Control of discrete time nonlinear systems with a time-varying structure

In this paper, we present a control methodology for a class of discrete time nonlinear systems that depend on a possibly exogenous scheduling variable. This class of systems consists of an interpolation of nonlinear dynamic equations in strict feedback form, and it may represent systems with a time-varying nonlinear structure. Moreover, this class of systems is able to represent some cases of gain scheduling control, Takagi-Sugeno fuzzy systems, as well as input-output realizations of nonlinear systems which are approximated via localized linearizations. We present two control theorems, one using what we call a “global” approach (akin to traditional backstepping), and a “local” approach, our main result, where backstepping is again used but the control law is an interpolation of local control terms. An aircraft wing rock regulation problem with varying angle of attack is used to illustrate and compare the two approaches.     

Stochastic nonlinear stabilization — II: Inverse optimality

After considering the stabilization of a specific class of stochastic nonlinear systems in a companion paper, in this second part, we address the classical question of when is a stabilizing (in probability) controller optimal and show that for every system with a stochastic control Lyapunov function it is possible to construct a controller which is optimal with respect to a meaningful cost functional. Then we return to the problem from Part I and design an optimal backstepping controller whose cost functional includes penalty on control effort and which has an infinite gain margin.     

Multivariable adaptive control: A survey

Adaptive control is a control methodology capable of dealing with uncertain systems to ensure desired control performance. This paper provides an overview of some fundamental theoretical aspects and technical issues of multivariable adaptive control, and a thorough presentation of various adaptive control schemes for multi-input–multi-output systems, literature reviews on adaptive control foundations and multivariable adaptive control methods, and related technical problems. It covers some basic concepts and issues such as certainty equivalence, stability, tracking, robustness, and parameter convergence. It discusses some of the most important topics of adaptive control: plant uncertainty parametrization, stable controller adaptation, and design conditions for different adaptive control schemes. The paper also presents a detailed study of well-developed multivariable model reference adaptive control theory and design techniques. It provides an introduction to multivariable adaptive pole placement and adaptive nonlinear control, and it concludes by identifying some open research problems.     

捷联式惯性导航系统初始对准扰动补偿控制算法

提出了一种捷联惯性导航系统初始对准扰动补偿二级控制器的设计方法。选取载体的飞行姿态、速度与位置增量建立了扰动补偿控制的状态空间数学模型,基于Backstepping控制方法,通过引入虚拟反馈控制变量设计了非线性控制器,保证大初始扰动条件下系统状态稳定收敛到系统的平衡点集。在平衡点集,设计了H2最优状态反馈控制律,以保证系统状态在平衡点集的渐进收敛。仿真和系统试验结果表明,这种二级补偿控制方法能有效抑制初始对准扰动误差,导航解算精度能够满足工程实际需要。     

基于扩张状态观测器的反馈线性化无人飞行器姿态控制

随着集成电子等技术逐渐成熟,无人飞行器得到了广泛的关注和应用;其中,由于飞行器在飞行阶段具有高响应速度、耦合动力学和非线性等特点,使其在飞行阶段的姿态控制成为该领域重点研究的方向之一;针对该研究方向,文章提出了一种基于反步法技术的反馈线性化无人飞行器姿态跟踪控制方案来解决其在受到环境干扰的条件下可以精准跟踪姿态角度的问题;在该方法中,设计了反步法技术拆分简化模型和反馈线性化减少调节参数,并利用扩张状态观测器(ESO)来对扰动进行估计和补偿,同时给出了ESO的收敛性和闭环系统的稳定性来证明该方法的可实施性;最后给出了仿真结果,验证了该方法在干扰的环境下仍可以精准控制无人飞行器姿态。     

一类具有未建模动态的非线性系统的稳定性研究

研究了一类具有未建模动态的非线性系统的稳定性问题.针对系统的不确定性,首先设计一状态观测器,对系统的全部状态进行估计;然后基于Lyapunov稳定性理论,采用Backstepping方法设计了输出反馈自适应控制器;最后证明了控制器在原点处平衡,可使系统的信号一致有界或者渐近收敛,且仿真举例验证了本文方法的有效性.     

基于Backstepping的欠驱动船舶神经滑模航迹控制

在外界干扰和参数不确定的情况下,设计一种基于Backstepping的自适应神经滑模控制器对欠驱动船舶神经滑模航迹进行控制。采用趋近律的滑模控制,抑制常规滑模的固定切换增益系数带来的抖振现象;利用神经网络辨识对象,减少趋近律滑模控制对对象模型参数的依赖。以某实习船为例进行仿真,结果表明:在标称参数下,所设计的控制器能够有效跟踪设定的航迹并抑制常规滑模控制器的抖振现象;在外部环境扰动以及参数摄动的情况下,仍然能够实现较好的控制,表现出强鲁棒性。     

带有时滞的未知非仿射非线性系统自适应模糊跟踪控制

应用自适应模糊逼近方法研究了一类带有时滞的未知非仿射非线性系统的跟踪控制问题.系统的实际控制器是按照Backstepping设计过程经逐步反推而得到,在每一步设计中需要用自适应模糊逻辑系统来逼近未知的非线性函数.为了降低控制设计对先验知识的依赖性,取消须事先已知模糊基函数的限制,采用非线性参数化的模糊逻辑系统作为逼近器.由于逼近器中的未知参数彼此之间呈非线性关系,无法直接得到在线估计这些参数的自适应律.为了实现对相关参数的在线调节,先应用Taylor展开式将呈非线性关系的参数分离,使其相互之间具有线性关系,然后再基于Lyapunov第2方法给出相应参数的自适应调节律.最后,通过一个仿真实例来验证所给方法的有效性.结果表明:所得自适应模糊控制器能有效补偿时滞的影响,保证闭环系统中所有信号均有界,而且输出跟踪误差能收敛到原点的任意小邻域内.     

带有多非线性干扰观测器的电液伺服反演控制

针对高阶不匹配不确定非线性电液伺服系统,提出一种动态面反演控制策略,以实现对电液伺服系统的位置控制.采用多个非线性干扰观测器观测出电液伺服系统的各阶子系统的不确定项和干扰项,对使用非线性干扰观测器后的系统实行反演控制,使用动态面方法来解决传统反演控制中虚拟控制量随着系统阶数的增加而愈加繁杂的问题.基于Lyapunov方法从理论上证明了所设计的系统控制器能够保证闭环系统有界稳定,系统中所有信号是一致最终有界的,仿真结果验证了反演控制方法的正确性.