Regulation of nonlinear systems using conditional integrators

This paper studies the regulation of nonlinear systems using conditional integrators. Previous work introduced the tool of conditional integrators that provide integral action inside a boundary layer while acting as stable systems outside, leading to improvement in transient response while achieving asymptotic regulation in the presence of unknown constant disturbances or parameter uncertainties. The approach, however, is restricted to a sliding mode control framework. This paper extends this tool to a fairly general class of state feedback control laws, with the stipulation that we know a Lyapunov function for the closed‐loop system. Asymptotic regulation with improvement in transient response is done by using the Lyapunov redesign technique to implement the state feedback control as a saturated high‐gain feedback and introducing a conditional integrator to provide integral action inside a boundary layer. Improvement in the transient response using conditional integrators is demonstrated with an experimental application to the pendubot. Copyright © 2005 John Wiley & Sons, Ltd.     

Prespecifiable fixed‐time control for a class of uncertain nonlinear systems in strict‐feedback form

In this paper, we investigate the prespecifiable fixed‐time control problem for a class of uncertain nonlinear systems in strict‐feedback form, where the settling (convergence) time is not only bounded but also user‐assignable in advance. One of the salient features of the proposed method lies in the fact that it makes it possible to achieve any practically allowable settling time by using a simple and effective control parameter selection recipe. Both fixed‐time stabilization and fixed‐time tracking are considered for uncertain strict‐feedback systems. Firstly, by adding exponential state feedback and using fractional power integration as Lyapunov function candidate, a global stabilizing control strategy is developed. It is proved that all the system states converge to zero within prespecified fixed‐time with continuous and bounded control action. Secondly, under more general uncertain nonlinearities and external disturbances, an adaptive fixed‐time controller is derived such that the tracking error converges to a small neighborhood of zero within preassigned time. Theoretical results are also illustrated and supported by simulation studies.     

非线性积分滑模控制方法

针对一类不确定非线性系统的滑模控制,提出了一类具有"小误差放大,大误差饱和"功能的光滑非线性饱和函数来改进传统的积分滑模控制,以形成非线性积分滑模控制.在保持传统积分滑模控制跟踪精度的同时获得更好的暂态性能.应用Lyapunov稳定性理论和LaSalle不变性原理证明了对最终常值干扰可以完全抑制.考虑控制受限时,所设计...     

Regional stability of two‐dimensional nonlinear polynomial Fornasini‐Marchesini systems

This paper addresses the problem of regional stability analysis of 2‐dimensional nonlinear polynomial systems represented by the Fornasini‐Marchesini second state‐space model. A method based on a polynomial Lyapunov function is proposed to ensure local asymptotic stability and provide an estimate of the domain of attraction of the system zero equilibrium point. The proposed results that build on recursive algebraic representations of the polynomial vector function of the system dynamics and Lyapunov function are tailored via linear matrix inequalities that are required to be satisfied at the vertices of a given bounded convex polyhedral region of the state space. Numerical examples demonstrate the effectiveness of the proposed method.     

一类高次随机非线性系统的自适应动态面控制

针对一类含非线性参数高次随机非线性系统的输出跟踪控制问题,基于自适应增加幂次积分方法,利用参数分离技术和动态面技术,给出了一种自适应光滑状态反馈控制器设计方法。利用Sigmoid函数设计参数自适应律,保证了其导数连续。将低通滤波器引入控制器设计过程,避免了“微分爆炸”现象。通过构造适当形式的控制Lyapunov函数进行稳定性分析,证明了系统输出能被依概率地调节至参考信号的邻域范围。仿真结果验证了所提控制器设计方案的有效性。     

Time sub-optimal nonlinear PI and PID controllers applied to longitudinal headway car control

Nonlinear proportional-integral and proportional-integral-derivative (PID) controllers combining time-(sub)optimality with linear control robustness and anti-windup properties are proposed for first-order and second-order integrator systems, without assuming that the control lower-bound and upper-bound are the opposite of each other. A complementary contribution is the introduction of an integral action with anti-windup properties into the control law, under the constraint of ensuring global asymptotic stability. For illustration purposes, the proposed PID solution is applied to the longitudinal headway control of a vehicle following another vehicle.     

