一种改进的CVP方法及其在动态优化中的应用

针对控制向量参数化方法敏感度方程求解耗时长、时间节点数难确定等问题,提出一种改进的控制向量参数化方法．首先利用分段常数对系统敏感度方程进行近似处理,有效地得到了敏感度方程的近似解析解,避免了对高维敏感度方程数值积分的计算负担;然后根据目标函数关于控制参数的敏感度来选择需要细化的控制参数,得到满足优化精度要求的最优时间节点数．针对非线性ＣＳＴＲ 的仿真研究验证了所提出算法的可行性和有效性．

     

非线性离散系统的近似最优跟踪控制

研究非线性离散系统的最优跟踪控制问题. 通过在由最优控制问题所导致的非线性两点边值问题中引入灵敏度参数, 并对它进行Maclaurin级数展开, 将原最优跟踪控制问题转化为一族非齐次线性两点边值问题. 得到的最优跟踪控制由解析的前馈反馈项和级数形式的补偿项组成. 解析的前馈反馈项可以由求解一个Riccati差分方程和一个矩阵差分方程得到. 级数补偿项可以由一个求解伴随向量的迭代算法近似求得. 以连续槽式反应器为例进行仿真验证了该方法的有效性．     

时滞离散系统最优输出跟踪控制的灵敏度法

针对具有有限时间二次型性能指标的时滞离散系统,研究了最优输出跟踪控制问题.通过引入一个灵敏度参数,将原最优输出跟踪控制问题转化为不含超前项和时滞项的一族两点边值问题.得到的最优输出跟踪控制律由状态向量的线性解析函数和伴随向量级数形式的补偿项组成,其解析函数由一次性求解R iccati矩阵差分方程和矩阵差分方程得到,补偿项由求解伴随向量差分方程的递推公式得到.仿真结果表明了该方法的有效性.     

基于不确定作业时间的FSM P 调度问题研究

针对一类加工时间不确定的FSMP调度问题，建立了基于扩展期望区间数近似不确定参数的优化模型．提出了利用扩展期望区间数构造参数近似边界的取极大运算方法，给出了包含不确定度控制指标的多目标优化模型．基于算例，讨论了决策因子和不确定度控制指标对调度性能的影响，仿真结果及分析表明了该模型和算法的有效性与鲁棒性．     

双足机器人逆运动学的模糊自适应算法

针对双足机器人逆运动学的数值解法中存在的雅可比矩阵奇异性和调节参数固定问题,提出了一种改 进的求解方法．运用微分运动方程的近似解避开雅可比矩阵求逆,利用能够减小跟踪误差的自适应模糊控制法,调 节自适应参数以使近似解任意逼近精确解,从而得到了精确性极高和强鲁棒性的模糊自适应算法．通过双足机器人 运动学的仿真分析,验证了该算法的有效性．而且整套算法的计算时间约为0.35 ms,可以用于实际双足机器人的实 时控制．     

平面有理曲线几何连续隐式化的优化方法

文中提出了平面有理曲线隐式化的优化方法,证明了隐式方程的系数实际上是一个这二次型的极小解向量,或是一个齐次线性方程的非平凡解。鉴于隐式方程的复杂性和实际中的近似计算,文中还提出了用低次隐式方程来逼近有理曲线的近似隐式化优化方法,由于加上了端点处的插值性和ＧＣ＾１连续性,最后得到的隐式方程是ＧＣ＾１连续的。数值例子说明这种近似隐式化方法的效果是不错的。     

用二次插值实现近似弧长参数化

分段二次Ｈｅｒｍｉｔｅ插值用来保单调地反插值参数曲线的弧长函数．所作近似弧长参数化曲线在插值节点处,近似弧长是精确的,并且具有与精确弧长参数曲线同方向的单位切矢．在整个近似弧长参数区间,近似弧长的误差可达到０（△ｔ）＾２（△ｔ为节点步长）．数值实例得到了很好的结果．     

基于状态反馈和参数调整稳定混沌系统的不稳定平衡点

针对OGY方法需要预先找到系统的一个可调参数的不足，基于状态反馈和参数调整，提出了稳定混沌系统不稳定平衡点的一种简单控制方法．根据线性控制理论选择控制参数，并研究了设计控制参数的准则．该方法不需系统的动力学知识，也不需要系统内部的任何控制参数．仿真结果验证了该方法的有效性．     

含状态和输入时滞的离散时间系统的近似最优跟踪控制

针对状 态和控制输入均含有时滞的离散时间系统, 提出最优跟踪控制的设计方法. 通 过引入一种新的状态向量, 将含有状态和控制输入时滞的离散时间系统转化为 含有虚拟扰动项的无时滞离散时间系统. 根据最优控制理论, 构造离散Riccati矩阵方 程和离散Stein矩阵方程的序列, 并证明该解序列一致收敛于变换后的离散时间系统的最优跟 踪控制策略. 利用最优控制的逐次逼近设计方法, 得到最优跟踪控制的近似 解, 并给出求解最优跟踪控制律的算法. 仿真算例表明了所提出最优跟踪控制 方法的有效性.     

