从守恒到开放 ——广义哈密顿控制系统的理论和应用*

本文力图从能量的观点处理经典哈密顿控制系统、Poission括号和辛几何.将其推广到具有能量耗散以及与环境有能量交换的广义哈密顿控制系统.提出伪Poission流形与广义辛流形作为一般哈密顿控制系统状态空间的几何框架.讨论了它们的相互关系及一些基本性质.提出广义辛群、辛代数的概念作为广义哈密顿系统的代数结构.基于此研究了广义哈密顿系统的保结构性.然后讨论哈密顿系统的Casimir 流形方法及反馈镇定等问题.得到的结果为进一步研究提供了基础.作为例子,将一些结果应用于电力系统的励磁控制.     

广义分数阶受迫Birkhoff方程

研究受迫Birkhoff系统的分数阶变分问题,建立具有这两种分数阶微分算子的广义分数阶受迫Birkhoff方程.〖JP〗然后,给出具有这两种分数阶微分算子的分数阶Hamilton方程和分数阶Lagrange方程.最后,讨论广义分数阶Lotka 生化振子模型和广义分数阶Hojman Urrutia模型.     

风能转换系统的哈密顿控制器设计

基于哈密顿能量理论,本文提出了一种用于风能转化系统的桨距角和励磁转矩的控制器,设计所得的闭环系统具有良好的稳定性.在系统中存在干扰时,该系统在哈密顿控制器作用下具有限增益L2稳定.哈密顿理论提供给了一个全新的理论视角和控制器设计的方法,仿真结果证明所提出的方法的有效性。     

基于微分反馈法的随机受迫Brusselator模型的混沌控制

研究了一个随机参数受迫Brusselator模型的非线性微分反馈控制，首先将其用Chebyshev多项式逼近得到扩阶的等价确定性系统，然后设计了非线性微分反馈控制器，使得混沌的受迫Brusselator模型被稳定在了某一条不稳定的周期轨道上．数值结果验证了方法的有效性．     

一类受迫振荡混沌系统的自适应控制

针对一类受迫振荡混沌系统,提出了一种普遍适用的自适应控制方法,给出了自适应控制器及参数自适应律的设计方法.基于Lyapunov稳定性理论,证明了系统的稳定性.仿真实验表明,本文所提方法避免了混沌系统中除受迫振荡项外的不确定参数的影响,实现了一类混沌系统的有效控制及受迫振荡项参数的准确辨识,方法具有良好的可实现性和工程应用价值.     

基于互连网络系统故障的新型自适应诊断算法

互连网络的故障诊断是网络系统可靠性分析的重要内容。PMC模型是一种重要的网络故障模型。针对具有哈密顿环的互连网络(也称哈密顿网络),利用分治回环思想,提出了一种新的基于PMC故障模型自适应的诊断算法。其核心思想是,首先对哈密顿网络进行序列划分,然后对得到的每个01序列的结节进行回环诊断,最后利用回环诊断的结果对非01序列的节点进行诊断。对于一个具有多个01序列的互连网络,该算法通过有限次轮回的测试,能准确的定位系统中的故障节点,对于正确节点的诊断可靠度能无限接近100%。当系统中存在的回测边越多,该算法的诊断效果越好。     

给水管网的能量需求建模及其节能研究

为了实现给水管网系统能量的供需平衡,对管网建模进行了研究。针对目前大多数给水系统更适合建立宏观模型的特点,提出了为给水系统建立具有较好精度的输入与输出非线性关系的神经网络宏观模型的方案。在某给水系统中的应用结果表明,该方案的实施能够获得较大的节能空间,为给水系统的能量供给提供节能依据。该建模方法具有普适性,可将其推广应用到其他给水系统。     

