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.     

Design of finite-time H∞ controller for uncertain nonlinear systems and its application

This paper studies the problem of finite-time H _∞ control for strict feedback nonlinear systems with external disturbance. The finite-time stability theory, H _∞ control method, backstepping technique, together with adding a power integrator tool are combined to design a finite-time H _∞ state feedback controller. The obtained controller can make the closed-loop system finite-time convergent, and the influence of the external disturbance is attenuated to a given degree. Two numerical examples are presented to show the effectiveness and feasibility of the proposed method. Meanwhile, the proposed method is also applied to robot manipulators.     

一类线性离散时间系统有限时间控制问题

讨论一类具有时变、有限能量外部扰动的线性离散时间系统的有限时间控制问题.首先研究问题可解的充分条件,并讨论了状态反馈控制器存在的条件,这些条件可归结为基于线性矩阵不等式(LMI)的可解性问题;然后给出状态反馈控制器和输出反馈控制器的具体设计;最后通过仿真验证了该方案的有效性.     

Finite-time sliding surface constrained control for a robot manipulator with an unknown deadzone and disturbance

This paper presents finite-time sliding mode control (FSMC) with predefined constraints for the tracking error and sliding surface in order to obtain robust positioning of a robot manipulator with input nonlinearity due to an unknown deadzone and external disturbance. An assumed model feedforward FSMC was designed to avoid tedious identification procedures for the manipulator parameters and to obtain a fast response time. Two constraint switching control functions based on the tracking error and finite-time sliding surface were added to the FSMC to guarantee the predefined tracking performance despite the presence of an unknown deadzone and disturbance. The tracking error due to the deadzone and disturbance can be suppressed within the predefined error boundary simply by tuning the gain value of the constraint switching function and without the addition of an extra compensator. Therefore, the designed constraint controller has a simpler structure than conventional transformed error constraint methods and the sliding surface constraint scheme can also indirectly guarantee the tracking error constraint while being more stable than the tracking error constraint control. A simulation and experiment were performed on an articulated robot manipulator to validate the proposed control schemes.     

Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control

In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method.     

Continuous finite-time control for robotic manipulators with terminal sliding mode

A continuous finite-time control scheme for rigid robotic manipulators is proposed using a new form of terminal sliding modes. The robustness of the controller is established using the Lyapunov stability theory. Theoretical analysis and simulation results show that faster and high-precision tracking performance is obtained compared with the conventional continuous sliding mode control method.     

Finite-time control with H-infinity constraints of linear time-invariant and time-varying systems

This paper presents finite-time control methods with H-infinity constraints for linear time-invariant (LTI) and time-varying (LTV) systems. The basic idea of the proposed approaches is to construct controllers for the LTI and LTV in such a way that a constant quadratic Lyapunov function and a time-varying quadratic Lyapunov function can be used to establish the finite-time stability and the H-infinity performance of the resulting closed-loop systems. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities (LMIs) and Differential Riccati Inequalities (DRIs) that are numerically feasible with commercially available software. Finally, the results are illustrated by application to the design of guidance law for a class of terminal guidance system.     

Finite-time robust stochastic stability of uncertain stochastic delayed reaction-diffusion genetic regulatory networks

This paper is concerned with the problem of finite-time stability analysis for uncertain stochastic delayed reaction-diffusion genetic regulatory networks. The parameter uncertainties are assumed to be norm-bounded, and the time delays are assumed to be time-varying. Based on the Lyapunov functional method, sufficient conditions ensuring the networks to be finite-time robustly stochastically stable are established. When there are no norm-bounded parameter uncertainties in the networks, a finite-time stochastic stability condition is also established. All the conditions are diffusion-dependent as well as delay-dependent. Numerical examples are given to illustrate the effectiveness of the proposed results.     

复杂热源下不可逆诺维科夫热机最大功率输出

考虑实际热机工作下的旁通热漏和内部耗散等不可逆因素,建立了包括连续均匀分布、三角形分布、二次分布和帕累托分布等四种不同的统计概率分布高温热源温度下的广义不可逆诺维科夫热机模型,导出了热机最大输出功率及相应的热效率和熵产率随高温热源温度、内部不可逆性等因素变化的关系式。结果表明：热漏和内部耗散分别对热机性能有着不同的影响,热漏使统计热源温度分布下最大功率输出对应的热效率减小,同时也增大了熵产率,但对热机的最大功率输出无影响;内部耗散不可逆性使热机的最大输出功率及相应热效率均明显减小,但使熵产率先增大后减小;熵产率随高温热源温度的标准差增大而减小。研究结果对太阳能发电厂性能提升具有一定理论指导意义。     

Step-size sequence design for finite-time average consensus in secure wireless sensor networks

This paper concerns the study of average consensus in wireless sensor networks with aim of providing a way to reach consensus in a finite number of steps. In particular, we investigate the design of consensus protocols when, for security reasons for instance, the underlying graph is constrained to be strongly regular or distance regular. The proposed design method is based on parameters of the intersection array characterizing the underlying graph. With this protocol, at execution time, average consensus is achieved in a number of steps equal to the diameter of the graph, i.e. the smallest possible number of steps to achieve consensus.