基于动态参数化的二次B样条插值曲线

参数化为构造B样条插值曲线提供了自由度，但在以往的研究中，这些自由度并未得到充分利用．该文给出的二次B样条曲线插值方法充分利用了参数化的自由度，直接利用插值曲线直观的几何约束条件如曲线在数据点处的切向、曲线段的相对高度等进行参数化，使得构造出的插值曲线不仅在两端，而且在中间各段具有预期的几何性质．该文的方法比起以往的参数化方法来，能更直观有效地控制插值曲线的形状．而且，所构造的插值曲线具有局部性质或近似局部性质，即当改变某个数据点的位置时，插值曲线的形状只作局部改变或除局部范围外，曲线形状改变很小或完全不变．不同于以往的插值方法，该文的方法在构造插值曲线的过程中根据曲线的几何约束条件动态地递推确定参数值、节点向量和控制顶点，整个过程不必解方程组，计算简便．该文还给出了相应的算法和应用例子．实验结果表明，该文的方法十分有效．     

Sensitivity of Optimal Linear Systems to Small Variations in Parameters†

Optimal linear systems with quadratic performance indexes are analysed for sensitivity to small parameter variations. In particular, if the parameters can be separated in a certain way, it is shown that calculation of the sensitivity coefficients depends on the solution of sets of linear equations similar in form to the well-known Lyapunov matrix equation. An important example is when the elements of the matrices of the linear system are themselves regarded as the parameters. Expressions arc obtained for the sensitivity of the performance index, the optimal control law and the state vector.     

Sensitivity analysis of time-delay systems

A method is developed for the computation of general sensitivity coefficients of time-delay systems to the variation of initial data, control, time delays, and other parameters appearing in the differential-difference equations of retarded type. Using the variational approach, it is shown that integration of the adjoint equations is sufficient to determine all the effects of parameter variations from the nominal solution.     

A general approach to constructing parameter identification algorithms in the class of square root filters with orthogonal and J-orthogonal tranformations

We study modern implementations of the discrete Kalman filter, namely array square-root algorithms. An important feature of such algorithms is the use of orthogonal and J-orthogonal transformations on each filtering step. For the first time, we develop for this class of algorithms a simple universal approach that lets us generalize any numerically stable implementation of this type to the case of updates in sensitivity equations of the filter with respect to unknown system model parameters. An advantage of the resulting adaptive schemes is their numerical stability with respect to machine rounding errors. Estimation of the noisy state vector of the system and identification of unknown system parameters occur simultaneously. The proposed approach can be used for parameter identification problems, adaptive control problems, experiment planning, and others.     

Some optimal control results for differential-difference systems

A brief development of necessary conditions for an extremal path in the case where the system equations and the performance index contain a time delay in both the state and the control variables is given. An analytic solution is also presented for a linear system with a quadratic performance index in the case where the control variable appears in the system equations evaluated both at the present time and at a previous time. Unspecified constants in the solution are obtained by the inversion of a specified matrix. Results for some examples are illustrated.     

带马尔科夫跳和乘积噪声的随机系统的最优控制

讨论了N个选手随机系统的最优控制问题. 设计了无限时间的带有马尔科夫跳和乘积噪声的随机系统的Pareto最优控制器. 应用推广的Lyapunov方法和解随机Riccati代数方程得到了系统的Pareto最优解, 证明了最优控制器是稳定的反馈控制器, 以及对应于最优控制器的反馈增益中的随机Riccati代数方程的解是最小解.     

