基于不确定逼近的机械手自适应鲁棒预测控制

针对具有参数不确定性和未知外部干扰的机械手轨迹跟踪问题提出了一种多输入多输出自适应鲁棒预测控制方法. 首先根据机械手模型设计非线性鲁棒预测控制律, 并在控制律中引入监督控制项; 然后利用函数逼近的方法逼近控制律中因模型不确定性以及外部干扰引起的未知项. 理论证明了所设计的控制律能够使机械手无静差跟踪期望的关节角轨迹. 仿真验证了本文设计方法的有效性.     

基于神经网络的不确定机器人自适应滑模控制

提出一种机器人轨迹跟踪的自适应神经滑模控制。该控制方案将神经网络的非线性映射能力与变结构控制理论相结合,利用RBF网络自适应学习系统不确定性的未知上界,神经网络的输出用于自适应修正控制律的切换增益。这种新型控制器能保证机械手位置和速度跟踪误差渐近收敛于零。仿真结果表明了该方案的有效性。     

一类非线性参数化系统的自适应鲁棒控制

针对一类含有非线性参数化不确定项的非线性系统,本文提出了一种基于浸入和不变流形的自适应鲁棒控制器.由于浸入和不变流形方法将调节函数引入到参数估计律的设计中,增加了控制器设计自由度,保证对系统中未知参数的渐近估计,使得设计出的自适应鲁棒控制器在克服非线性参数化不确定项和外界扰动影响的同时,保证了良好的动态和稳态性能.最后通过仿真实例验证了所提算法的有效性.     

卫星姿态直接自适应模糊预测控制

对具有模型不确定性和未知外干扰的卫星姿态系统提出了多输入多输出直接自适应模糊预测跟踪控制设计方法. 此方法先基于卫星姿态动力学模型设计出非线性广义预测控制律, 再构造直接自适应模糊控制器逼近预测控制律中因模型不确定性引起的未知项. 文中证明了所设计的控制律能使卫星跟踪给定的期望姿态轨迹, 跟踪误差收敛到原点的小邻域内. 仿真结果验证了此方法的有效性.     

基于非线性增益递归滑模的船舶轨迹跟踪动态面自适应控制

针对三自由度全驱动船舶存在模型不确定和未知外部环境扰动的情况,设计出一种基于非线性增益递归滑模的船舶轨迹跟踪动态面自适应神经网络控制方法.该方法综合考虑船舶位置和速度误差之间关系设计递归滑模面,引入神经网络对船舶模型不确定部分进行逼近,设计带σ-修正泄露项的自适应律对神经网络逼近误差与外界环境扰动总和的界进行估计,并应用一种非线性增益函数构造动态面控制律,选取李雅普诺夫函数证明了该控制律能够保证轨迹跟踪闭环系统内所有信号的一致最终有界性.最后,基于一艘供给船进行仿真验证,结果表明,船舶轨迹跟踪响应速度快、精度高,所设计控制器对系统模型参数摄动及外界扰动具有较强的鲁棒性.     

一类非线性参数化系统自适应重复学习控制

针对一类高阶非线性参数化系统, 利用分段积分机制, 提出了一种新的自适应重复学习控制方法. 该方法结合反馈线性化, 可以处理参数在一个未知紧集内周期性快时变的非线性系统, 通过引进微分-差分混合型参数自适应律, 设计了一种自适应控制策略, 使广义跟踪误差在误差平方范数意义下渐近收敛于零, 通过构造Lyapunov泛函, 给出闭环系统收敛的一个充分条件. 实例仿真结果说明了该方法的可行性.     

基于S类函数的严格反馈非线性周期系统的自适应控制

针对一类严格反馈非线性周期系统, 在周期非线性可时变参数化的条件下设计自适应控制器. 通过将周期时变参数展开成傅里叶级数, 并采用微分自适应律估计未知系数, 进行控制器反推设计. 引入S类函数, 并在控制器设计中应用S类函数处理截断误差项对系统跟踪性能的影响, 同时, S类函数能确保虚拟控制的可微. 给出几种不同的S类函数设计, 分析比较将其应用于控制器设计时产生的不同效果. 理论分析与仿真结果表明, 提出的控制方法能够实现系统输出跟踪期望轨迹, 且闭环系统所有信号有界.     

