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。     

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.     

反步自适应方法实现混沌系统的同步

针对基于滞环非线性参数未知的多涡卷混沌系统,提出了一种自适应反步变结构的控制方案来实现其同步。通过逐步修正的方法设计镇定控制器,在每一步把状态坐标的变化、不确定参数的调节函数和一个Lyapunov函数的虚拟系统的镇定函数联系起来,以达到实现系统的全局调节。采用所设计的控制器实现了两个混沌系统的同步控制,使得误差系统在有限时间内到达所设定的滑模面,并沿着滑模面渐进收敛到原点,同时估计出系统中存在的未知参数。由于自适应算法和滑模方法的使用,控制器对参数扰动和外部干扰具有较强的抑制作用,理论分析和仿真结果验证了所提出方法的有效性。     

Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients

In this paper, a novel adaptive fuzzy control scheme is proposed for a class of uncertain single-input and single-output (SISO) nonlinear time-delay systems with the lower triangular form. Fuzzy logic systems are used to approximate unknown nonlinear functions, then the adaptive fuzzy tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the backstepping approach. The proposed controller guarantees uniform ultimate boundedness of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme.