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.     

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 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.     

PID control for global finite-time regulation of robotic manipulators

This paper addresses the global finite-time regulation problem of robotic manipulators. A simple nonlinear proportional-integral-derivative (PID) control is proposed by adding a nonlinear proportional and derivative term to the commonly used PID controller. Lyapunov's stability theory and geometric homogeneity technique are employed to prove global finite-time stability. Advantages of the proposed control include the absence of modelling information in the control law formulation and the global finite-time stability featuring fast transient and high-precision positioning. Explicit conditions on the controller parameters to ensure global finite-time regulation stability are obtained. Simulations are presented to demonstrate the effectiveness and the improved performances of the proposed approach.     

Local-homogeneity-based global continuous control for mechanical systems with constrained inputs: finite-time and exponential stabilisation

A global continuous control scheme for the finite-time or (local) exponential stabilisation of mechanical systems with constrained inputs is proposed. The approach is formally developed within the theoretical framework of local homogeneity. This has permitted to solve the formulated problem not only guaranteeing input saturation avoidance but also giving a wide range of design flexibility. The proposed scheme is characterised by a saturating-proportional-derivative type term with generalised saturating and locally homogeneous structure that permits multiple design choices on both aspects. The work includes a simulation implementation section where the veracity of the so-cited argument claiming that finite-time stabilisers are faster than asymptotical ones is studied. In particular, a way to carry out the design so as to, indeed, guarantee faster stabilisation through finite-time controllers (beyond their finite-time convergence) is shown.     

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.     

喷水推进型无人艇航向跟踪的反步自适应滑模控制*

针对单泵喷水推进型无人滑行艇的航向跟踪非线性系统,提出了一种反步自适应滑模控制方法。该系统由无人艇运动非线性响应模型和舵机伺服系统组成,并考虑运动响应模型的建模误差、外界干扰力等非匹配不确定性,利用全局微分同胚坐标变换将原系统变换为具有下三角特征的非线性系统。基于Backstepping方法和滑模控制理论,提出了一种自适应滑模控制律;利用Lyapunov函数,证明该控制律保证了航向跟踪系统的全局渐近稳定性。仿真对比结果验证了所提出控制器的有效性。     

一类机械臂系统自适应有限时间有界H∞跟踪控制

考虑一种电机驱动的单连杆机械臂系统在受到输出约束时的自适应有限时间H∞跟踪控制问题.一个有限时间有界H∞性能的新概念被提出,并结合障碍Lyapunov函数(BLF)、神经网络自适应技术、有限时间控制理论和H_∞控制理论,提出了一种该系统在输出受限条件下的自适应神经有限时间有界H_∞跟踪控制器设计方法,避免了许多有限时间控制文献中控制器设计时出现的奇点问题,实现了该机械臂系统的有限时间有界H_∞轨迹跟踪控制.所设计的控制器保证了系统跟踪误差能够被约束在预先给定的范围内,并且所有状态能在有限时间内收敛到平衡状态的邻域内,同时对外部扰动具有H_∞性能.仿真结果验证了所设计控制器的有效性和优越性.     

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.     

多自由度机械臂的饱和输出反馈有限时间同步位置控制EI北大核心CSCD

针对输入受限的多自由度机械臂高精度位置控制问题,本文充分考虑驱动器饱和非线性的影响,提出了多自由度机械臂输出反馈饱和有限时间比例–微分(PD)+同步位置控制策略,应用Lyapunov稳定性理论和几何齐次性技术证明了闭环系统的全局有限时间稳定性.非线性饱和函数的恰当引入,使得所提出的控制器具有清晰明确的上界,可以通过预先选择满足特定条件的控制器参数有效避免驱动器饱和问题;同步控制项的恰当引入,使得所提出的控制器兼顾了多自由度机械臂各轴间的同步协调性,从而获得更快的收敛速度和更好的系统整体性能,满足工程实际对机械臂的高精度要求.本文的数值仿真结果验证了所提出的控制方法的有效性和可行性.     

控制增益未知的船舶航向非线性自适应跟踪控制

针对参数不确定的船舶运动非线性控制系统控制方向未知的困难,将逆推算法与Nussbaum增益方法相结合,提出一种新的自适应非线性控制策略,从而实现船舶运动航向跟踪控制.首先,从理论上证明了所设计的自适应控制器保证最终的控制系数符号未知的参数不确定船舶运动非线性系统中所有信号一致有界,船舶的实际航向全局自适应地渐近跟踪期望的参考航向.对两条船舶数学模型的仿真实验结果表明,所设计的自适应非线性跟踪控制器具有良好的适应性及鲁棒性.     

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.     

