基于混合系统模型的非线性系统最大可控不变集求解

针对非线性系统线性化在状态约束下最优鲁棒控制求解问题,提出了一种基于混合系统的分段仿射系统(PWA)建模,通过多次优化迭代的方法求解系统的最大鲁棒控制不变集的方法,并求得不变集内的最优控制器,解决系统的状态约束问题.通过一个非线性系统实例进行建模、仿真,证明了本方法的可行性.     

空中机器人的混合系统建模与优化控制

针对空中机器人(小型无人直升机)非线性系统最优控制求解问题,提出了一种解决方法,该方法基于混合系统建模、降阶,求得系统约束下的状态最大可控不变集,在该集合内通过混合整数二次规划(MIQP)的方法以求得系统的最优控制。最后通过一个实际的样机进行建模、仿真,证明了本方法的可行性与有效性。     

基于混合系统与终端不变集约束的混合整数规划优化控制

首先给出了混合系统的混合逻辑动态(Mixed logic dynamic, MLD)模型建模; 提出了基于终端不变集约束的混合整数规划优化控制, 通过建立Lyapunov函数证明了该方法的可行性; 利用混合整型二次规划(Mixed-integer quadratic programming, MIQP)的方法对终端不变集约束混合系统的优化控制进行求解; 最后通过一个实例进行建模、仿真, 证明了本方法的可行性与优越性.     

空中机器人多模态控制研究

研究空中机器人(小型无人直升机)的约束优化控制问题:对小型无人直升机的非线性系统模型进行系统约简,建立混合系统的分段仿射系统模型,针对该问题求解中遇到的在线计算量大,不利于实时控制等问题,提出利用多参数二次规划离线计算出混合系统最优控制律的方法.基于多参数二次规划的方法,在最大可控不变集的可行域内进行显式优化控制器设计,通过反向动态规划,求出对应每一步的优化解,从而求得不变集作为可行域的优化解.通过实际参数的系统仿真,证明了方法的有效性.     

基于反馈线性化系统的非线性鲁棒控制μ方法

对于可状态反馈线性化的一类仿射非线性系统，本文提出一种非线性鲁棒控制的μ方法。首先给出非线性鲁棒控制问题，然后利用状态反馈线性化方法，把非线性系统线性化，并利用μ综合方法，对线性化系统进行鲁棒控制器的设计，最后通过回代构成非线性鲁棒控制系统。     

一类干扰有界约束非线性系统的鲁棒模型预测控制

针对一类干扰有界约束非线性系统设计了基于控制不变集切换策略的鲁棒模型预测控制算法.针对非线性系统线性化之后的结果,给出了平衡点的非线性标称系统控制不变集的计算方法.然后在考虑线性化误差和加性有界干扰影响的基础上,构造了平衡点附近最小鲁棒正不变集.结合不变集切换策略和Tube不变集控制方法,提出了干扰有界约束非线性系统的不变集切换策略.最后将该算法应用到一类典型的非线性化工过程连续搅拌反应釜(CSTR)中,仿真结果验证了算法的有效性.     

基于微粒群优化算法的非线性系统PWA多模型建模

针对复杂非线性系统,将微粒群优化(PSO)算法与多模型建模相结合,设计了一种基于PSO算法的非线性系统分段仿射(PWA)多模型建模算法。该算法将PWA多模型建模问题转化为混合整数二次规划（MIQP）问题,并基于PSO算法对其进行优化求解。在求解的过程中,采用分层优化求解方法,有效降低优化问题的维数,减小了陷入局部最优的概率,并通过仿真验证了该算法的有效性。     

基于输入输出线性化的连续系统非线性模型预测控制

非线性约束预测控制关键是求得可行性优化解. 输入输出反馈线性化是非线性控制一种常用的方法, 其系统的初始线性输入约束转化成非线性基于状态的约束, 因而无法采用常规的二次规划(QP)求解优化问题. 针对连续状态空间模型系统, 本文提出迭代二次规划方法来寻求非线性优化解. 为了保证算法的收敛性, 系统加入另外一种迭代算法来保证其在整个预测时域上能得到可行解. 仿真控制结果表明了该方法的有效性.     

混合系统在matlab环境下的建模和仿真

混合系统是集连续动态系统和离散事件为一体的复杂动态系统,是近年来控制理论研究领域的热门课题.由于混合系统既含连续变量义含离散事件,给处理这类系统带来了复杂性.一般混合系统建立模方法有:混合自动机,混合petri,时段演算及其扩展等模型.在概述混合系统概念与特点的基础上,介绍了混合系统研究中的建模与仿真问题.结合超市冰柜系统用混合自动机建模,并用MATLAB中的SIMULINK和STATEFLOW进行仿真.仿真结果表明效果很好,为系统分析和设计提供了有力的工具.     

