Finite-time observer-based output-feedback control for the global stabilisation of the PVTOL aircraft with bounded inputs

In this work, an output-feedback scheme for the global stabilisation of the planar vertical take-off and landing aircraft with bounded inputs is developed taking into account the positive nature of the thrust. The global stabilisation objective is proven to be achieved avoiding input saturation and by exclusively considering the system positions in the feedback. To cope with the lack of velocity measurements, the proposed algorithm involves a finite-time observer. The generalised versions of the involved finite-time stabilisers have not only permitted to solve the output-feedback stabilisation problem avoiding input saturation, but also provide additional flexibility in the control design that may be used in aid of performance improvements. With respect to previous approaches, the developed finite-time observer-based scheme guarantees the global stabilisation objective disregarding velocity measurements in a bounded input context. Simulation tests corroborate the analytical developments. The study includes further experimental results on an actual flying device.     

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 of high-order nonlinear systems: a dynamic gain-based approach

This paper deals with finite-time stabilisation problem for a class of high-order nonlinear systems. By generalising a dynamic gain design method and adding a power integrator technique, a new state feedback controller is constructed by choosing an appropriate Lyapunov function. It is proved that the corresponding closed-loop system is globally finite-time stable by the constructed controller, and the proposed method can accelerate the convergent speed and decrease the settling time. Finally, a simulation example is given to verify the effectiveness of the proposed scheme.     

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.     

Input–output finite-time stabilisation of nonlinear stochastic system with missing measurements

This paper considers the problem of the input–output finite-time stabilisation for a class of nonlinear stochastic system with state-dependent noise. The phenomenon of the missing measurements may occur when state signals are transmitted via communication networks. An estimating method is proposed to compensate the lost state information. And then, a compensator-based controller is designed to ensure the input–output finite-time stochastic stability (IO-FTSS) of the closed-loop system. Some parameters-dependent sufficient conditions are derived and the corresponding solving approach is given. Finally, numerical simulations are provided to demonstrate the feasibility and effectiveness of the developed IO-FTSS scheme.     

Adaptive finite-time control for a class of switched nonlinear systems using multiple Lyapunov functions

This paper investigates the problem of global adaptive finite-time stabilisation for a class of switched nonlinearly parameterised systems. Without requiring that each subsystem is globally adaptively finite-time stabilisable, a switched adaptive finite-time control scheme is developed by exploiting the multiple Lyapunov functions method and adding a power integrator technique. By using the parameter separation technique, the unknown parameters are separated from nonlinear functions. On the basis of finite-time Lyapunov stability theory, it is proved that the proposed controller can guarantee that the state of the resulting closed-loop system converges to the origin in finite time. Finally, an example is given to demonstrate the effectiveness of the proposed method.     

Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay

This paper is concerned with the problems of finite-time stability (FTS) and finite-time stabilisation for a class of nonlinear systems with time-varying delay, which can be represented by Takagi–Sugeno fuzzy system. Some new delay-dependent FTS conditions are provided and applied to the design problem of finite-time fuzzy controllers. First, based on an integral inequality and a fuzzy Lyapunov–Krasovskii functional, a delay-dependent FTS criterion is proposed for open-loop fuzzy system by introducing some free fuzzy weighting matrices, which are less conservative than other existing ones. Then, the parallel distributed compensation controller is designed to ensure FTS of the time-delay fuzzy system. Finally, an example is given to illustrate the effectiveness of the proposed design approach.     

Global finite-time stabilisation for a class of stochastic nonlinear systems by output feedback

In this paper, the problem of global finite-time stabilisation by output feedback is considered for a class of stochastic nonlinear systems. First, based on homogeneous systems theory and the adding a power integrator technique, a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system. Then, the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms; it is shown that the proposed output-feedback control law can guarantee that the closed-loop system is global finite-time stable in probability. Finally, simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme.     

Adaptive finite-time stabilisation of a class of high-order nonlinear systems with inverse dynamics

This paper investigates the adaptive finite-time stabilisation of a class of high-order nonlinear systems with inverse dynamics and time-varying control coefficients. Under the assumptions that the inverse dynamics of the subsystem are input-to-state stable , and nonlinear terms depend upon the inverse dynamics, the states and unknown parameters, we present a systematic design procedure for an adaptive finite-time state-feedback control law by using a recursive design approach. It is shown that under the proposed adaptive control law, the state of the closed-loop system is finite-time convergent. Two examples are provided to show the effectiveness of the proposed method.     

Modelling and finite-time stability analysis of psoriasis pathogenesis

A new systems model of psoriasis is presented and analysed from the perspective of control theory. Cytokines are treated as actuators to the plant model that govern the cell population under the reasonable assumption that cytokine dynamics are faster than the cell population dynamics. The analysis of various equilibria is undertaken based on singular perturbation theory. Finite-time stability and stabilisation have been studied in various engineering applications where the principal paradigm uses non-Lipschitz functions of the states. A comprehensive study of the finite-time stability properties of the proposed psoriasis dynamics is carried out. It is demonstrated that the dynamics are finite-time convergent to certain equilibrium points rather than asymptotically or exponentially convergent. This feature of finite-time convergence motivates the development of a modified version of the Michaelis–Menten function, frequently used in biology. This framework is used to model cytokines as fast finite-time actuators.     

