov approach, the authors develop a delay-dependent H_∞ robust control technique based on the decentralised coordinated control structure. Some sufficient conditions for the system stabilisation are presented in terms of linear matrix inequalities dependent only on the upper bounds of the time delays. Finally, the effectiveness of the proposed control scheme is demonstrated through simulation examples.