Nonlinear and Adaptive Control Systems

Robust modification of nonlinear L1 adaptive flight control system via noise attenuation

Theory of nonlinear control

Parametric study of nonlinear adaptive control algorithm with magneto-rheological suspension systems

A model reference adaptive inverse control system (MRAICS) based on fuzzy neural networks (FNN), which comprises adaptive disturbance canceller and feedback compensation, is presented in This work. The feedback compensation can counteract the MRAIC system's direct current zero-frequency drift. The adaptive disturbance canceler can best erase disturbances. Nonlinear filters based on FNN are used in the nonlinear plant modeling, the design of the controller and adaptive disturbance canceller. The nonlinear filters can deal with nonlinear system and result in fast convergence. Simulation result shows that the approach is effective.

International audience

In this paper, we develop a discrete-time controller for continuous-time nonlinear plant. The exact dynamics of the plant are unknown, but some bounds of the dynamics are assumed. The controller consists of a supervisory controller and an adaptive fuzzy controller. The supervisory controller is designed to guarantee the boundedness of the state, and the adaptive fuzzy controller is designed to control the state to track a given trajectory. More specifically, the supervisory controller is constructed from the bounds of the plant dynamics in such a way that once the state moves outside the stable region, the supervisory controller will take action to draw it back. The adaptive fuzzy controller is constructed from the measured state and control data using the nearest neighborhood clustering algorithm. Both the supervisory controller and the adaptive fuzzy controller operate at discrete-time points, whereas the plant keeps running continuously. We give rigorous proofs of the properties of this sampled-data nonlinear adaptive control system.

Motivated by the recent advance in adaptive output feedback control of affine nonlinear systems [8-10], an adaptive variable structure controller is proposed in this paper for solving the model reference adaptive control of nonlinear time-varying systems. Asymptotic output tracking performance can be achieved for relative degree one case. When the relative degree of the nonlinear system is greater than one, a systematic design procedure is given under a modified sector-type condition so that the closed-loop stability and the tracking performance are achieved similar to that in relative degree one case.

In this paper, a stable adaptive neural sliding mode controller is developed for a class of multivariable uncertain nonlinear systems. For these systems not all state variables are available for measurements. By designing a state observer, adaptive neural systems, which are used to model unknown functions, can be constructed using the state estimations. Based on Lyapunov stability theorem, the proposed adaptive neural control system can guarantee the stability of the whole closed loop system and obtain good tracking performances. Adaptive laws are proposed to adjust the free parameters of the neural models. Simulation results illustrate the design procedure and demonstrate the tracking performances of the proposed controller.

The objective of this study is to enhance the responsiveness and precision of control systems through the acceleration of evolutionary programming in the optimization of nonlinear fuzzy control systems. Nonlinear systems are ubiquitous in engineering practice, presenting significant challenges due to their complexity and uncertainty for traditional control methodologies. Fuzzy control, an intelligent control approach rooted in empirical rules, possesses the capability to navigate uncertain and nonlinear issues. However, conventional fuzzy controllers struggle to achieve optimal control performance when confronted with highly complex nonlinear systems. Consequently, this paper introduces the application of accelerated evolutionary programming (RGA) for the optimization of fuzzy controllers, aiming to augment their performance in nonlinear systems. By merging genetic algorithms with a fuzzy adaptive PID controller, the optimized fuzzy controller is better equipped to adapt to the dynamic changes of nonlinear systems, offering robust and efficient control strategies. The results of simulation experiments demonstrate a marked improvement in response time, stability, and error reduction with the fuzzy control system based on RGA optimization. This study offers novel insights and methodologies for the further optimization of control within nonlinear systems, while providing theoretical support for the practical applications of complex systems.

