Reliable nonlinear control system design using duplicated control elements

Reliable L₂ gain bounding (i.e., H_∞) controllers for nonlinear systems are designed by using redundant control elements. One sensor and one actuator are duplicated, and the resulting closed-loop system is reliable with respect to both the single contingency case and the primary contingency case. The design procedures for reliable controllers are developed by using the Hamilton–Jacobi inequalities from nonlinear H_∞ control theory. Linear reliable controller design methods are also obtained by restricting the proposed nonlinear methods to the linear case, and the linear methods are found to be less conservative than existing methods for linear reliable controller design. Examples are given to illustrate the design procedures for both linear and nonlinear reliable controllers and the advantages of the proposed linear method over existing ones. © 1997 by John Wiley & Sons, Ltd.     

Nonlinear robust state feedback control system design for nonlinear uncertain systems

This paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust PI controller design for nonlinear systems via fuzzymodeling approach

The design problem of proportional and proportional-plus-integral (PI) controllers for nonlinear systems is studied. First, the Takagi-Sugeno (T-S) fuzzy model with parameter uncertainties is used to approximate the nonlinear systems. Then a numerically tractable algorithm based on the technique of iterative linear matrix inequalities is developed to design a proportional (static output feedback) controller for the robust stabilization of the system in T-S fuzzy model. Next, we transform the problem of PI controller design to that of proportional controller design for an augmented system and thus bring the solution of the former problem into the configuration of the developed algorithm. Finally, the proposed method is applied to the design of robust stabilizing controllers for the excitation control of power systems. Simulation results show that the transient stability can be improved by using a fuzzy PI controller when large faults appear in the system, compared to the conventional PI controller designed by using linearization method around the steady state     

Guaranteed cost control of stochastic uncertain systems with slope bounded nonlinearities via the use of dynamic multipliers

This paper presents a new approach to constructive output feedback robust nonlinear guaranteed cost controller design. The approach involves a class of controllers which include copies of the slope bounded nonlinearities occurring in the plant. Dynamic multipliers are introduced to exploit these repeated nonlinearities. The linear part of the controller is synthesized using minimax LQG control theory.     

Sliding mode control for uncertain nonlinear systems with multiple inputs containing sector nonlinearities and deadzones.

In this paper, we investigate a novel robust control approach for a class of uncertain nonlinear systems with multiple inputs containing sector nonlinearities and deadzones. Sliding mode control (SMC) is suggested to design stabilizing controllers for these uncertain nonlinear systems. The controllers guarantee the global reaching condition of the sliding mode in these systems. They can work effectively for systems either with or without sector nonlinearities and deadzones in the inputs. Moreover, the controllers ensure that the system trajectories globally exponentially converge to the sliding mode. Illustrative examples are demonstrated to verify the effectiveness of the proposed sliding mode controller.     

New methodology for analytical and optimal design of fuzzy PIDcontrollers

Describes a methodology for the systematic design of fuzzy PID controllers based on theoretical fuzzy analysis and, genetic-based optimization. An important feature of the proposed controller is its simple structure. It uses a one-input fuzzy inference with three rules and at most six tuning parameters. A closed-form solution for the control action is defined in terms of the nonlinear tuning parameters. The nonlinear proportional gain is explicitly derived in the error domain. A conservative design strategy is proposed for realizing a guaranteed-PID-performance (GPP) fuzzy controller. This strategy suggests that a fuzzy PID controller should be able to produce a linear function from its nonlinearity tuning of the system. The proposed PID system is able to produce a close approximation of a linear function for approximating the GPP system. This GPP system, incorporated with a genetic solver for the optimization, will provide the performance no worse than the corresponding linear controller with respect to the specific performance criteria. Two indexes, linearity approximation index (LAI) and nonlinearity variation index (NVI), are suggested for evaluating the nonlinear design of fuzzy controllers. The proposed control system has been applied to several first-order, second-order, and fifth-order processes. Simulation results show that the proposed fuzzy PID controller produces superior control performance to the conventional PID controllers, particularly in handling nonlinearities due to time delay and saturation     

Global decentralised stabilisation for a class of uncertain large-scale high-order upper-triangular nonlinear systems

This paper considers the global decentralised stabilisation problem for a class of uncertain large-scale high-order upper-triangular nonlinear systems. First, a local linear decentralised controller is recursively constructed based on the generalised homogeneous system theory and the adding a power integrator method. Second, aiming for global stabilisation, a series of nested saturation functions are integrated with the proposed local linear decentralised controller. Then, it is proved that the obtained decentralised saturated controller will render the whole closed-loop system globally asymptotically stable. Due to the flexibility of the generalised homogeneous method, the proposed control approach not only weakens the existing restrictions imposed on the interconnected nonlinearities, but also can be applied to a more general class of upper-triangular nonlinear systems. Furthermore, two simulations examples are conducted to show the effectiveness of the proposed control scheme.     

