Stabilization and disturbance rejection for the wave equation

We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function of the complex variable and may contain a single pole at the origin and a pair of complex conjugate poles on the imaginary axis, provided that the residues corresponding to these poles are nonnegative; the rest of the transfer function is required to be a strictly positive real function. We then show that depending on the location of the pole on the imaginary axis, the closed-loop system is asymptotically stable. We also consider the case where the output of the controller is corrupted by a disturbance and show that it may be possible to attenuate the effect of the disturbance at the output if we choose the controller transfer function appropriately. We also present some numerical simulation results which support this argument     

An exponential stability result for the wave equation

We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize this system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function which consists of a strictly positive real function and some poles on the imaginary axis. We then show that under some conditions the closed-loop system is exponentially stable.     

Nonlinear control of a coupled PDE/ODE system modeling a switched power converter with a transmission line

We consider an infinite dimensional system modeling a boost converter connected to a load via a transmission line. The governing equations form a system coupling the telegraph partial differential equation with the ordinary differential equations modeling the converter. The coupling is given by the boundary conditions and the nonlinear controller we introduce. We design a nonlinear saturating control law using a Lyapunov function for the averaged model of the system. The main results give the well-posedness and stability properties of the obtained closed loop system.     

Discrete-time Lyapunov-based small-gain theorem for parameterized interconnected ISS systems

Input-to-state stability (ISS) of a feedback interconnection of two discrete-time ISS systems satisfying an appropriate small gain condition is investigated via the Lyapunov method. In particular, an ISS Lyapunov function for the overall system is constructed from the ISS Lyapunov functions of the two subsystems. We consider parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used in controller design for a sampled-data system.     

Extended LQG self-tuning controller in a mixed background

We consider the problem of constructing a LQG-based adaptive controller so that the control system can track a deterministic command signal and simultaneously regulate stochastic disturbances. A new measure for mixed signal in the feedback loop is first introduced. Then a generalized cost function is formulated and the optimal ‘extended LQG controller’ can be constructed by solving a diophantine equation. Based on the extended LQG design, a self-tuning controller can be constructed. System tracking performance under ergodic process noise is analysed in detail and better results are obtained. Finally, the optimal tracking performance is attained if the parameter estimates converge to their true values.     

A nonlinear quadrotor trajectory tracking controller with disturbance rejection

This paper addresses the problem of designing and experimentally validating a controller for steering a quadrotor vehicle along a trajectory, while rejecting constant force disturbances. The proposed solution consists of a nonlinear adaptive state feedback controller that asymptotically stabilizes the closed-loop system in the presence of force disturbances. We consider two methods of angular actuation for the quadrotor, angular velocity and torque, and ensure that the actuation does not grow unbounded as a function of the position error. The constant force disturbance is estimated through the use of a sufficiently smooth projector operator. A prototyping and testing architecture, developed to streamline the implementation and the tuning of the controller, is also described. Experimental results are presented to demonstrate the performance and robustness of the proposed controller.     

输入饱和与姿态受限的四旋翼无人机反步姿态控制

本文针对四旋翼无人机研究了鲁棒反步姿态控制策略.由于四旋翼无人机结构复杂,其非线性数学模型难以精确建立,因此在控制器设计过程中需要综合考虑模型不确定性、未知外部干扰、输入饱和以及姿态受限等因素.针对模型中的不确定项,使用神经网络进行逼近;对于外部未知干扰,使用非线性干扰观测器进行补偿;使用双曲正切函数逼近饱和函数,解决输入饱和问题;同时使用界限Lyapunov函数设计控制器,确保姿态满足限制条件.最后,设计四旋翼无人机反步姿态控制器,并根据Lyapunov稳定性定理证明了闭环控制系统的有界稳定.仿真结果表明了所研究控制方法的有效性.     

A robust Markov game controller for nonlinear systems

This paper proposes a reinforcement learning (RL)-based game-theoretic formulation for designing robust controllers for nonlinear systems affected by bounded external disturbances and parametric uncertainties. Based on the theory of Markov games, we consider a differential game in which a ‘disturbing’ agent tries to make worst possible disturbance while a ‘control’ agent tries to make best control input. The problem is formulated as finding a min–max solution of a value function. We propose an online procedure for learning optimal value function and for calculating a robust control policy. Proposed game-theoretic paradigm has been tested on the control task of a highly nonlinear two-link robot system. We compare the performance of proposed Markov game controller with a standard RL-based robust controller, and an H_∞ theory-based robust game controller. For the robot control task, the proposed controller achieved superior robustness to changes in payload mass and external disturbances, over other control schemes. Results also validate the effectiveness of neural networks in extending the Markov game framework to problems with continuous state–action spaces.     