控制方向未知的非线性系统的自适应输出跟踪控制

针对一类含有未知控制方向和时变不确定性的本质非线性系统,应用Nussbaum-type增益技术和Adding a power integrator递推设计方法,设计了一种鲁棒自适应状态反馈拉制器．所设计的控制器能保证闭环系统所有信号全局一致有界,特别是通过适当调整控制器设计参数,可使输出跟踪误差在有限时间后变得适当小．最后通过仿真实例对算法进行验证.     

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.     

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.     

带非三角结构的非线性系统自适应控制设计

针对一类带有非三角结构的不确定非线性系统,研究了其控制设计问题,提出了一种自适应跟踪控制设计方法。通过构造一种新的李雅普诺夫函数,并运用增加幂次积分方法和模糊控制方法,设计得到了一种新型自适应跟踪控制器。控制器只引入了一个参数自适应律,避免了反推设计中的过参数化问题,同时保证了输出跟踪误差可以任意小,且使得闭环系统的所有信号有界。最后,将控制方法应用到单连杆机械臂系统上,通过仿真研究验证了所提控制方案的有效性。     

不确定离散时间系统的复合非线性反馈积分滑模控制

针对不确定离散时间系统,提出一种基于离散复合非线性反馈的积分滑模(DCNF-ISM)控制策略,并将该算法应用于扰动下的磁盘跟踪问题.该算法由离散复合非线性反馈(DCNF)控制律与积分滑模(ISM)控制律两部分组成,其中DCNF控制律用于保证系统具有较好瞬态性能,基于改进的离散趋近律设计的ISM控制律用于保证系统鲁棒性.基于Lyapunov稳定性理论对本文提出的控制策略的稳定性进行了推导证明,证明了离散时间系统的一致最终有界性.仿真结果表明,本文提出的控制策略能保证系统在扰动下仍然能够精确跟踪给定的参考信号,与传统的DCNF控制相比,该算法能够保证系统具有响应速度快超调量小、鲁棒性强等优点.     

Nonlinear H ∞ output feedback control with integrator for polynomial discrete‐time systems

This paper investigates the problem of designing a nonlinear H _∞ output feedback controller for a class of polynomial discrete‐time systems. In general, this problem is hard to be formulated in a convex form because the relation between the control input and the Lyapunov function is always not jointly convex. Therefore, the problem cannot be solved via semidefinite programming (SDP). On the basis of the sum of squares (SOS) approach and incorporation of an integrator into the controller, sufficient conditions for the existence of a nonlinear H _∞ output feedback controller are given in terms of SOS conditions, which can be solved by an SDP solver. In contrast to the existing methods, a less conservative result is obtained. Finally, numerical examples are used to demonstrate the validity of this integrator approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust control for a class of state-constrained high-order switched nonlinear systems with unstable subsystems

This paper addresses the issue of robust stabilisation for a class of state-constrained high-order switched nonlinear systems whose subsystems are allowed to be all unstabilizable. A novel robust control scheme is established based on effective coupling of the technique of adding a power integrator and the method of multiple barrier Lyapunov functions. Explicitly, a sufficient condition for robustly stabilising the resulting closed-loop system in a domain is presented, which meanwhile can also guarantee that the violation of the constraints does not happen. Moreover, in the switching law design, we do not require the connection of barrier Lyapunov functions for two adjacent subsystems, and even a certain amount of jump is also allowed. Finally, the effectiveness of the provided control strategy is demonstrated via a simulation example.     

Adaptive reliable guaranteed performance control of uncertain nonlinear systems by using exponent‐dependent barrier Lyapunov function

This paper investigates the issue of adaptive reliable tracking control for a class of uncertain nonlinear parametric strict‐feedback systems under actuator faults. To guarantee better transient performance of adaptive systems especially when actuator faults occur, a novel prescribed performance bounds (PPBs) method based on exponent‐dependent barrier Lyapunov function is developed. Differing from the existing results where the control schemes have introduced the strictly monotone smooth function to achieve constrained error transformation, the proposed PPBs scheme is designed by using the time‐varying barriers to constrain the error trajectories, which accurately characterizes the convergence rates and convergence bounds of errors. Finally, under the framework of backstepping technique and Lyapunov stability theorem, an adaptive reliable controller is designed to ensure that all the closed‐loop signals are semiglobally uniformly ultimately bounded with the tracking errors converging to the specified PPBs. Simulation results demonstrate the effectiveness of the proposed approach.     