Due to the increase in wind power accessing power system in recent years, the low-frequency oscillation of power system is more complicated. Therefore, a new adaptive switching control method combined with a nonlinear system is proposed for the complex operating conditions of the grid-connected power system. Firstly, this method decomposes the low-frequency oscillation control problem of the power system into two parts, which are the linear system control and the nonlinear system control. Then, in the linear system control part, the iterative identification method is used to control this part. In the nonlinear system control part, the nonlinear term is decomposed into a combination of the previous beating measurable and the nonlinear estimation increment. Secondly, the nonlinear system is divided into three different operating conditions by the nonlinear estimation increment. Thus, four different adaptive controllers are obtained. Then, the designed controller is switched according to the controlled object with four controllers by the switching function, which not only ensures the stability of the closed-loop system, but also improves the control performance of the controller under different operating conditions. Finally, the feasibility and effectiveness of this method are verified, and the controller can fit the control efficiency of the real power system well.

摘要: 确定学习运用自适应控制和动力学系统的概念与方法, 研究未知动态环境下的知识获取、表达、存储和利用等问题. 针对产生周期或回归轨迹的连续 非线性动态系统, 确定学习可以对其未知系统动态进行局部准确建模, 其基本要 素包括: 1)使用径向基函数(Radial basis function, RBF)神经网络; 2)对于周期(或回归)状态轨迹 满足部分持续激励条件; 3)在周期(或回归)轨迹的邻域内实现对非线性系统动态的局部准确神经网络逼近(局部准确建模); 4)所学的知识以时不变且空间分布的方式表达、以常值神经网络权值的方式存储, 并可在动态环境下用于动态模式的快速识别或者闭环神经网络控制. 本文针对离散动态系统, 扩展了确定学习理论, 提出一个根据时态数据序列对离散动态系统进行建模与控制的框架. 首先, 运用确定学习原理和离散系统的自适应辨识方法, 实现对产生时态数据的离散非线性系统的未知动态进行局部准确的神经网络建模, 并利用此建模结果对时态数据序列进行时不变表达. 其次, 提出时态数据序列的基于动力学的相似性定义, 以及对离散动态系统产生的时态数据序列(亦可称为动态模式)进行快速识别方法. 最后, 针对离散非线性控制系统, 实现了基于时态数据序列对控制系统动态的闭环辨识(局部准确建模). 所学关于闭环动态的知识可用于基于模式的智能控制. 本文表明确定学习可以为时态数据挖掘的研究提供新的途径, 并为基于数据的建模与控制等问题提供新的研究思路. 关键词: 确定学习 / 时态数据序列 / 离散动态系统 / 基于数据的建模 / 部分持续激励条件 / 时态数据挖掘 / 动态模式识别 / 基于模式的控制

