Dynamical properties of an adaptive control system with a nonlinear reference model. II

We consider the problem of constructing an adaptive control system with nonlinear reference model for a low order nonstationary dynamical object with a nonlinear actuator. We show the structure, analysis, and mathematical modeling results for the adaptive control system.     

基于LS-SVM飞机大迎角动态辨识方法研究

确定飞机在大迎角飞行状态时的动态系统参考模型,对于支持飞机控制系统的稳定性和控制增稳设计有着重要的影响。为了精确描述飞机大迎角机动非定常、非线性数学模型,提出利用最小二乘支持向量机(LS-SVM)对飞机大迎角状态飞行时的非线性动态系统进行辨识,利用网络搜索和交叉验证的方法选择支持向量机参数,并建立了飞机大迎角动力学参考模型,仿真验证显示方法具有较强的泛化能力和较高的辨识效果。     

Optimal control based on a preposteriori estimates of set-membership uncertainty

We consider the optimal control problem for a linear nonstationary dynamical system under set-membership uncertainty with a combined discrete closable loop. Our solution is based on an a preposteriori analysis of the surveillance and control subsystems. Based on the surveillance subsystem analysis, we introduce closures and construct an optimal closable program (a preposteriori analysis of the control subsystem) that yields a positional solution for the optimal control problem. We present an optimal control quasi-realization method with optimal estimators and a real-time controller. We illustrate our results with an example.     

Hidden control neural architecture modeling of nonlinear timevarying systems and its applications

The application of neural networks to modeling time-invariant nonlinear systems has been difficult for complicated nonstationary signals, such as speech, because the networks are unable to characterize temporal variability. This problem is addressed by proposing a network architecture, called the hidden control neural network (HCNN), for modeling signals generated by nonlinear dynamical systems with restricted time variability. The mapping implemented by a multilayered neural network is allowed to change with time as a function of an additional control input signal. The network is trained using an algorithm based on ;backpropagation' and segmentation algorithms for estimating the unknown control together with the network's parameters. Application of the network to the segmentation and modeling of a signal produced by a time-varying nonlinear system, speaker-independent recognition of spoken connected digits, and online recognition of handwritten characters demonstrates the ability of the HCNN to learn time-varying nonlinear dynamics and its potential for high-performance recognition of signals produced by time-varying sources.     

Input-to-state stability of switched systems and switching adaptive control

In this paper we prove that a switched nonlinear system has several useful input-to-state stable (ISS)-type properties under average dwell-time switching signals if each constituent dynamical system is ISS. This extends available results for switched linear systems. We apply our result to stabilization of uncertain nonlinear systems via switching supervisory control, and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide ISS properties with respect to the estimation errors. Detailed illustrative examples are included.     

基于T-S模型的Chua混沌系统模糊变结构控制

针对Chua混沌系统这一复杂的非线性系统给出一种基于T-S模型的模糊变结构控制律设计。首先采用T-S模糊动态模型描述非线性系统,得到混沌系统的全局模糊模型;然后采用Lyapunov稳定性理论设计出确保模糊动态模型全局渐近稳定的变结构控制器,将模糊控制与成熟的线性变结构控制相结合,来解决非线性系统控制问题。仿真验证了方案的有效性。模糊控制器简单,规则少。     

Multiple model-based reinforcement learning

We propose a modular reinforcement learning architecture for nonlinear, nonstationary control tasks, which we call multiple model-based reinforcement learning (MMRL). The basic idea is to decompose a complex task into multiple domains in space and time based on the predictability of the environmental dynamics. The system is composed of multiple modules, each of which consists of a state prediction model and a reinforcement learning controller. The "responsibility signal," which is given by the softmax function of the prediction errors, is used to weight the outputs of multiple modules, as well as to gate the learning of the prediction models and the reinforcement learning controllers. We formulate MMRL for both discrete-time, finite-state case and continuous-time, continuous-state case. The performance of MMRL was demonstrated for discrete case in a nonstationary hunting task in a grid world and for continuous case in a nonlinear, nonstationary control task of swinging up a pendulum with variable physical parameters.     

The Lie algebra of a nonlinear dynamical system and its application to control

Using a recently introduced Lie algebra associated with a nonlinear system, several new results in dynamical systems and control theory are obtained. In particular, we show that the solutions carry the structure of the associated Lie group. A number of stability and boundedness results are given and a generalization of classical modal control is developed.     

基于在线支持向量回归的非线性模型预测控制方法

针对非线性模型预测控制中离线模型难以适应非线性对象实时变化的缺点, 提出一种基于在线支持向量回归的非线性模型预测控制方法. 该方法通过在线支持向量回归离线训练与在线学习相结合的方式, 建立具有在线校正特性的预测模型, 同时采用最速下降原理滚动优化非线性模型预测控制的目标函数, 求得多步控制量. 通过对非线性对象的控制结果表明, 所提出方法有效且具有良好的自适应性.

