Nonsmooth finite-time control of uncertain second-order nonlinear systems

Nonsmooth finite-time stabilizing control laws have been developed for the double integrator system. The objective of this paper is to further explore the finite-time tracking control problem of a general form of uncertain second-order affine nonlinear system with the new forms of terminal sliding mode (TSM). Discontinuous and continuous finite-time controllers are also developed respectively without the singularity problem. Complete robustness can be acquired with the former, and enhanced robustness compared with the conventional boundary layer method can be expressed as explicit bounded function with the latter. Simulation results on the stabilizing and tracking problems are presented to demonstrate the effectiveness of the control algorithms.     

Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance

In this paper, a new approach is presented for finite-time control problems for linear systems subject to time-varying parametric uncertainties and exogenous disturbance. The disturbance is assumed to be time varying and bounded. Sufficient conditions are obtained for the existence of a linear parameter-dependent state feedback gain, which can ensure that the closed-loop system is finite-time bounded （FTB）. The conditions can be reduced to feasibility problems involving LMIs. Numerical examples show the validity of the proposed methodology.     

Particle swarm optimization for time-optimal control design

In this paper,a particle swarm optimization(PSO)based method is proposed to obtain the time-optimal bang-bang control law for both linear and nonlinear systems.By introducing a penalty function,the method can be modified to deal with systems with constraints.Compared with existing computational methods,the proposed method can be implemented in a straightforward manner.The convergent solutions can be achieved by selecting suitable PSO parameters regardless of the initial guess of the switching times.A double integrator and a third-order nonlinear system are used to demonstrate the effectiveness and robustness of the proposed method.The method is applied to obtain the time-optimal control law for a high performance linear motion positioning system.The results show the practicality of the proposed algorithm.     

具有干扰输入的不确定奇异系统的有限时间控制器设计

The concept of finite-time stability for linear singular system isinduced in this paper. Finite-time control problem is considered for linear singular systems with time-varying parametricuncertainties and exogenous disturbances. The disturbance satisfies a dynamical system with parametric uncertainties. Asufficient condition is presented for robust finite-ime stabilization via state feedback. The condition is translated to a feasibility problem involving restricted linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, an example is given to show the validity of the results.     

Leader-following consensus for uncertain second-order nonlinear multi-agent systems

This paper studies the leader-following consensus problem for a class of second-order nonlinear multi-agent systems subject to linearly parameterized uncertainty and disturbance. The problem is solved by integrating the adaptive control technique and the adaptive distributed observer method. The design procedure is illustrated by an example with a group of Van der Pol oscillators as the followers and a harmonic system as the leader.     

A nonsmooth IMC method for mechanical systems with backlash

This paper proposes a discrete-time nonsmooth internal model control （NSIMC） approach for mechanical transmission systems described by so-called sandwich system with backlash. In this method, a dynamic compensator is introduced to compensate for the effect of the input linear subsystem. Thus, the sandwich systems with backlash can be simplified as a pseudo-Hammerstein system with backlash. The corresponding NSIMC strategy is designed to control this system. The design procedure of the controller is presented based on the analysis on the robust stability by considering the model errors involved with the effect of backlash as well as the compensated error of the input linear subsystem. Moreover, as the model is switched among the different operating zones, the robust filters are proposed to guarantee the robust stability and satisfactory control performance of the system.     

Output regulation of nonaffine nonlinear systems using singular perturbation theory

A control synthesis method for output regulation based on singular perturbation theory combined with inverting design is considered for a class of nonaffine nonlinear systems. The resulting control signal is defined as a solution to ＂fast＂ dynamics which inverts a series error model, whose state is exponentially stable. It is shown that, under sufficient conditions being consistent with the assumptions of singular perturbation theory, this problem is solvable with （ε） tracking error if and only if a set of first-order nonlinear partial differential equations are solvable. The control law can be easily constructed and the simulations show the feasibility and effectiveness of the controller.     

未知相对度非线性系统的一阶D型迭代学习控制

The classical D-type iterative learning control law depends crucially on the relative degree of the controlled system, high order differential iterative learning law must be taken for systems with high order relative degree. It is very difficult to ascertain the relative degree of the controlled system for uncertain nonlinear systems. A first-order D-type iterative learning control design method is presented for a class of nonlinear systems with unknown relative degree based on dummy model in this paper. A dummy model with relative degree 1 is constructed for a class of nonlinear systems with unknown relative degree. A first-order D-type iterative learning control law is designed based on the dummy model, so that the dummy model can track the desired trajectory perfectly, and the controlled system can track the desired trajectory within a certain error. The simulation example demonstrates the feasibility and effectiveness of the presented method.     