三维非线性自适应容错导引律设计

本文针对部分执行器失效情形下的三维鲁棒导引律设计问题,利用输入–状态稳定性原理,设计一种三维非线性自适应容错导引律.与已存在结果相比,所设计算法能够实现对部分执行器失效的自动补偿,并且具备克服机动目标未知机动性对制导效果的影响.理论分析和数值仿真验证了该算法的有效性,并且数值仿真还表明其能够恢复特定时间段内执行器完全失效时的系统稳定性,具有很强的鲁棒性.     

应用于力矩受限自由漂浮空间机器人的神经网络自适应控制

在控制力矩受限情况下,为实现具有模型不确定性自由漂浮空间机器人的轨迹跟踪控制,文章设计了一种新的神经网络自适应控制策略;首先,用双曲函数对控制力矩输入进行限制;其次,设计一种神经网络自适应控制律,对输入力矩受限条件下的非线性系统模型进行在线逼近,同时,利用鲁棒项对神经网络逼近误差和外界干扰进行消除;最后,根据李雅普诺夫理论,证明了所设计控制策略能够使自由漂浮空间机器人系统渐进稳定;仿真实验表明,该控制策略在无需建立复杂系统模型的情况下,便能够对控制力矩进行有效限制,从而使自由漂浮空间机器人在控制力矩受限情况下得到较好的控制.     

基于干扰观测器的高速列车RBF自适应滑模控制方法

针对高速列车动力学模型的不确定性和存在外部干扰难以实现高速列车对目标轨迹的高精度跟踪控制的问题,设计了一种基于非线性干扰观测器的RBF神经网络自适应滑模控制方法。首先,针对高速列车模型非线性系统的不确定性问题,设计自适应RBF神经网络鲁棒控制器进行跟踪控制,基于RBF神经网络的特性设计神经网络权值自适应律,对列车模型中的未知函数进行估计。其次,针对高速列车跟踪控制外部干扰问题,采用指数收敛干扰观测器进行干扰补偿,提高高速列车对目标轨迹追踪的抗干扰能力。最后,李雅普诺夫(Lyapunov)稳定性分析保证了闭环系统的渐近稳定性,以秦沈客运专线为仿真对象。结果表明,所设计的控制方法不仅解决了列车模型未知阻力部分的自适应逼近,而且在此基础上引入干扰观测器对外部非线性干扰进行补偿实现了对期望轨迹的高精度快速跟踪。     

Immersion and invariance adaptive control of a class of continuous stirred tank reactors

An immersion and invariance(I&I) manifold based adaptive control algorithm is presented for a class of continuous stirred tank reactors(CSTR) to realize performance-oriented control in this paper. The nonlinear contraction method is combined into the control law design to render the closed-loop CSTR system globally asymptotically stable, firstly. Then, the I&I method is used to form the adaptation law such that the off-the-manifold coordinate(the parameter estimation error) converges to zero using P-monotone property enforced by selecting tuning function in manifold. As a result, the state of the closed-loop CSTR converges to its desired value asymptotically. The simulation is given to illustrate the effectiveness of the presented algorithm.     

A constructive solution for stabilization via immersion and invariance: The cart and pendulum system

Immersion and Invariance (I&I) is the method to design asymptotically stabilizing control laws for nonlinear systems that was proposed in [Astolfi, A., & Ortega, R. (2003). Immersion and invariance: A new tool for stabilization and adaptive control of nonlinear systems. IEEE Transactions on Automatic Control, 48, 590-606]. The key steps of I&I are (i) the definition of a target dynamics, whose order is strictly smaller than the order of the system to be controlled; (ii) the construction of an invariant manifold such that the restriction of the system dynamics to this manifold coincides with the target dynamics; (iii) the design of a control law that renders the manifold attractive and ensures that all signals are bounded. The second step requires the solution of a partial differential equation (PDE) that may be difficult to obtain. In this short note we use the classical cart and pendulum system to show that by interlacing the first and second steps, and invoking physical considerations, it is possible to obviate the solution of the PDE. To underscore the generality of the proposed variation of I&I, we show that it is also applicable to a class of n-dimensional systems that contain, as a particular case, the cart and pendulum system.     

Immersion‐ and invariance‐based adaptive stabilization of switched nonlinear systems

This paper presents a novel framework to asymptotically adaptively stabilize a class of switched nonlinear systems with constant linearly parameterized uncertainty. By exploiting the generalized multiple Lyapunov functions method and the recently developed immersion and invariance (I&I) technique, which does not invoke certainty equivalence, we design the error estimator, continuous state feedback controllers for subsystems, and a switching law to ensure boundedness of all closed‐loop signals and global asymptotical regulation of the states, where the solvability of the I&I adaptive stabilization problem for individual subsystems is not required. Then, along with the backstepping method, the proposed design technique is further applied to a class of switched nonlinear systems in strict‐feedback form with an unknown constant parameter so that the I&I adaptive stabilization controllers for the system is developed. Finally, simulation results are also provided to demonstrate the effectiveness of the proposed design method.     