Fundamentals of the theory of non-linear pluse control systems

A EROSPACE engineering applications greatly stimulated the development of optimal control theory during the 1950s and 1960s, where the objective was to drive the system states in such a way that some defined cost was minimized. This turned out to have very useful applications in the design of regulators (where some steady state is to be maintained) and in tracking control strategies (where some predetermined state trajectory is to be followed). Among such applications was the problem of optimal flight trajectories for aircraft and space vehicles. Linear optimal control theory in particular has been very well documented and widely applied, where the plant that is controlled is assumed linear and the feedback controller is constrained to be linear with respect to its input. However, the availability of powerful low-cost microprocessors has spurred great advantages in the theory and applications of nonlinear control. The competitive era of rapid technological change, particularly in aerospace exploration, now demands stringent accuracy and cost requirements in nonlinear control systems. This has motivated the rapid development of nonlinear control theory for application to challenging, complex, dynamical real-world problems, particularly those that bear major practical significance in aerospace, marine, and defense industries. Infinite-time horizon nonlinear optimal control (ITHNOC) presents a viable option for synthesizing stabilizing controllers for nonlinear systems by making a state-input tradeoff, where the objective is to minimize the cost given by a performance index. The original theory of nonlinear optimal control dates from the 1960s. Various theoretical and practical aspects of the problem have been addressed in the literature over the decades since. In particular, the continuous-time nonlinear deterministic optimal control problem associated with autonomous (time-invariant) nonlinear regulator systems that are affine (linear) in the controls has been studied by many authors. The long-established theory of optimal control offers quite mature and well-documented techniques for solving this control-affine nonlinear optimization problem, based on dynamic programming or calculus of variations, but their application is generally a very tedious task. Bellman’s dynamic programming approach reduces to solving a nonlinear first-order partial differential equation (PDE), expressed by the Hamilton–Jacobi–Bellman (HJB) equation. The solution to the HJB equation gives the optimal performance/cost value (or storage) function and determines an optimal control in feedback form under some smoothness assumptions. Alternatively, in the classical calculus of variations, optimal control problems can be characterized locally in terms of the Hamiltonian dynamics arising from Pontryagin’s minimum principle. These are the characteristic equations of the HJB PDE, which result in a nonlinear, constrained two-point boundary value problem (TPBVP) that, in general, can only be solved by successive approximation of the optimal control input using iterative numerical techniques for each set of initial conditions. Numerically, even though the nonlinear TPBVP is somewhat easier to solve than the HJBPDE, control signals can only be determined offline and are thus best suited for feedforward control of plants for which the state trajectories are known a priori. Therefore, contrary to the dynamic programming approach, the resultant control law is not generally in feedback form. Open-loop control, however, is sensitive to random disturbances and requires that the initial state be on the optimal trajectory. In contrast, nonlinear optimal feedback has inherent robustness properties (inherent in the sense that it is obtained by ignoring uncertainty and disturbances). The potential difficulty with the HJB approach is that no efficient algorithm is available to solve the PDE when it is nonlinear and the problem dimension is high, making it impossible to derive exact expressions for optimal controls for most nontrivial problems of interest. The optimal can only be computed in special cases, such as linear dynamics and quadratic cost, or very low-dimensional systems. In particular, if the plant is linear time invariant (LTI) and the (infinite-time) performance index is quadratic, then the corresponding HJB equation for this infamous linear-quadratic regulator (LQR) problem reduces to an algebraic Riccati equation (ARE). Contrary to the well-developed and widely applied theory and computational tools for theRiccati equation (for example, see [1]), theHJB equation is difficult, if not impossible, to solve for most practical applications. The exact solution for the optimal control policies is very complex

In this brief, a novel robust nonlinear motion controller with disturbance observer (DOB) for positioning control of a nonlinear single-input-single-output (SISO) mechanical system is proposed. The controller is designed in a backstepping manner. First, a proportional-integral (PI) controller is designed to stabilize the position error. Consequently, a novel robust nonlinear velocity controller with DOB is designed to stabilize the velocity error. With the help of nonlinear damping terms, the input-to-state stability (ISS) property of the overall nonlinear control system is proven, which leads to a major contribution of construction of a theoretically guaranteed robust nonlinear controller with DOB. The performance of the proposed controller is verified through application to a magnetic levitation system. Comparative studies with an adaptive robust nonlinear controller are also carried out. It is shown that the proposed novel controller while being simple is superior over the adaptive robust nonlinear controller for the experimental setup under study.

A basic NAICS (nonlinear adaptive inverse control system) based on filtered-epsiv LMS algorithm has a complex structure. It is composed of more than ten adaptive nonlinear filters and four of them need to be trained on-line. Moreover, the disturbance canceller could not work well in the system. In order to simplify the structure and cancel the disturbance effectively of the system given above, an improved NAICS based on filtered-epsiv LMS algorithm is presented in this paper. It has a new disturbance canceller that candles the disturbances by a copy model of the left-inverse model of the nonlinear plant. Moreover, such disturbance canceller doesnpsilat need to train any filters. The improved system is composed of six adaptive nonlinear filters and three of them need to be trained on-line. Simulation results show the system can cancel the disturbance effectively and the inverse controller can converge quickly.