双馈风电机组网侧变换器哈密顿控制器设计

风力发电机组的发电过程,是通过网侧变换器输送稳定电压。由于电压受到变换器系统电感参数变化的影响,电压发生波动。为了抑制直流母线电压波动,提高母线电压的静态稳定性和动态响应速度,提出采用哈密顿能量理论的控制器设计方法,将网侧变换器的非线性系统转化为哈密顿系统模型,对双馈风力发电机组网侧变换器进行设计,使得系统的静态和动态性能得到改善。在Matlab上进行仿真,结果表明,改进的控制方法结构简单,系统稳定性好,且具有较强的鲁棒性,使电压波动小,能够快速稳定控制直流母线电压。     

基于多播的4用户BC网络自由度研究

提出一种基于多播的4用户Broadcast Channel(BC)系统模型。该系统采用"循环模式"为接收端分配期望消息,采用基于零空间交的迫零方案,将同一个接收端的多个干扰消息置于对应零空间的交空间中,以实现同时迫零多个干扰消息。对于同一个接收端只有一个干扰消息的情况,该迫零方案同样适用。对于该4用户系统,给出了最优天线配置方案及系统自由度的一般化结果。采用MATLAB对该系统进行仿真分析,结果表明,系统自由度的理论值与仿真结果是一致的,所提出的迫零方案是可行的。     

端口受控哈密顿多智能体系统的输出一致性协议设计

研究了端口受控哈密顿（PCH）多智能体系统分别在固定和切换拓扑下的输出一致性问题. 首先根据哈密顿系统特有的优势,运用能量整形思路设计了一个全局稳定的群组输出一致性协议,该协议通过构造虚拟邻居的方式将有向图转化成无向图. 其次通过利用推广的LaSalle's不变原理将切换拓扑的问题转化成切换系统来研究. 例子证明,本文很好的解决端口受控哈密顿（PCH）多智能体系统的输出一致性问题.     

Stabilization of synchronous generators with the Hamiltonian function approach

Using the Hamiltonian function approach, this paper proposes an energy-based stabilizing method for a fifth-order model of synchronous generators to keep the terminal machine voltage (output) remaining at a given expected value. By constructing a Hamiltonian function as the total energy function for the fifth-order model and changing the system into a forced Hamiltonian system with dissipation, an energy-based Lyapunov function is obtained. As the result, a suitable stabilizing controller is constructed for the system. Simulation shows the effectiveness of the stabilizing method proposed in this paper.     

Energy-based Lyapunov functions for forced Hamiltonian systems withdissipation

In this paper, we propose a constructive procedure to modify the Hamiltonian function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for nonzero equilibria. A key step in the procedure, which is motivated from energy-balance considerations standard in network modeling of physical systems, is to embed the system into a larger Hamiltonian system for which a series of Casimir functions can be easily constructed. Interestingly enough, for linear systems the resulting Lyapunov function is the incremental energy; thus our derivations provide a physical explanation to it. An easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given. Some examples that illustrate the method are given     

广义哈密顿实现及其在基于能量的准Lyapunov函数构造中的应用

首先研究一般非线性系统的Hamilton实现问题，给出了两个实现的充分条件，然后应用所得到的结果研究广义受控耗散Hamilton系统的基于能量的准Lyapunov函数构造问题，给出若干能通过改造Hamilton函数得到准Lyapunov函数的充分条件。     

Adaptive stabilization of generalized Hamiltonian systems with dissipation and its applications to power systems

The adaptive stabilization of the generalized Hamiltonian control systems with dissipation, which has a linearly parameterized Hamiltonian function with respect to unknown constants, is considered here. The theoretic result is then applied to power system that cannot be treated by backstepping introduced by Kokotovic et al. Simulations show that the designed adaptive control law is very effective.     

Power balancing for a new class of non-linear systems and stabilization of RLC circuits

In this paper the method of power shaping, as recently introduced for the stabilization of non-linear RLC circuits, is generalized to a larger class of systems showing similarities (and important differences) with the class of port-controlled Hamiltonian systems. Other than for port-controlled Hamiltonian systems, the stabilization of these new systems is not stymied by a ‘dissipation obstacle’ and, in fact, every power-shaping controller is power balancing as well. It is shown that the power-shaping controller can be realized as a port-controlled Hamiltonian system connected by means of a gyrator to the plant. The theoretical results are applied to the class of non-linear RLC circuits described by Brayton–Moser's equations, and a physical implementation of the controllers in terms of standard electrical circuit elements is given.     