Discrete‐time robust H∞control of a class of nonlinear uncertain systems

This paper presents an approach to discrete‐time robust H^∞ control for a class of nonlinear uncertain systems on the basis of the use of Sum Quadratic Constraints. The approach involves controllers, which include copies of the system nonlinearities in the controller. The nonlinearities being considered are those that satisfy a certain global Lipschitz condition. The linear part of the controller is synthesized using linear robust H^∞ control theory, and this leads to a nonlinear controller, which gives an upper bound on the attainable disturbance attenuation level. Copyright © 2012 John Wiley & Sons, Ltd.     

线性时滞系统的耗散控制

研究了一类线性时滞系统的二次耗散控制问题,基于线性矩阵不等式（LMI）方法导出了耗散控制器存在的充分条件,通过线性矩阵不等式的可行解构造出耗散态状态反馈和动态输出反馈控制律,相应的闭环系统是二次稳定和严格（Q,S,R）耗散的,本文的主要贡献是统一了线性时滞系统现有的H∞控制和无源控制结果。     

不确定非线性系统的高阶滑模控制器设计

针对一类不确定非线性SISO系统,结合系统有限时间稳定理论与积分滑模控制理论,提出了一种新的高阶滑模控制器设计方法,改善了现有高阶滑模控制中存在的缺陷.积分滑模保证了系统初始时刻就具有抗扰能力,同时采用有限时间稳定观测器实现了高阶滑模的输出反馈控制.仿真结果表明该控制器可使系统在有限时间内收敛,并有效地减小了系统抖振.     

Active control of adaptive optics system in a large segmented mirror telescope

For a large adaptive optics system such as a large segmented mirror telescope (SMT), it is often difficult, although not impossible, to directly apply common multi-input multi-output (MIMO) controller design methods due to the computational burden imposed by the large dimension of the system model. In this article, a practical controller design method is proposed which significantly reduces the system dimension for a system where the dimension required to represent the dynamics of the plant is much smaller than the dimension of the full plant model. The proposed method decouples the dynamic and static parts of the plant model by a modal decomposition technique to separately design a controller for each part. Two controllers are then combined using the so-called sensitivity decoupling method so that the resulting feedback loop becomes the superposition of the two individual feedback loops of the dynamic and static parts. A MIMO controller was designed by the proposed method using the H _∞ loop-shaping technique for an SMT model to be compared with other controllers proposed in the literature. Frequency-domain analysis and time-domain simulation results show the superior performance of the proposed controller.     

Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback

A novel model, termed the standard neural network model (SNNM), is advanced to describe some delayed (or non-delayed) discrete-time intelligent systems com- posed of neural networks and Takagi and Sugeno (T-S) fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based (or fuzzy) discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based (or fuzzy) discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.     

Safe Reinforcement Learning Algorithm and Its Application in Intelligent Control for CPS

The design of a safe controller for a Cyber-Physical System (CPS) is a hot research topic. The existing safety controller design based on formal methods has problems such as excessive reliance on models and poor scalability. Intelligent control based on Deep Reinforcement Learning (DRL) can handle high-dimensional nonlinear complex systems and uncertain systems and is becoming a very promising CPS control technology, but it lacks safety guarantees. This study addresses the safety issues of Reinforcement Learning (RL) control by analyzing a typical case of an industrial oil pump control system and carries out research on a Safe Reinforcement Learning (SRL) algorithm and intelligent control application. First, the SRL issue of the industrial oil pump control system is formalized, and a simulation environment of the oil pump is built. Then, by designing the structure and activation function of the output layer, an oil pump controller in the form of a neural network is constructed to satisfy the linear inequality constraints of the on-off operations of the oil pump. Finally, in order to better balance the safety and optimality control objectives, a new SRL algorithm is designed based on the Augmented Lagrange Multiplier (ALM) method. A comparative experiment on the industrial oil pump shows that the controller synthesized by the proposed algorithm surpasses existing similar algorithms both in safety and optimality. During the evaluation, the neural network controllers synthesized in this study pass rigorous formal verification with a probability of 90%. Meanwhile, compared with the theoretically optimal controller, neural network controllers achieve an optimal objective value loss of 2%. The proposed method is expected to be applied in more scenarios, and the case study scheme may provide a reference for other researchers in the field of safe intelligent control and formal verification.     