Control of systems with sector-bounded nonlinearities: robust stability and command effort minimization by disturbance rejection

The paper shows that a control strategy with disturbance rejection is able to reduce the control effort to a minimum, ensuring at the same time a desired performance level. The disturbance to be rejected is completely unknown, except for a sectorial bound. The control unit is endowed with an extended state observer which includes a disturbance dynamics, whose state tracks the unknown disturbance to be rejected. In summary, the novel contributions of the paper are the following. First, we derive a robust stability condition for the proposed control scheme, holding for all the nonlinearities that are bounded by a known (or estimated) maximum slope. Second, we propose a novel approach for designing the observer and state feedback gains, which guarantee robust closed-loop stability. Third, we show that the designed control system yields, with a minimum control effort, the same control performance as a robust state feedback control, which on the contrary may require a larger command activity. Two simulated case studies are presented to show the effectiveness of the proposed approach.     

一类带有传感器故障的混合系统的容错控制

A model-based fault tolerant control approach for hybrid linear dynamic systems is proposed in this paper. The proposed method, taking advantage of reliable control, can maintain the performance of the faulty system during the time delay of fault detection and diagnosis (FDD) and fault accommodation (FA), which can be regarded as the first line of defence against sensor faults. Simulation results of a three-tank system with sensor fault are given to show the efficiency of the method.     

机械系统的快速有限时间跟踪控制及其在航天器交会中的应用

针对一类具有匹配干扰的二阶机械系统,本文研究了快速有限时间跟踪控制问题.结合有限时间反步法和非奇异快速终端滑模,本文提出了一种新的快速有限时间控制律,并给出了控制器参数所需满足的充分条件以保证系统的快速有限时间稳定性.进一步地,在一定情形下,所设计的快速有限时间控制律能够退化为经典的反步法、有限时间控制律和非奇异快速终端滑模控制律.最终,将所设计的控制律应用于航天器交会系统,数值仿真结果验证了所提方法的有效性.     

考虑扰动与输入饱和的机械臂连续非奇异快速终端滑模控制

针对机械臂控制过程中由于扰动与输入饱和造成的控制精度低的问题,提出一种连续非奇异快速终端滑模控制算法.首先,针对输入饱和问题,设计饱和补偿系统以消除输入饱和特性;其次,为避免滑模控制的抖振问题,设计二阶模型不确定与扰动估计器(UDE)对扰动项进行估计;同时,为进一步提高控制精度,采用自适应方法对扰动估计误差进行控制;在此基础上,设计基于二阶模型不确定与扰动估计器及输入饱和补偿的自适应连续非奇异快速终端滑模控制算法,并采用Lyapunov函数证明该算法的有限时间收敛特性;最后,以3自由度并联机械臂为控制对象进行仿真,并开展算法对比研究.仿真结果表明,该方法可以实现考虑扰动与输入饱和时的机械臂高精度有限时间轨迹跟踪控制.     

输入饱和的充液航天器抗干扰有限时间滑模控制

研究三轴稳定充液航天器姿态控制过程中存在外部未知干扰、参数不确定和输入饱和的问题,提出一种抗干扰有限时间滑模控制的姿态机动控制方法.将部分充液贮箱内液体燃料晃动等效为球摆模型,采用动量矩守恒定律推导出充液航天器耦合动力学方程.首先,设计有限时间积分滑模干扰观测器,保证控制系统中集总干扰可以在有限时间内被估计;然后,基于所设计的干扰观测器,提出一种抗干扰有限时间快速终端滑模控制策略,并且证明在该控制律的作用下闭环系统的状态是有限时间稳定的,而且收敛到指定的快速终端滑模面上.此外,通过引入辅助变量补偿控制输入超调量,克服输入饱和的约束.仿真结果验证了该控制策略的有效性和鲁棒性.     

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein–Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.     