     

Nonstationary discrete-time deterministic and stochastic control systems: Bounded and unbounded cases

This paper is about nonstationary nonlinear discrete-time deterministic and stochastic control systems with Borel state and control spaces, with either bounded or unbounded costs. The control problem is to minimize an infinite-horizon total cost performance index. Using dynamic programming arguments we show that, under suitable assumptions, the optimal cost functions satisfy optimality equations, which in turn give a procedure to find optimal control policies. We also prove the convergence of value iteration (or successive approximations) functions. Several examples illustrate our results under different sets of assumptions.     

New algorithm for observer error linearization with a diffeomorphism on the outputs

In this paper, we give the necessary and sufficient conditions that guarantee the existence of a diffeomorphism which allows one to transform a multi-output nonlinear dynamical system into a normal observable canonical form. In particular, we propose an algorithm that permits one to derive such diffeomorphism. The main feature of the canonical form is that it is obtained by allowing a diffeomorphism on the outputs and it also allows one to design an observer with linear error dynamics. We first consider multi-output nonlinear dynamical system without inputs. We then extend the results obtained to multi-output nonlinear dynamical system with inputs.     

Static sliding-motion phenomena in dynamical systems

We present a new type of sliding motion which results from a novel choice of the sliding surfaces. We define these sliding surfaces such that they become explicitly dependent on the outputs of the discontinuous block. We prove under this design, a special sliding mode characterises the system dynamics, which we name static sliding mode, because it occurs along a static contour of the closed-loop system. We give constructive conditions when this dynamical behavior begins and continues its motion in a static sliding mode. We show and simulate a control application in robust stabilization of nonlinear systems.     

On partial detectability of the nonlinear dynamic systems

Conditions were obtained under which the uniform stability (uniform asymptotic stability) in one part of the variables of the zero equilibrium position of the nonlinear nonstationary system of ordinary differential equations implies the uniform stability (uniform asymptotic stability) of this equilibrium position relative to another, larger part of variables. Conditions were also obtained under which the uniform stability (uniform asymptotic stability) in one part of variables of the “partial” (zero) equilibrium position of the nonlinear nonstationary system of ordinary differential equations implies the uniform stability (uniform asymptotic stability) of this equilibrium position. These conditions complement a number of the well-known results of the theory of partial stability and partial detectability of the nonlinear dynamic systems. Application of the results obtained to the problems of partial stabilization of the nonlinear control systems was considered.     

Synchronization of complex networks with coupling delays via adaptive pinning intermittent control

The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.     

Nonlinear modelling and control of the flow over aerofoils using CFD simulations

A simulation based approach for nonlinear dynamical modelling and feedback control of the drag to lift ratio for aerofoils is investigated through case studies involving NACA 23012, ag13 and b737a aerofoils. The flow around the aerofoils is studied via numerical solutions of the 2D Navier–Stokes (NS) equations. A standard computational fluid dynamics (CFD) solver is extended to be able to measure desired feedback values and to apply a control input to the flow field. The proposed modelling and control approach is based on first determining the measurement points and injection points on the aerofoil for the control input. Then, to estimate the dynamical model, some input–output data are collected by injecting a chirp input flow to the field and saving the measurement data. Next a Hammerstein–Wiener (HW) type nonlinear dynamical model of the flow field is estimated using system identification. For control design, the nonlinear part of the model is eliminated by means of inverse functions, followed by the application of automated tuning methods to the linear part to obtain the closed-loop system. The results show that the designed feedback control system can reduce the drag to lift ratio considerably as compared to the unactuated case.     

Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input

Linear quadratic regulator(LQR) and proportional-integral-derivative(PID) control methods, which are generally used for control of linear dynamical systems, are used in this paper to control the nonlinear dynamical system. LQR is one of the optimal control techniques, which takes into account the states of the dynamical system and control input to make the optimal control decisions.The nonlinear system states are fed to LQR which is designed using a linear state-space model. This is simple as well as robust. The inverted pendulum, a highly nonlinear unstable system, is used as a benchmark for implementing the control methods. Here the control objective is to control the system such that the cart reaches a desired position and the inverted pendulum stabilizes in the upright position. In this paper, the modeling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using PID controller and LQR have been presented for both cases of without and with disturbance input. The Matlab-Simulink models have been developed for simulation and performance analysis of the control schemes. The simulation results justify the comparative advantage of LQR control method.     

A new approach to robust control of hybrid systems over infinitetime

The paper presents a new approach to output feedback robust control synthesis problems for hybrid dynamical systems. The hybrid system under consideration is a composite of a continuous plant and a discrete-event controller. An output feedback H^∞-control problem on an infinite time interval is considered. The main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a Riccati algebraic equation of the H^∞-filtering type. These results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control     

Box invariance in biologically-inspired dynamical systems

A dynamical system is box invariant if there exists a box-shaped positively invariant region. We show that box invariance can be checked in cubic time for linear and affine systems, and that it remains decidable for classes of nonlinear systems of interest (with polynomial structure). We present results on the robustness of box invariance for linear systems using spectral properties of Metzler matrices. We also present sufficient conditions for establishing box invariance of switched and hybrid systems. In general, we argue that box invariance is a characteristic of many biologically-inspired dynamical models.     

确定学习与基于数据的建模及控制

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.