Finite-time stabilisation for high-order nonlinear systems with low-order and high-order nonlinearities

This paper considers the finite-time stabilisation for a class of high-order nonlinear systems with both low-order and high-order nonlinearities. Based on the finite-time Lyapunov stability theorem together with the methods of dynamic gain control and adding one power integrator, a state feedback controller with gains being tuned online by two dynamic equations is proposed to guarantee the global finite-time stabilisation of the closed-loop system.     

Finite-time tracking control for robot manipulators with actuator saturation

This paper addresses the finite-time tracking of robot manipulators in the presence of actuator saturation. The commonly-used proportional-derivative (PD) plus dynamics compensation (PD+) scheme is extended by replacing the linear errors in the PD+ scheme with saturated non-smooth but continuous exponential-like ones. Advantages of the proposed controller include semi-global finite-time tracking stability featuring faster transient and high-precision performances and the ability to ensure that actuator constraints are not violated. This is accomplished by selecting control gains a priori, removing the possibility of actuator failure due to excessive torque input levels. Lyapunov's direct method and finite-time stability are employed to prove semi-global finite-time tracking. Simulations performed on a three degree-of-freedom (DOF) manipulator are provided to illustrate the effectiveness and the improved performance of the formulated algorithm.     

基于有限时间扰动观测器的无人水面艇精确航迹跟踪控制

针对复杂航行环境下的无人水面艇系统,提出一种基于有限时间扰动观测器的无人水面艇精确航迹跟踪控制策略.该控制方法具有以下显著特点:能够精确补偿未知海洋干扰,可实现精确跟踪控制;相比传统的渐近收敛控制算法,有限时间稳定性确保跟踪控制系统具有更快的收敛速度和更强的扰动抑制能力;能够同时确保扰动观测误差和航迹跟踪误差在有限时间内精确收敛到零.仿真结果验证了所提出控制方法的有效性和优越性.     

Finite-time H∞ control of periodic piecewise linear systems

In this paper, the finite-time stability, stabilisation, L₂-gain and H_∞ control problems for a class of continuous-time periodic piecewise linear systems are addressed. By employing a time-varying control scheme in which the time interval of each subsystem constitutes a number of basic time segments, the finite-time controllers can be developed with periodically time-varying control gains. Based on a piecewise time-varying Lyapunov-like function, a sufficient condition of finite-time stability and the relevant time-varying controller are proposed. Considering the finite-time boundedness of the closed-loop periodic system, the L₂-gain criterion with continuous time-varying Lyapunov-like matrix function is studied. A finite-time H_∞ controller is proposed based on the L₂-gain analysis. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed criteria.     

Finite-time output feedback control for a class of stochastic low-order nonlinear systems

This paper discusses the problem of finite-time stabilisation for a class of stochastic low-order nonlinear systems via output feedback. By generalising the adding a power integrator technique, constructing an implementable reduced-order observer and using the stochastic finite-time stability criterion, a finite-time output feedback controller is presented to guarantee that the closed-loop system is finite-time stable in probability. A simulation example is provided to verify the effectiveness of the proposed design method.     

Finite-time stabilisation of a class of switched nonlinear systems with state constraints

This paper investigates the finite-time stabilisation for a class of switched nonlinear systems with state constraints. Some power orders of the system are allowed to be ratios of positive even integers over odd integers. A Barrier Lyapunov function is introduced to guarantee that the state constraint is not violated at any time. Using the convex combination method and a recursive design approach, a state-dependent switching law and state feedback controllers of individual subsystems are constructed such that the closed-loop system is finite-time stable without violation of the state constraint. Two examples are provided to show the effectiveness of the proposed method.     

Finite-time boundedness and stabilisation of networked control systems with bounded packet dropout

In this paper, the finite-time boundedness and stabilisation problems of a class of networked control systems (NCSs) with bounded packet dropout are investigated. The main results provided in the paper are sufficient conditions for finite-time boundedness and stability via state feedback. An iterative approach is proposed to model NCSs with bounded packet dropout as jump linear systems (JLSs). Based on Lyapunov stability theory and JLSs theory, the sufficient conditions for finite-time boundedness and stabilisation of the underlying systems are derived via linear matrix inequalities (LMIs) formulation. Moreover, both sensor-to-controller and controller-to-actuator packet dropouts are considered simultaneously. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.     

Global finite-time stabilisation of a class of switched nonlinear systems

This paper is concerned with the global finite-time stabilisation problem for a class of switched nonlinear systems under arbitrary switchings. All subsystems of the studied switched system under consideration are in lower triangular form. Based on the adding one power integrator technique, both a class of non-Lipschitz continuous state feedback controllers and a common Lyapunov function are simultaneously constructed such that the closed-loop switched system is global finite-time stable under arbitrary switchings. In the controller design process, a common coordinate transformation of all subsystems is exploited to avoid using individual coordinate transformations for subsystems. Finally, two examples are given to show the effectiveness of the proposed method.     

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.     

基于单向耦合法的不确定复杂网络间有限时间同步

针对具有不确定性的复杂网络有限时间同步问题, 提出一种新颖的单向耦合控制方法. 构建含有未知参量及未知拓扑结构的驱动?响应复杂网络模型, 考虑两个网络具有不同的节点数, 同时受到时变耦合时滞的影响, 并且网络内部分别具有不同的节点系统. 基于有限时间稳定性理论和线性矩阵不等式变换, 通过在响应网络中引入单向耦合项, 实现两个网络间的有限时间同步, 同时准确辨识未知参量及未知拓扑结构. 仿真实验验证所提同步方法的有效性, 对比实验结果表明所提方法在减少耦合数量的同时具有更快的同步速率及更小的波动范围.