线性混杂系统优化控制的Monte Carlo统计预测方法

针对含扩散项的线性混杂切换系统优化控制问题, 为降低优化求解的计算复杂性, 提出了Monte Carlo统计预测方法. 首先通过数值求解技术把连续时间优化控制问题转化为离散时间的Markov决策过程问题; 然后在若干有限状态子空间内, 利用反射边界技术来求解相应子空间的最优控制策略; 最后根据最优控制策略的结构特性, 采用统计预测方法来预测出整个状态空间的最优控制策略. 该方法能有效降低求解涉及大状态空间及多维变量的线性混杂切换系统优化控制的计算复杂性, 文末的仿真结果验证了方法的有效性.     

线性矩阵方程异类约束最小二乘解的迭代算法

多矩阵变量线性矩阵方程(LME)约束解的计算问题在参数识别、结构设计、振动理论、自动控制理论等领域都有广泛应用。本文借鉴求线性矩阵方程(LME)同类约束最小二乘解的迭代算法,通过构造等价的线性矩阵方程组,建立了求多矩阵变量LME的一种异类约束最小二乘解的迭代算法,并证明了该算法的收敛性。在不考虑舍入误差的情况下,利用该算法不仅可在有限步计算后得到LME的一组异类约束最小二乘解,而且选取特殊初始矩阵时,可求得LME的极小范数异类约束最小二乘解。另外,还可求得指定矩阵在该LME的异类约束最小二乘解集合中的最佳逼近解。算例表明,该算法是有效的。     

Towards a Hybrid Dynamic Logic for Hybrid Dynamic Systems

We introduce a hybrid variant of a dynamic logic with continuous state transitions along differential equations, and we present a sequent calculus for this extended hybrid dynamic logic. With the addition of satisfaction operators, this hybrid logic provides improved system introspection by referring to properties of states during system evolution. In addition to this, our calculus introduces state-based reasoning as a paradigm for delaying expansion of transitions using nominals as symbolic state labels. With these extensions, our hybrid dynamic logic advances the capabilities for compositional reasoning about (semialgebraic) hybrid dynamic systems. Moreover, the constructive reasoning support for goal-oriented analytic verification of hybrid dynamic systems carries over from the base calculus to our extended calculus.     

精确求解一类动态规划问题的神经网络

根据一类动态规划问题（ＤＦＤＰ）的特点，提出一种能够精确求解此问题的神经网络（ＬＤＰＮＮ）。ＬＤＰＮＮ具有结构简单、易于硬件实现、求解速度快并且能够求得精确最优解等优点，特别适合于大规模动态规划问题的求解。在复杂系统的实时优化与控制等方面具有广阔的应用前景。     

水库优化调度中随机动态规划方法的研究与应用

该文应用随机优化方法，以清江隔河岩水电站为例，对水电站的兴利优化调度问题进行了研究。并用此方法建立了隔河岩水电站随机动态规划水库优化调度模型，计算编制了电站的优化发电调度图。     

Hamilton-Jacobi-Bellman formalism for optimal climate control of greenhouse crop

The paper describes a simplified dynamic model of a greenhouse tomato crop, and the optimal control problem related to the seasonal benefit of the grower. A HJB formalism is used and the explicit form of the Krotov-Bellman function is obtained for different growth stages. Simulation results are shown.     

随机运动目标搜索问题的最优控制模型

提出了Rn空间中做布朗运动的随机运动目标的搜索问题的最优控制模型.采用分析的方法来研究随机运动目标的最优搜索问题,并将原问题转化为由一个二阶偏微分方程(HJB方程)所表示的确定性分布参数系统的等价问题,推导出随机运动目标的最优搜索问题的HJB方程,并证明了该方程的解即是所寻求的最优搜索策略.由此给出了一个计算最优搜索策略的算法和一个实例.     

混合动态系统的混合Petri网（HSPN）模型

针对混合动态系统,提出一种混合Ｐｅｔｒｉ网（ＨＳＰＮ）模型,分析了该模型具有的特点及其运行规则。以冶金加热炉为例,给出了该系统的ＨＳＰＮ模型。     

混合动态系统的联通格式

混合动态系统是指即具有连续动力学特性又具有离散事件驱动性质的一类特殊的动力系统,并且两者之间存在着相互耦合作用.例如在"机群作战战术与防空系统效能"仿真中,有诸如飞机及导弹飞行等的连续事件系统,有探测模型、目视模型、火力击中目标、高炮发射过程等离散事件系统.混合系统有明显的外部特征,如不连续性、自治/受控切换以及自治/受控状态跳变等.为了研究这类系统的动态特性,研究人员开发了各类仿真软件,这些软件一些实现了产生系统模型的功能,一些实现了实时仿真功能,一些实现了实时监控模型运行的功能.而在一个系统仿真过程中需要用到不同软件来完成整个仿真任务,这就要求各个软件之间能够实现数据通信.而混合动态系统的联通格式实现了软件之间的数据共享.     

Differential Dynamic Logic for Hybrid Systems

Hybrid systems are models for complex physical systems and are defined as dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. With the goal of developing a theoretical and practical foundation for deductive verification of hybrid systems, we introduce a dynamic logic for hybrid programs, which is a program notation for hybrid systems. As a verification technique that is suitable for automation, we introduce a free variable proof calculus with a novel combination of real-valued free variables and Skolemisation for lifting quantifier elimination for real arithmetic to dynamic logic. The calculus is compositional, i.e., it reduces properties of hybrid programs to properties of their parts. Our main result proves that this calculus axiomatises the transition behaviour of hybrid systems completely relative to differential equations. In a case study with cooperating traffic agents of the European Train Control System, we further show that our calculus is well-suited for verifying realistic hybrid systems with parametric system dynamics.     