Lyapunov-based switching control of nonlinear systems using high-gain observers

We consider output feedback stabilization of uniformly observable uncertain nonlinear systems when the uncertain parameters belong to a known but comparably large compact set. In a previous paper, we proposed a new logic-based switching control to improve the performance of continuous high-gain-observer-based sliding mode controllers. Our main goal here is to show that similar techniques can be exploited for solving challenging control problems for a more general class of uncertain nonlinear systems. We require neither the sign of the high-frequency gain to be known nor the system to be minimum-phase. The key idea is to split the set of parameters into smaller subsets, design a controller for each of them, and switch the controller if, after a dwell-time period, the derivative of the Lyapunov function does not satisfy a certain inequality. A high-gain observer is used to estimate the derivatives of the output as well as the derivative of the Lyapunov function. Another goal of this paper is to introduce a switching strategy that uses on-line information to decide on the controller to switch to, instead of using a pre-sorted list as in our previous work. The new strategy can improve the transient performance of the system.     

Robust Adaptive Output Control of Uncertain Nonlinear Plants With Unknown Backlash Nonlinearity

In this note, we consider a class of uncertain dynamic nonlinear systems preceded by unknown backlash nonlinearity. The control design is achieved by introducing a smooth inverse function of the backlash and using it in the controller design with backstepping technique. For the design and implementation of the controller, no knowledge is assumed on the unknown system parameters. It is shown that the proposed controller not only can guarantee stability, but also transient performance     

Unfalsifying Pole Locations Using a Fading Memory Cost Function

Given a feedback control system with an unknown plant, the problem of choosing a stabilizing controller is considered. Working within the framework of unfalsified adaptive control, we consider a finite‐dimensional linear time invariant system as a special case of the standard adaptive configuration. A fading memory cost function is presented in which the influence of older data is reduced exponentially. With this cost function, the location of the poles can be detected with only input‐output data. Compared with existing results, the cost function can detect changes affecting stability sooner and be used in adaptive switching control to improve the performance of controller switching.     

Single-layer economic model predictive control for periodic operation

In this paper we consider periodic optimal operation of constrained periodic linear systems. We propose an economic model predictive controller based on a single layer that unites dynamic real time optimization and control. The proposed controller guarantees closed-loop convergence to the optimal periodic trajectory that minimizes the average operation cost for a given economic criterion. A priori calculation of the optimal trajectory is not required and if the economic cost function is changed, recursive feasibility and convergence to the new periodic optimal trajectory is guaranteed. The results are demonstrated with two simulation examples, a four tank system, and a simplified model of a section of Barcelona's water distribution network.     

Controller synthesis for safety and reachability via approximate bisimulation

In this paper, we consider the problem of controller design using approximately bisimilar abstractions with an emphasis on safety and reachability specifications. We propose abstraction-based approaches to controller synthesis for both types of specifications. We start by synthesizing a controller for an approximately bisimilar abstraction. Then, using a concretization procedure, we obtain a controller for our initial system that is proved “correct by design”. We provide guarantees of performance by giving estimates of the distance of the synthesized controller to the maximal (i.e., the most permissive) safety controller or to the time-optimal reachability controller. Finally, we use these techniques, combined with discrete approximately bisimilar abstractions of switched systems developed recently, for switching controller synthesis.     

Feedback stabilisation of an Euler–Bernoulli beam with the boundary time-delay disturbance

In this paper, we consider the feedback stabilisation of an Euler–Bernoulli beam with the boundary time-delay disturbance. Due to unknown time-delay coefficient, the system might be exponentially increasing at the lack of control. We design the feedback control law based on Lyapunov function method. Different from usual use of Lyapunov function method, our approach is to combine the construction of Lyapunov functionals with the controller design, which will guarantee the system energy function decays exponentially. In this procedure, we deduce the inequality equations satisfied by the system parameters. We prove the well-posedness of the corresponding closed-loop system by using semigroup theory and the inequality equations are solvable. Moreover, the exponential decay rate of the system is estimated. In addition, some numerical simulations are also presented to support the obtained results.     