一类不确定非线性系统的全局鲁棒有限时间镇定

对一类不确定非线性系统提出了一种连续的全局鲁棒有限时间控制律．首先,针对标称系统设计出了一种状态反馈控制律,应用Lyapunov直接稳定性理论和Lasalle不变性原理证明了闭环标称系统的全局渐近稳定性,同时具有负的齐次度;其次,引入辅助变量和采用有限时间收敛的二阶滑模Super—twisting算法,设计出了对不确定性和干扰进行抑制的补偿控制项,并根据有限时间Lyapunov函数给出了补偿控制项参数的取值范围;最后,综合得到一种连续的使实际闭环系统有限时间收敛到平衡点的鲁棒镇定控制律．仿真结果表明了所提控制律的有效性．     

Nonsingular terminal sliding mode based finite-time control for spacecraft attitude tracking

This paper studies finite-time attitude tracking control problem of a rigid spacecraft system with external disturbances and inertia uncertainties. Firstly, a new finite-time attitude tracking control law is designed using nonsingular terminal sliding mode concepts. In the absence and presence of external disturbances and inertia uncertainties, this controller can drive the attitude and angular velocity tracking errors to reach zero in finite time. Secondly, a finite-time disturbance observer is introduced to estimate the disturbance, and a composite controller is developed which consists of a feedback control based on nonsingular terminal sliding mode method and compensation term based on finite-time disturbance observer. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system is ensured by the Lyapunov approach. Numerical simulations on attitude control of spacecraft are also given to demonstrate the performance of the proposed controllers.     

Nonlinear feedback design for fixed-time tracking of a class of nonlinear systems

Fixed-time control is more preferable than finite-time control in practical applications since the settling time is independent of the system initial condition in a fixed-time control problem. Moreover, systems in real world usually suffer from unfavourable factors, such as unknown control coefficients and external disturbance. In this paper, we consider the fixed-time tracking control for a class of nonlinear systems by considering the aforementioned two points. A strategy for specifying the control input is established by the method of adding a power integrator. The designed control law guarantees that the reference signal can be followed in a fixed time. As an application, the bank-to-turn missile system is used to show the efficiency of the proposed fixed-time tracking scheme.     

带有不匹配干扰的二阶多自主体系统有限时间包容控制

针对多自主体系统群集运动问题,本文研究了带有不匹配干扰的二阶系统有限时间包容控制.运用现代控制理论,设计了非线性观测器,对系统未知状态和干扰进行估计.在状态估计的基础上,构建了基于干扰观测器的多自主体系统的协同控制算法.应用代数图论和齐次性理论等方法,分析了二阶多自主体系统有限时间包容控制.数据仿真中应用基于观测器的包容控制算法,使得系统的运动状态最终都收敛到由多个领导者所围成的目标区域中,验证了本文结果的有效性.     

Robust consensus algorithm for second-order multi-agent systems with external disturbances

This article investigates the problem of robust consensus for second-order multi-agent systems with external disturbances. Based on a non-smooth backstepping control technique, a class of novel continuous non-smooth consensus algorithms are proposed for the multi-agent network with/without communication delays. The controller design is divided into two steps. First, for the kinematic subsystem, the velocity is regarded as a virtual input and designed such that the states consensus can be achieved asymptotically. Then for the dynamic subsystem, a finite-time control law is designed such that the virtual velocity can be tracked by the real velocity in a finite time. Under the proposed control law, it is shown that if the communication topology graph contains a directed spanning tree, the states consensus can be achieved asymptotically in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a small region around the origin. By building a relationship between control parameters and the bound of steady tracking errors, it is demonstrated that the disturbance rejection performance of the resulting closed-loop system can be enhanced by adjusting the fractional power in the non-smooth controller. Finally, an example is given to verify the efficiency of the proposed method.     

交会对接模拟系统姿态跟踪有限时间抗干扰控制

针对交会对接模拟系统的姿态同步问题,在存在扰动和系统不确定性的情况下,利用改进的快速非奇异终端滑模面和改进的自适应律设计两个有限时间抗干扰控制器.改进的自适应律保证了两个控制器的连续性和对干扰的鲁棒性,且第2个控制器能解决边界层理论存在的边界层内有限时间稳定性丢失的问题.李雅普诺夫理论推导和仿真结果表明,提出的两个控制器能保证系统的有限时间稳定性,系统能快速收敛到平衡点.