安全强化学习算法及其在CPS智能控制中的应用

信息物理系统(cyber-physicalsystem,CPS)的安全控制器设计是一个热门研究方向,现有基于形式化方法的安全控制器设计存在过度依赖模型、可扩展性差等问题.基于深度强化学习的智能控制可处理高维非线性复杂系统和不确定性系统,正成为非常有前景的CPS控制技术,但是缺乏对安全性的保障.针对强化学习控制在安全性方面的不足,围绕一个工业油泵控制系统典型案例,开展安全强化学习算法和智能控制应用研究.首先,形式化了工业油泵控制的安全强化学习问题,搭建了工业油泵仿真环境;随后,通过设计输出层结构和激活函数,构造了神经网络形式的油泵控制器,使得油泵开关时间的线性不等式约束得到满足;最后,为了更好地权衡安全性和最优性控制目标,基于增广拉格朗日乘子法设计实现了新型安全强化学习算法.在工业油泵案例上的对比实验表明,该算法生成的控制器在安全性和最优性上均超越了现有同类算法.在进一步评估中,所生成神经网络控制器以90%的概率通过了严格形式化验证;同时,与理论最优控制器相比实现了低至2%的最优目标值损失.所提方法有望推广至更多应用场景,实例研究的方案有望为安全智能控制和形式化验证领域其他学者提供借鉴.     

VIBRATION CONTROL OF A CLASS OF GENERALIZED GRADIENT SYSTEMS

The suppression of oscillations in a class of generalized gradient systems using nonlinear dynamic output feedback is investigated. A class of controllers is considered which, in addition to a linear dynamic component, possess several types of nondynamic nonlinearities. Frequency domain conditions on the transfer matrix of the controller's linear component are presented that ensure the convergence of all closed-loop solutions to an equilibrium point in state space, thus eliminating the occurrence of sustained oscillations. Practically important technical applications include a.o. the set point control of mechanical systems described by the Euler–Lagrange equations and their equivalent Hamiltonian formulation. The obtained results constitute a systems theoretical basis for a new method of nonlinear vibration controller design.     

A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances

This paper is concerned with the state feedback control problem for a class of discrete-time stochastic systems involving sector nonlinearities and mixed time-delays. The mixed time-delays comprise both discrete and distributed delays, and the sector nonlinearities appear in the system states and all delayed states. The distributed time-delays in the discrete-time domain are first defined and then a special matrix inequality is developed to handle the distributed time-delays within an algebraic framework. An effective linear matrix inequality (LMI) approach is proposed to design the state feedback controllers such that, for all admissible nonlinearities and time-delays, the overall closed-loop system is asymptotically stable in the mean square sense. Sufficient conditions are established for the nonlinear stochastic time-delay systems to be asymptotically stable in the mean square sense, and then the explicit expression of the desired controller gains is derived. A numerical example is provided to show the usefulness and effectiveness of the proposed design method.     

高阶不确定非线性系统线性状态反馈自适应控制设计

研究了一类控制系数未知的高阶不确定非线性系统的自适应镇定控制设计. 尽管该问题已经得到解决,但是所设计的控制器是非线性反馈形式,较为复杂. 与现有文献不同,本文通过综合运用增加幂积分技术和切换自适应控制方法,给出了该控制问题的更为简单且易于实现的新型线性反馈控制器,使得系统状态有界且最终趋于零. 值得指出的是,与切换自适应控制文献相比,本文所研究的非线性系统具有更严重的不确定/未知性和更强的非线性,这主要体现在未知的系统控制系数和更高的系统幂次中.     

Stabilization Criteria for Singular Fuzzy Systems With Random Delay and Mixed Actuator Failures

The problem of reliable sampled‐data control design for uncertain singular fuzzy system with randomly occurring delay and nonlinear actuator failures is studied in this paper. The fault model is composed of two parts in which, linear part stands for the gain missing of actuators that vary with the true control input linearly, while the nonlinear part indicates some bounded nonlinear variation. Moreover, the time delay which encountering in the proposed controller is assumed to be randomly varying and satisfies Bernoulli distributed probabilities. By constructing a proper time‐dependent Lyapunov functional, some novel sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for the existence of robustly stochastically stabilizing reliable sampled‐data controllers. Two simulation examples are given to demonstrate the effectiveness of the proposed method.     

不确定非线性系统自适应动态事件触发输出反馈镇定

本文研究了一类不确定非线性系统的动态事件触发输出反馈镇定问题. 显著不同的是系统具有依赖于不可测状态的增长且增长率为输出的未知多项式. 尽管已有一些连续自适应控制器, 但需要巧妙融合非线性状态观测器、系统未知性的动态补偿以及非线性的抵御, 因此这些控制器具有一定的脆弱性, 不能平凡地拓展到不连续情形 (采样误差导致). 为此, 首先通过引入动态高增益和基于高增益的观测器来分别抵御未知增长率和重构系统不可测状态. 进而, 意识到静态事件触发机制的无效性, 通过引入动态事件触发机制, 成功设计出了事件触发输出反馈控制器, 确保了系统状态的全局有界性和收敛性. 数值仿真验证了所设计控制器的有效性.