基于自适应模糊滑模控制的船舶航向控制器设计

针对船舶运动系统中固有的非线性、模型不确定性和风、浪、流等的干扰.提出了自适应模糊滑模控制(AFSMC)策略解决船舶的航向控制问题.通过采用模糊逻辑系统逼近系统未知函数,将滑模控制技术与自适应模糊控制技术相结合,设计了船舶航向AFSMC控制器.在滑模边界层内应用PI (proportional-integral)控制代替滑模控制中的切换项,削弱了滑模控制带来的抖振现象.借助李亚普诺夫函数证明了船舶运动系统中的信号都一致有界并利用Barbalat引理证明了跟踪误差渐近收敛到零.在参数摄动和外界干扰情况下进行了航向保持与改变仿真试验,采用AFSMC控制器得到了与无摄动和无干扰情况下相似的输出响应.实验结果表明,所提控制器能有效地处理系统不确定性和外界干扰,控制性能良好,具有很强的鲁棒性.     

Buck型变换器自适应有限时间降压控制算法研究

针对负载未知情况下Buck型DC-DC变换器系统, 基于有限时间控制技术和自适应控制技术, 提出了一种新的快速降压控制算法.首先, 基于时间尺度变换, 对系统的平均状态空间方程进行变换; 然后, 利用饱和有限时间控制理论设计出一类新的快速降压控制算法, 以实现输出电压在有限时间内收敛到参考电压.由于控制器设计过程中考虑了饱和约束条件, 使得变换器的占空比函数满足0到1之间的约束条件.对于负载未知情况, 设计了有限时间观测器以估计未知负载, 最终得到自适应式的有限时间控制算法.与PI控制结果进行了仿真对比, 验证了所提出的控制算法既具有快速的调节性能, 又具有较强的抗负载变化性能.     

航向保持鲁棒最小二乘支持向量机控制

考虑到船舶航向控制中,存在的大量不确定因素及对控制系统的实时性要求,提出一种基于鲁棒最小二乘支持向量机(RLSSVM)的船舶航向保持控制方案.该控制策略充分利用最小二乘支持向量机良好的非线性映射能力、自学习适应能力和并行信息处理能力,并与H~2/H~∞鲁棒控制算法相结合,优势互补,形成闭环控制.仿真结果表明,该系统对海情的变化有良好的自适应能力,鲁棒性强,实现了航向保持精确控制.     

Adaptive control of system involving complex hysteretic nonlinearities: a generalised Prandtl–Ishlinskii modelling approach

In this article an adaptive control approach is proposed for a class of nonlinear systems preceded by unknown hysteretic nonlinearities, which is described by a generalised Prandtl–Ishlinskii (P-I) model. The main feature is that the generalised P-I hysteresis model is counted in the controller design without constructing a hysteresis inverse. The developed controller guarantees the global stability of the system and tracking a desired trajectory to a certain precision is achieved. The effectiveness of the proposed control approach is demonstrated through simulation example.     

输入饱和下的非线性积分系统的全局有限时间镇定

针对一类非线性积分系统, 利用有限时间控制技术, 提出了一种输入饱和情况下的全局有限时间控制方案. 首先, 基于有限时间 Lyapunov 稳定性理论, 设计镇定系统的全局有限时间递归控制器. 然后,将该递归控制器与饱和函数结合得到饱和控制器. 数学上严格证明了在该饱和控制器的作用下, 闭环系统满足全局有限时间稳定性. 仿真结果验证了该方法的有效性.     

基于预设性能的非仿射非线性系统自适应有限时间控制

针对一类具有死区的非仿射非线性系统,将预设性能控制与有限时间控制相结合,提出一种具有预设性能的自适应有限时间跟踪控制方法.基于Backstepping技术、模糊逻辑系统及有限时间Lyapunov稳定理论,给出使系统半全局实际有限时间稳定(semi-globally practically finite-time stable,SGPFS)的充分条件和设计步骤.该控制策略不仅使系统的输出误差在有限时间内收敛到一个预先设定区域,同时保证其收敛速度、最大超调量和稳态误差均满足预先设定的性能要求.最后通过仿真示例验证了所提出设计方法的有效性.     

基于输入输出线性化的自适应模糊滑模航迹控制

针对船舶直线航迹控制的非线性特性,设计一种基于输入输出线性化的自适应模糊滑模控制器,并利用Lyapunov理论,证明该系统在所设计控制器作用下全局渐近稳定,Simulink仿真结果表明,所设计控制器能够有效抑制常规滑模所固有的稳态抖振现象,且在参数摄动及风浪干扰下具有强鲁棒性,较好的实现了对设定航迹的跟踪。     

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.