一类混杂系统建模和优化控制的研究

为解决混杂系统优化控制的计算复杂性问题，针对结合逻辑规则的工业过程混杂模型，采用结合约束程序的混合整数非线性规划算法，求解这种混杂模型的优化控制。计算实例表明，通过混杂建模方法，可以充分利用工业对象的机理模型以及操作工经验或专家经验，建立系统的更精确模型；结合约束程序混合整数非线性规划算法可以较迅速地求解混杂模型优化控制问题，从而使该方法可以用于工业过程实时控制中。     

Computation of maximal safe sets for switching systems

The problem of determining maximal safe sets and hybrid controllers is computationally intractable because of the mathematical generality of hybrid system models. Given the practical and theoretical relevance of the problem, finding implementable procedures that could at least approximate the maximal safe set is important. To this end, we begin by restricting our attention to a special class of hybrid systems: switching systems. We exploit the structural properties of the graph describing the discrete part of a switching system to develop an efficient procedure for the computation of the safe set. This procedure requires the computation of a maximal controlled invariant set. We then restrict our attention to linear discrete-time systems for which there is a wealth of results available in the literature for the determination of maximal controlled invariant sets. However, even for this class of systems, the computation may not converge in a finite number of steps. We then propose to compute inner approximations that are controlled invariant and for which a procedure that terminates in a finite number of steps can be obtained. A tight bound on the error can be given by comparing the inner approximation with the classical outer approximation of the maximal controlled invariant set. Our procedure is applied to the idle-speed regulation problem in engine control to demonstrate its efficiency.     

约束分段仿射系统的鲁棒最小时间控制

针对一类有界附加扰动的分段仿射系统,提出了一种离线低复杂性的鲁棒预测控制方法-鲁棒最小时间控制.首先计算系统的最大鲁棒正不变集和相关的局部稳定控制律,然后基于最大鲁棒正不变集通过多参数规划离线迭代计算系统的鲁棒一步集,得到的最小时间控制器覆盖最大鲁棒可稳定集.提出的鲁棒最小时间控制确保系统状态在最小时间内进入鲁棒正不变...     

基于编码控制机制的混杂系统半全局实用镇定

混杂系统的鲁棒镇定是复杂控制系统领域的重要研究课题之一.提出了一种编码机制下的混杂控制策略,它能有效地克服传统连续反馈控制或不连续反馈控制在处理局部鲁棒镇定平衡点或不变集问题中的局限性,获得更好的控制效果.首先针对编码状态反馈,构建了一般的混杂系统模型来描述编码状态反馈作用下非线性系统的闭环系统模型.然后,基于逆Lyapunov定理开展了非线性系统的混杂控制鲁棒性分析,提出了闭环混杂系统的半全局实用渐近稳定性判据.最后,结合一个经典控制问题来说明所提出控制策略的优越性.     

On the computation of convex robust control invariant sets for nonlinear systems

In this paper we provide a method to compute robust control invariant sets for nonlinear discrete-time systems. A simple criterion to evaluate if a convex set in state space is a robust control invariant set for a nonlinear uncertain system is presented. The criterion is employed to design an algorithm for computing a polytopic robust control invariant set. The method is based on the properties of DC functions, i.e. functions which can be expressed as the difference of two convex functions. Since the elements of a wide class of nonlinear functions have DC representation or, at least, admit an arbitrarily close approximation, the method is quite general. The algorithm requires relatively low computational resources.     

Robust MPC of constrained discrete-time nonlinear systems based on approximated reachable sets

A robust MPC for constrained nonlinear systems with uncertainties is presented. Outer bounds of the reachable sets of the system are used to predict the evolution of the system under uncertainty. A method that uses zonotopes to represent the approximated reachable sets is proposed. The closed-loop system is ultimately bounded thanks to a contractive constraint that drives the system to a robust invariant set.     

Offline Robust Model Predictive Control for Lipschitz Non‐Linear Systems Using Polyhedral Invariant Sets

In this paper the concept of maximal admissible set (MAS) for linear systems with polytopic uncertainty is extended to non‐linear systems composed of a linear constant part followed by a non‐linear term. We characterize the maximal admissible set for the non‐linear system with unstructured uncertainty in the form of polyhedral invariant sets. A computationally efficient state‐feedback RMPC law is derived off‐line for Lipschitz non‐linear systems. The state‐feedback control law is calculated by solving a convex optimization problem within the framework of linear matrix inequalities (LMIs), which leads to guaranteeing closed‐loop robust stability. Most of the computational burdens are moved off‐line. A linear optimization problem is performed to characterize the maximal admissible set, and it is shown that an ellipsoidal invariant set is only an approximation of the true stabilizable region. This method not only remarkably extends the size of the admissible set of initial conditions but also greatly reduces the on‐line computational time. The usefulness and effectiveness of the method proposed here is verified via two simulation examples.     

Computation of discriminating kernel and robust capture basin with regulation map by interval methods

This paper proposes a novel algorithm that characterizes the robust capture basin and the discriminating kernel for constrained nonlinear systems with uncertainties based on viability theory. For nonlinear systems with constrained inputs and bounded uncertainties, the viability kernel is the largest set of states possessing a possibility to be viable in a set, and the capture basin is the largest set of states possessing a possibility to reach a target in a finite time, and keeping viable in a set before reaching the target. However, in the viability theory, both control and uncertainty in a parameterized system are considered as parameters: the discriminating kernel and the proposed robust capture basin link viability theory with robust control, which take both control and uncertainties into account. For the constrained uncertain nonlinear systems, the discriminating kernel is the largest set of states that is robust invariant in a set with proper control, and the robust capture basin is the largest set of states reaching their target in finite time with proper control despite of uncertainties and keeping viable in a set before reaching the target. Furthermore, we map all the states to optimal regulatory control such that the systems are regulated by a regulation map. To compute the robust capture basin and the discriminating kernel, we use interval methods to provide guaranteed solutions. The proposed algorithms in this paper approximate an outer approximation of the minimum reachable target and inner approximations of the robust capture basin and the discriminating kernel in a guaranteed way.