ℓ2 Gain Estimation and Visualization of A Control Parameter Set in 3D Space Using Plant Response Data

In this paper, a novel parameter space approach that uses volume rendering is proposed to visualize controller parameter sets that consist of three controller parameters. An off‐line design method for robust control using plant response data is also studied. A solution set with equal ?₂ gain can be visualized as isosurfaces in three‐dimensional space, and the designer can visually select an appropriate parameter. This numerical method is applicable to many practical specifications, in contrast to analytical methods based on solving equations. An estimation method based on the extension theorem and a method using bandpass filters are both considered as possible methods for estimating the ?₂ gain of the sensitivity functions when using grid points on the order of tens of thousands to create the volume data.The former method is superior to the latter with respect to accuracy but impractical with respect to computational load. The latter method is hence practical, because the computing time is reduced to less than 0.05 s for about 300,000 grid points by parallel computation with a graphical processing unit.     

基于微分/代数方程的多体系统动力学设计灵敏度分析的伴随变量方法

基于多体系统动力学微分/代数方程数学模型和通用积分形式的目标函数,建立了多体系统动力学设计灵敏度分析的伴随变量方法,避免了复杂的设计灵敏度计算,对于设计变量较多的多体系统灵敏度分析具有较高的计算效率.文中给出了通用公式以及具体的计算过程和验证方法,并将目标函数及其导数积分形式的计算转化为微分方程的初值问题,进一步提高了计算效率和精度.文末通过一曲柄-滑块机构算例对算法的有效性进行了验证.     

Solving Fixed Final Time Fractional Optimal Control Problems Using the Parametric Optimization Method

In this paper, the parametric optimization method is used to find optimal control laws for fractional systems. The proposed approach is based on the use for the fractional variational iteration method to convert the original optimal control problem into a nonlinear optimization one. The control variable is parameterized by unknown parameters to be determined, then its expression is substituted into the system state‐space model. The resulting fractional ordinary differential equations are solved by the fractional variational iteration method, which provides an approximate analytical expression of the closed‐form solution of the state equations. This solution is a function of time and the unknown parameters of the control law. By substituting this solution into the performance index, the original fractional optimal control problem reduces to a nonlinear optimization problem where the unknown parameters, introduced in the parameterization procedure, are the optimization variables. To solve the nonlinear optimization problem and find the optimal values of the control parameters, the Alienor global optimization method is used to achieve the global optimal values of the control law parameters. The proposed approach is illustrated by two application examples taken from the literature.     

Upwind finite volume solution of sensitivity equations for hyperbolic systems of conservation laws with discontinuous solutions

An upwind, finite volume method is proposed for the direct solution of one-dimensional, hyperbolic systems-based sensitivity equations. Sensitivity equations for hyperbolic systems of conservation laws require a specific treatment of discontinuities, across which Dirac source terms appear, thus leading to modify the classical jump relationships. The modified jump relationships are used to derive an extension of the HLL and HLLC Riemann solvers for the solution of one-dimensional, hyperbolic systems-based sensitivity equations. The solver is developed for 3 × 3 systems where the central wave is a contact wave. A specific treatment is needed to preserve the invariance property of the third component of the sensitivity vector along the contact wave. The proposed solver is applied to the one-dimensional, Saint Venant equations with passive, scalar advection and tested successfully against analytical solutions including the influence of topography-induced source terms in both the flow and sensitivity equations.     

Restricted second order information for the solution of optimal control problems using control vector parameterization

A new scheme using a Truncated Newton algorithm with and exact Hessian-search direction vector product is presented for the solution of optimal control problems. The derivation of formulae for second order parametric sensitivity analysis of differential-algebraic equations is presented, following earlier published work [V.S. Vassiliadis, E. Balsa-Canto, J.R. Banga, Second order sensitivities of general dynamic systems with application to optimal control problems. Chem. Eng. Sci. 54 (17) (1999) 3851–3860]. An original result in this work is the derivation of Hessian matrix-vector product forms which are shown to have the same computational complexity as the evaluation of first order sensitivities. This result for optimal control Hessian-vector products using control vector parameterization is shown to be a very effective way to solve optimal control problems. It is also noted that this work introduces the use of suitable Truncated Newton solvers which can exploit the exact vector products in using conjugate gradient iterations to converge the Newton equations. Such a solver is the TN algorithm of Nash [(S.G. Nash-Newton type minimization via the Lanczos method. SIAM J. Num. Anal. 21, (1984) 770–778)]. Because no full Hessian update is necessary it is demonstrated that the resulting optimal control solver performs very well for a very large number of degrees of freedom, limited only by the necessity for many right-hand-side calculations in the first and second order sensitivity equations (the Hessian vector product). It is also demonstrated by several case studies that the scheme is capable of starting far from the solution and yet arrive there in almost invariant performance.