基于动力学等价的一种通用控制器的设计

在动力学运动方程的基础上,构建了一种系统状态观测器,该观察器能够精确估计被控对象的位置、速度和加速度而无需知道其数学模型。在此基础上,设计了一种通用控制器,该控制器通过系统运动的位置、速度和加速度的负反馈作用,把原被控对象的输出轨迹引导控制到期望的系统输出轨迹,能提高系统的控制品质和鲁棒性能。分析了PID控制器、内模控制器、状态控制器、预测控制器和鲁棒控制器的算法特性,指出这些控制器与所设计的通用控制器在动力学意义上具有等价性。     

DoS干扰攻击下的信息物理系统状态反馈稳定

基于网络的工业控制系统作为信息物理系统(CPSs)的一种重要应用正迅猛发展.然而,近年来针对工业控制系统的恶意网络攻击引起了人们对CPS安全问题的广泛关注.拒绝服务(DoS)干扰攻击作为CPS中最容易发生的攻击方式得到了深入研究.对此,提出一种能量受限的、周期的DoS干扰攻击模型,攻击的目的是增大无线信道发生数据包随机丢包的概率.基于一类CPS简化模型,考虑CPS中传感器与控制器(S-C)之间无线信道同时存在DoS干扰攻击和固有随机数据包丢失的情况,采用状态反馈,基于随机Lyapunov函数和线性矩阵不等式方法得到可以保证系统稳定的充分条件,并利用系统稳定的充分条件和锥补线性化算法设计控制器.最后,通过两个数值仿真例子验证所提出控制策略的有效性.     

H∞ ALMOST DISTURBANCE DECOUPLING FOR MIMO BILINEAR SYSTEMS

The H_∞ almost disturbance decoupling problem is considered. In this paper, a nonlinear design is proposed to find a state feedback controller for bilinear systems. The closed‐loop system is internally stable and achieves disturbance attenuation in nonlinear H_∞ sense. We defined a special form of Lyapunov function, which is constructed in terms of one or a set of positive definite constant matrices. If, except of the origin of system, the corresponding polynomial of the positive definite matrix (or several polynomials relevant to the positive definite constant matrices) has (have) no zero on a given subset of state space, then we can construct a controller to solve our problem. It is found that the controller structure could be complicated, but is feasible in computation and may require optimization technique to search the solution. We consider both SIMO and MIMO cases with illustrated examples.     

Decentralized and adaptive control of multiple nonholonomic robots for sensing coverage

This work deals with decentralized control of multiple nonholonomic mobile sensors for optimal coverage of a given area for sensing purposes. We assume a density function over the region to be covered, which can be viewed as a probability density of the phenomena to be sensed. The density function is unknown but assumed to be linearly parameterized with unknown parameter weights. We consider a second‐order dynamic model for the mobile agents and derive decentralized adaptive control laws to achieve optimal coverage of the region. We then consider the case where the dynamic model of the agents are not fully known, and then develop parameter adaptation laws to achieve the optimal coverage objective. We test the derived algorithms using simulations and compare our proposed controllers with kinematics‐based controllers. We find that the feedback control design based on the dynamic model performs significantly better than controllers solely relying on kinematic models. Furthermore, for the unknown dynamics case, our controller outperforms the nonadaptive controller with poor initial parameter estimates.     

Compensating for a multisinusoidal disturbance based on Youla–Kucera parametrization

We consider the problem of compensation for a multisinusoidal disturbance for a linear stationary system with a given nominal control law. We consider the general structure of a controller that lets one use arbitrary algorithms for identification of disturbance parameters satisfying certain assumptions. The proposed structure is based on the Youla–Kucera parametrization and lets one compensate for a disturbance while preserving nominal behavior of a control system with respect to the reference.     

A control design method for a class of switched linear systems

In this note we consider the stability properties of a system class that arises in the control design problem of switched linear systems. The control design we are studying is based on a classical pole-placement approach. We analyse the stability of the resulting switched system and develop analytic conditions which reduce the complexity of the stability problem. We further consider two special cases for which strongly simplified conditions are obtained that support the analytic controller design.