基于后推设计的直接自适应模糊控制

针对一类严格反馈不确定非线性动态系统，提出一种直接鲁棒自适应模糊控制新方案．利用模糊系统的逼近能力、后推设计方法和积分型李亚普诺夫函数，依次确定各虚拟控制及模糊系统中可调参数的自适应律，并最终确定出控制律．为改善控制系统的性能，引入逼近误差的自适应补偿项．通过李亚普诺夫方法，证明了闭环系统是一致终结有界的．仿真结果表明了该方法的有效性。     

非线性状态空间模型遗忘性研究

动态系统的遗忘性是描述系统行为主要取决于其近期输入的概念，与系统的稳定性、鲁棒性等密切相关。对于非线性状态空间模型，遗忘性在很弱的条件下与整体一致非常吸引等价。系统在凸集或不变区集上的遗忘性可由一类特殊Ｌｙａｐｕｎｏｖ函数的存在性保证。遗忘区域的大小可利用矩阵不等式来估计。     

Composite quadratic Lyapunov functions for constrained control systems

A Lyapunov function based on a set of quadratic functions is introduced in this paper. We call this Lyapunov function a composite quadratic function. Some important properties of this Lyapunov function are revealed. We show that this function is continuously differentiable and its level set is the convex hull of a set of ellipsoids. These results are used to study the set invariance properties of continuous-time linear systems with input and state constraints. We show that, for a system under a given saturated linear feedback, the convex hull of a set of invariant ellipsoids is also invariant. If each ellipsoid in a set can be made invariant with a bounded control of the saturating actuators, then their convex hull can also be made invariant by the same actuators. For a set of ellipsoids, each invariant under a separate saturated linear feedback, we also present a method for constructing a nonlinear continuous feedback law which makes their convex hull invariant.     

控制输入受限的准全控制利用率有限时间稳定控制

针对控制输入受限的非线性系统,分6种情况证明有限时间稳定控制器(finite time stable controller,FTSC)作用下的系统状态收敛速度在论域空间中每一点必快于非有限时间稳定控制器(non-FTSC,NFTSC)作用下的系统状态收敛速度,并给出每一类情况下设计参数应满足的充分性约束条件,同时证明这些条件的存在性.在此基础上,提出全控制利用率控制器(CCUC)的定义,证明CCUC必然引起抖振,进而提出准全控制利用率控制器(QCCUC)设计的思想,并证明控制输入受限条件下,FTSC的控制利用率必优于任意快速FTSC(FFTSC),即具有更优的控制性能,从而得到一系列关于参数优化的结论.理论证明的结论通过图表、数例和仿真得到了验证.所得结论对终端滑模控制、加幂积分控制、有限时间稳定backstepping控制等多种FTSC均广泛适用.     

New results on robust tracking control for a class of high-order nonlinear time-delay systems

This paper considers the global tracking control problem for a class of nonlinear systems. Compared with the existing results, one significant distinction of this work is that it allows the high-order powers, zero dynamics, time-delay and external disturbances. By constructing a new Lyapunov–Krasovskii (L–K) functional and using the modified adding a power integrator method, we successfully design a non-smooth tracking controller which guarantees that all the signals of the closed-loop system are bounded. The tracking error can be adjusted small enough using the designed parameters. As a practical application, in the simulation, the single-link robot system is studied to show the validness of the strategy.     

Event-triggered adaptive fuzzy control for nonstrict-feedback nonlinear systems with output hysteresis

This paper concentrates upon the issue of adaptive fuzzy tracing control for a class of nonstrict-feedback nonlinear systems output with hysteresis via an event-triggered strategy. To handle the difficulty caused by the nonstrict nonlinear systems, the variable separation technique is introduced. The design difficulty of output hysteresis is addressed by employing a hysteresis inverse function and Nussbaum function to compensate unmeasurable state signal. Meanwhile, the fuzzy logic system (FLS) is used to estimate the unknown function at each step of recursion. Moreover, by devising the relative threshold event-triggered mechanism (ETM), the frequency of actuators and controllers can be largely decreased. Thus, the adaptive fuzzy event-triggered tracing control strategy is proposed by combining the barrier Lyapunov function and backstepping technique. With the proposed scheme, it is theoretically demonstrated that all signals in the closed-loop system are bounded, and the tracing errors are driven to a small neighborhood of the origin under the output constraint. Eventually, two examples demonstrate the efficacy of the proposed control strategy.