一类非线性系统的迭代学习控制

讨论一类非线性系统的迭代学习控制,系统的非线性动态对状态不快于多项式增长,而量测方程含有噪声.控制序列并非直接输给系统,而是先经过死区、预载及饱和等非线性函数.递推地给出了学习控制序列,并证明它的有界性及最优跟踪性.     

Stability Analysis of Optimal Control Systems via Liapunov Method

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｅｃｏｎｄｍｅｔｈｏｄｏｆＬｉａｐｕｎｏｖｎｅｅｄｎｏｔｓｏｌｖｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ,ｂｕｔｉｔｃａｎｄｉｒｅｃｔｌｙｇｉｖｅｓｔａｂｉｌｉｔｙｉｍｆｏｒｍａｔｉｏｎｏｆｓｙｓｔｅｍｅｑｕｉｌｉｂｒｉｕｍｓｔａｔｅｂｙｃｏｎｓｔｉｔｕｔｉｎｇＬｉａｐｕｎｏｖｆｕｎｃｔｉｏｎ．Ｉｔｉｓｖｅｒｙｕｓｅｆｕｌｆｏｒｔｈｏｓｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｈｉｃｈｃａｎｎｏｔｅａｓｉｌｙｂｅｓｏｌｖｅｄ．Ｆｏｒｇｅｎｅｒａｌｓ…     

线性定常广义系统的D型迭代学习控制收敛性

给出了线性定常广义系统在D型学习律作用下的迭代控制收敛性结果,这一结果是全新的,其对时变系统也成立,而且,本文结果和方法大部分可以移植到线性定常广义离散时间系统.     

On Quantitative Stability in Optimization and Optimal Control

We study two continuity concepts for set-valued maps that play central roles in quantitative stability analysis of optimization problems: Aubin continuity and Lipschitzian localization. We show that various inverse function theorems involving these concepts can be deduced from a single general result on existence of solutions to an inclusion in metric spaces. As applications, we analyze the stability with respect to canonical perturbations of a mathematical program in a Hilbert space and an optimal control problem with inequality control constraints. For stationary points of these problems, Aubin continuity and Lipschitzian localization coincide; moreover, both properties are equivalent to surjectivity of the map of the gradients of the active constraints combined with a strong second-order sufficient optimality condition.     

快速路交通微分系统的脉冲迭代学习策略研究

针对快速路交通微分系统,结合该交通系统具有明显的重复性和周期性等特点,设计了一种脉冲迭代学习策略,并建立了迭代学习误差的收敛性条件.其次,利用λ范数和脉冲Gronwall不等式等方法证明了算法的收敛性.结合脉冲控制与学习控制的特点,该方法的优点在于容易实现和经济环保,且能有效地达到控制目的.最后,通过数值仿真实证进一步说明所设计控制方法的有效性.     

Inexact Iterative Bregman Method for Optimal Control Problems

In this article, we investigate an inexact iterative regularization method based on generalized Bregman distances of an optimal control problem with control constraints. We show robustness and convergence of the inexact Bregman method under a regularity assumption, which is a combination of a source condition and a regularity assumption on the active sets. We also take the discretization error into account. Numerical results are presented to demonstrate the algorithm.     

基于异步序列迭代法优化的单交叉口多策略模糊控制算法

针对城市交通流随机、时变和非线性的特点,在基于通行需求度的单交叉口模糊控制算法的基础上,提出多策略模糊控制算法,并用基于GA的异步序列迭代法进行了优化.仿真结果表明,多策略模糊控制算法的适应能力更强,稳定性更好.     

Optimal Control of Constrained Piecewise Affine Discrete-Time Systems

This paper makes two contributions; firstly, it provides a characterization of the solution of the optimal control problem for piecewise affine discrete-time systems with a quadratic cost function (the generally preferred option) and, secondly, provides a simple method (reverse transformation) for solving this and the previously solved &ell problem. The characterization is useful for on-line implementation.     

Approximate Optimal Control and Stability of Nonlinear Finite- and Infinite-Dimensional Systems

We consider first nonlinear systems of the formx=A(x)x+B(x)u together with a standard quadratic cost functional and replace the system by a sequence of time-varying approximations for which the optimal control problem can be solved explicitly. We then show that the sequence converges. Although it may not converge to a global optimal control of the nonlinear system, we also consider a similar approximation sequence for the equation given by the necessary conditions of the maximum principle and we shall see that the first method gives solutions very close to the optimal solution in many cases. We shall also extend the results to parabolic PDEs which can be written in the above form on some Hilbert space.     

State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets

The state analysis and optimal control of time-varying discrete systems via Haar wavelets are the main tasks of this paper. First, we introduce the definition of discrete Haar wavelets. Then, a comparison between Haar wavelets and other orthogonal functions is given. Based upon some useful properties of the Haar wavelets, a special product matrix and a related coefficient matrix are proposed; also, a shift matrix and a summation matrix are derived. These matrices are very effective in solving our problems. The local property of the Haar wavelets is applied to shorten the calculation procedures.