Robust nonlinear control of atomic force microscope via immersion and invariance

This paper reports an immersion and invariance (I&I)–based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed‐loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov‐based analysis of the closed‐loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method.     

Hybrid adaptive robust control of static var compensator in power systems

To improve the transient response of an electric power transmission system, a hybrid adaptive robust control method is proposed in this paper for the static var compensator by incorporating the immersion and invariance adaptive (I&I adaptive) and L₂‐gain control. In contrast to the standard I&I adaptive control algorithm, establishing a target system is not required in constructing the robust control law with the proposed method. Thus, the procedure of solving PDEs to satisfy the immersion condition can be avoided. In addition, both parametric and non‐parametric uncertainties, which commonly exist in electric power transmission systems, are considered. The parametric uncertainty induced by the damping coefficient of the system is estimated by the designed adaptive law, which is constructed by ensuring the estimation error converges to zero. The non‐parametric uncertainty is caused by external disturbances and approximation errors in modeling the uncertain structure. By assuming that the L₂‐gain of the system to the non‐parametric uncertainties satisfies a dissipation inequality, we found that the robustness of the controller can be guaranteed. It is proved that all the system states are globally bounded and converge to a new stable equilibrium. Simulation results are also presented to show the effectiveness of the proposed control method in improving the transient response of the system and the convergence speed of the system states. Copyright © 2013 John Wiley & Sons, Ltd.     

A New Robust Adaptive Control of Uncertain Nonlinear Systems and Pendulum Application

A new robust adaptive control of uncertain nonlinear systems is proposed in this paper. The proposed method combines sliding mode control with the immersion and invariance (I&I) adaptive scheme, and it has more available degrees of freedom than using the backstepping scheme. Via the proposed method, a class of nonlinear systems with mismatched parametric perturbations can be rendered asymptotically stable and the performance of the system can also be improved. Finally, the proposed method is applied to a simple pendulum with motor dynamics, and simulation results show the effectiveness and performance of the proposed method.     

A New Adaptive Sliding Mode Control of Uncertain Nonlinear Systems

In this paper, a new adaptive sliding mode control is proposed to control nonlinear systems with parametric uncertainties and matched and unmatched external disturbances. The proposed method first combines immersion and invariance (I&I) adaptive scheme with sliding mode control (SMC), which preserves the advantages of the two methods. The proposed method is different from the approach of combining the backstepping adaptive scheme and sliding mode control in the parameter estimation law, which allows for prescribed dynamics to be assigned to the estimation error and is easier to tune. Finally, the method is applied to control a class of power systems, and simulation results show the advantages of the proposed method.     

可逆冷带轧机速度张力系统的耗散Hamilton 控制

研究基于侵入与不变流形(I&I)自适应方法和非线性干扰观测器(NDO)的可逆冷带轧机速度张力系统耗散Hamilton控制问题。首先采用I&I自适应方法估计系统的摄动参数;其次,通过预反馈建立系统速度张力外环的耗散Hamilton模型,并利用互联和阻尼配置以及能量整形方法设计耗散Hamilton控制器;再次,选用NDO对系统电流内环的外扰进行观测,并引入设计的积分滑模控制器中进行补偿;最后将该方法应用于某1422 mm可逆冷带轧机速度张力系统中进行仿真,结果验证了所提出方法的有效性。     

High performance nonlinear adaptive control of temperature in cryogenic wind tunnel

A new nonlinear adaptive control method based on Immersion and Invariant (I&I) approach is proposed for the temperature control of a cryogenic wind tunnel. The proposed control method can be applied to wide range temperature operation of the tunnel by incorporating the nonlinear dynamic model of temperature into the controller design. By constructing globally stable nonlinear observer, and rendering an invariant and attractive manifold in the state space of plant and observer, the uncertain gain of known disturbance and unknown wind tunnel wall temperature are considered in the same manner within the adaptive I&I control frame. In the design, nominal heat transfer coefficient is deployed to avoid complicated design process involving nonlinear parameterization. This design leads to an adaptive output feedback stabilization control law for the temperature with guaranteed transient and steady performance, which exhibits reasonable robustness to time delay in the control input channel and other uncertainties. The analysis and simulation show the effectiveness of the proposed control methodology.