Stabilization of Hamiltonian systems with nonholonomic constraints based on time-varying generalized canonical transformations

This paper is concerned with the stabilization of nonholonomic systems in port-controlled Hamiltonian formulae based on time-varying generalized canonical transformations. A special class of time-varying generalized canonical transformations are introduced which modify the kinetic energy of the original system without changing the generalized Hamiltonian structure with passivity. Utilizing these transformations, time-varying asymptotically stabilizing controllers for the nonholonomic Hamiltonian systems are derived. Since the proposed method is a natural generalization of passivity based control for conventional holonomic systems, it is expected that the tools developed for conventional systems will be applicable to nonholonomic systems based on the proposed method.     

Generalized Hamiltonian representation of thermo-mechanical systems based on an entropic formulation

In this work, we present an approach to construct generalized Hamiltonian representations for thermo-mechanical systems. Using entropic formulation of thermodynamic systems, the construction is applied to a class of thermo-mechanical systems. The proposed approach leads to an explicit expression of the dissipation along the trajectories of the dynamics. The considered thermo-mechanical systems are, in a thermodynamical sense, systems for which the dynamics of the extensive variables are functions of the intensive variables with respect to an entropic formulation. Using the entropy as the storage function, the dissipative structures of an analogue to a port-controlled Hamiltonian (PCH) representation are identified with irreversible phenomena, while the conservative structures are identified with reversible or isentropic phenomena. Examples are presented to illustrate the application of the proposed methodology, including a reacting system.     

Robust Adaptive Control for Robotic Systems With Input Time-Varying Delay Using Hamiltonian Method

This paper addresses the problem of robust adaptive control for robotic systems with model uncertainty and input time-varying delay. The Hamiltonian method is applied to develop the stabilization results of the robotic systems. Firstly, with the idea of shaping potential energy and the pre-feedback skill, the n degree-of-freedom (DOF) uncertain robotic systems are realized as an augmented dissipative Hamiltonian formulation with delay. Secondly, based on the obtained Hamiltonian system formulation and by using of the Lyapunov-Krasovskii (L-K) functional method, an adaptive controller is designed to show that the robotic systems can be asymptotically stabilized depending on the input delay. Meanwhile, some sufficient conditions are spelt out to guarantee the rationality and validity of the proposed control law. Finally, study of an illustrative example with simulations shows that the controller obtained in this paper works very well in handling uncertainties and input delay in the robotic systems.      

Stabilization of Hamiltonian systems with dissipation

Stabilization of generalized Hamiltonian systems with dissipation is investigated. First, we generalize the Casimir submanifold approach with constant controls to the static state feedback control case. Secondly, a direct Hamiltonian function method is proposed and it is shown that this method is equivalent to the Casimir sub-manifold approach. Furthermore, a dynamic state feedback control is proposed. Some sufficient conditions and a constructive process for determining controllers are provided. It is shown that the dynamic state feedback control is more powerful than the static one. Finally, the problem of a dissipative type realization of the general controlled Hamiltonian system is discussed.     

Some Properties of Conservative Port Contact Systems

The dynamics of open irreversible thermodynamic systems, that is systems including both the balance equation of the energy and the entropy, has been formulated as contact vector fields with generating functions depending on some external (control) variable and called conservative port contact systems. In this paper we relate the dynamical properties of these systems (equilibrium points, asymptotic stability) to properties of the generating functions (the contact Hamiltonian functions). We show that the equilibrium points of the system satisfy certain conditions involving the contact Hamiltonian function. We also consider Lyapunov's first theorem to emphasize a stability criterion for the equilibrium points in terms of this contact Hamiltonian function and relate it to some thermodynamical properties. These results are then related to the physical phenomena that are taking place in the system.