Optimal Control of Switching Surfaces in Hybrid Dynamical Systems

This paper concerns an optimal control problem defined on a class of switched-mode hybrid dynamical systems. The system's mode is changed (switched) whenever the state variable crosses a certain surface in the state space, henceforth called a switching surface. These switching surfaces are parameterized by finite-dimensional vectors called the switching parameters. The optimal control problem is to minimize a cost functional, defined on the state trajectory, as a function of the switching parameters. The paper derives the gradient of the cost functional in a costate-based formula that reflects the special structure of hybrid systems. It then uses the formula in a gradient-descent algorithm for solving an obstacle-avoidance problem in robotics. The work of Boccadoro has been partially supported by MIUR under Grant PRIN 2003090090. The work of Wardi has been partly supported by a grant from the Georgia Tech Manufacturing Research Center. The work of Egerstedt has been partly supported by the National Science Foundation under Grant \# 0237971 ECS NSF-CAREER, and by a grant from the Georgia Tech Manufacturing Research Center.     

Controllability Problems for Differential Gompertzian Dynamic Equations

Control problems are considered in the class of differential Gompertzian dynamics equations. Controllability conditions in the nonstationary case are formulated. A general form of a controller for a stationary system and of a scalar controller are obtained in generalized functions. Criteria for different cases of convex closed control sets are presented.     

动态规划最优控制在非线性系统中的应用

应用一种新的自适应动态最优化方法(ADP),在线实现对非线性连续系统的最优控制。首先应用汉密尔顿函数（Hamilton-Jacobi-Bellman, HJB）求解系统的最优控制,并应用神经网络BP算法对汉密尔顿函数中的性能指标进行估计,进而得到非线性连续系统的最优控制。同时引进一种新的自适应算法,基于参数误差,在线实现对系统进行动态最优求解,而且通过李亚普诺夫方法对参数收敛情况也进行详细的分析。最后,用仿真结果来验证所提出的方法的可行性。     

仿真系统中VC和Matlab混合编程的研究

论述了在构建系统时,高效方便地实现系统的仿真的重要性。对3种VC和Matlab混合编程的方法做了简单介绍,并具体说明了如何使用Madab的mcc命令实现混合编程,给出了编程环境的具体配置及信号采集系统的仿真实现。通过一个实际工程,说明了该方法的具体应用,得到了正确的结果,方便快捷地实现了信号采集系统的仿真。     

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。     

基于混合逻辑动态的混杂系统研究及应用

综述了一种在工业领域中使用的混杂系统建模方法,即基于混合逻辑动态MLD（Mixed Logic Dynamic）的建模方法。分析了在该建模框架下系统的可观性、可控性、形式验证、稳定性、状态估计及故障检测、最优控制和预测控制,并且以水电厂为例讨论了该方法在实际工程中的应用。基于MLD的混杂系统研究目前仍处于起步阶段,在理论上混杂系统预测控制、最优控制、多目标控制及混合整数二次规划求解都有待研究,在应用上如何根据不同问题有效地建模混杂系统也有待研究。     

Comparison of Hybrid Systems and Fluid Stochastic Petri Nets

Hybrid Systems are modelsof interacting digital and continuous devices with applicationsin the control of aircraft, computers, or modern cars for instance.Concurrently, Fluid Stochastic Petri Nets (FSPNs) have been introducedas an extension of stochastic Petri nets to model physical systemsthat contain continuous fluid quantities controlled by discretelogic, as well as a means to deal with the possible state explosionof discrete models. Of course, an FSPN is by definition a hybridsystem but in this paper, we compare a general hybrid systemsformalism with FSPN formalism. The conclusion of this paper,suplemented by some examples, is that fluid stochastic Petrinets and hybrid system formalism can be converted from one tothe other. Although there is a price to pay for such a conversion,the conversion can transfer the solution methods from one tothe other and thus help the development of both formalisms.     

混杂系统的存在与研究

混杂系统（HDS）是由连续变量动态系统（CVDS）与离散事件动态系统（DEDS）共同组成的大型动态系统。随着CIMS的兴起与发展，人们应该关注HDS的建模、分析与优化运行。本文通过分析实例介绍了HDS的存在、特征与研究前景。     

Optimal worst case estimation for LPV–FIR models with bounded errors

This work presents an approximate solution method for the infinite-time nonlinear quadratic optimal control problem. The method is applicable to a large class of nonlinear systems and involves solving a Riccati equation and a series of algebraic equations. The conditions for uniqueness and stability of the resulting feedback policy are established. It is shown that the proposed approximation method is useful in determining the region in which the constrained and unconstrained optimal control problems are identical. A reactor control problem is used to illustrate the method.     

Robust Hybrid Control of Constrained Robot Manipulators via Decomposed Equations

Basing on a constraint Jacobian induced orthogonal decomposition of the task space and by requiring the force controller to be orthogonal to the constraint manifold, the dynamics of the constrained robots under hybrid control is decomposed into a set of two equations. One describes the motion of robots moving on the constraint manifold, while the other relates the constraint force with the hybrid controller. This decomposition does not require the solution of the constraint equation in partition form. In this setting, the hybrid control of constrained robots can be essentially reduced to robust stabilization of uncertain nonlinear systems whose uncertainties do not satisfy the matching condition. A continuous version of the sliding-mode controller (from Khalil [12]) is employed to design a position controller. The force controller is designed as a proportional force error feedback of high gain type. The coordination of the position controller and the force controller is shown to achieve ultimately bounded position and force tracking with tunable accuracy. Moreover, an estimate of the domain of attraction is provided for the motion on the constraint manifold. Simulation for a planar two-link robot constraining on an ellipse is given to show the effectiveness of a hybrid controller. In addition, the friction effect, viewed as external disturbance to the system, is also examined through simulations.