基于两级算法的对偶控制

考虑具有未知参数的随机系统的最优控制问题.采用包含新息方差指数项的损失函数优化系统的性能.新的损失函数由两部分组成:第一部分反映了对输出的调节作用;第二部分反映了辩识系统中未知参数应尽可能多地收集系统信息的需求.提出了一种两级优化算法.该算法首先把不可分问题转化为可分的两目标优化问题,再从两目标优化的非劣解集中挑出原问题的最优解.该控制律易于实施且具有对偶特点.仿真结果表明本文所得的控制律的有效性.     

基于两级参数算法的对偶控制

针对具有未知参数的随机系统，从随机次优的角度出发，将原不可解的动态规划问题转化为优化一个效用函数，该效用函数考虑了输出调节要求和参数学习要求及两者之间的折衷，充分利用了对偶控制较常规自适应控制的优越性．提出利用两级参数算法来最小化效用函数，从而获得控制信号．仿真结果表明，这种控制器具有良好的对偶性质，能得到较好的学习和控制效果．     

多变量自适应极点配置对偶控制的研究

针对参数未知的多变量差分方程形式的系统,首先利用Kalman滤波器进行参数辨识,根据确定性等价原理对系统进行极点配置;然后利用极点配置得到的非对偶控制器作为标称输入,其对应的输出作为标称输出,进而根据双指标准则进行对偶控制器的设计;最后给出一个仿真实例,验证该算法的可行性和有效性.     

一类对偶自适应预测函数控制算法

针对未知参数系统的自适应预测函数控制,模型尚未辨识完成或外界干扰造成的模型不准确,会严重影响控制效果,并产生较大的超调和波动.由此,提出一类对偶自适应预测函数控制(Dtml Adaptive Predictive Function Control,DAPFC)算法.在模型辨识的过程中,通过辨识误差的大小,利用对偶控制方法来调整原有自适应控制律,尽可能地获取未知参数信息并抑制由于模型失配造成的控制量的波动.改善了系统在模型失配时的控制效果,并具有较强的鲁棒性.仿真结果表明,该算法具有良好的控制品质.     

随机自适应控制的信息论方法

从Ｓｈａｎｎｏｎ信息理论的角度，分别应用最小熵方法和最大互信息方法，对摸型参数不确定的随机系统的自适应控制问题进行了研究和比较．对于这类系统，由最大互信息方法导出的自适应控制律本质上具有双重控制的特性．     

红外成像目标模拟器方位系统的

红外成像目标模拟器方位系统是一参数快时变系统,针对该系统的具体情况,提出了一种对偶自校正PID控制器.在每一自适应步,通过谱分解得到最优PID参数,然后基于双重指标进行对偶校正,得到一种既保持对偶效应,又十分简单易行的对偶自校正PID控制器,成功地消除了传统自适应控制系统的"关断”、"终止”和"猝发”等现象,收到了良好的控制效果.该控制器适于参数随机变化或快时变系统.     

具有学习特点的控制器设计算法

对于普遍存在的具有未知参数的随机最优控制问题,本文提出了一种具有学习特点的控制器设计算法.该算法用Kalman滤波估计系统的未知参数,在滚动优化机制下用动态规划获取控制增益,为了赋予控制器的学习特点,在LQG控制律中附加使下一时刻估计方差最小的学习控制分量.仿真结果表明了算法的有效性.     

基于滚动优化的对偶控制策略

考虑具有未知参数的随机系统的最优控制问题.提出了一种新的基于滚动优化的对偶控制算法.在动态规划泛函方程中,用Kalman滤波对系统的状态进行估计;用线性化方法对阶段损失函数中的后验概率进行近似,然后,用滚动优化策略对控制与学习之间的耦合关系进行解耦.从而获得了原不可解泛函方程的解析递推表达式和一个易于实施的控制律的解析解.用一个例子说明了控制律的性能,仿真结果表明:该控制律具有良好的对偶性质,在学习和控制之间实现了较好的平衡.     

切换网络拓扑下Euler-Lagrange系统的分布式协调控制

研究切换网络拓扑下含未知参数的分布式Euler-Lagrange系统(简称EL系统)的自适应协调控制问题.通过引入一种新颖的自适应控制构架,设计了分散式控制器,使其容许未知的系统参数.基于图论,Lyapunov稳定性理论以及切换控制理论证明了算法的稳定性.本文特色在于在同一理论框架下处理EL系统协调控制中的未知参数问题与切换拓扑问题,实现静态和动态两种情况下的控制目标.仿真结果验证了算法的有效性.     

带未知模型参数和衰减观测率系统自校正分布式融合估计

研究了带未知模型参数和衰减观测率多传感器线性离散随机系统的信息融合估计问题.在模型参数和衰减观测率未知的情形下,应用递推增广最小二乘(Recursive extend least squares,RELS)算法和加权融合估计算法提出了分布式融合未知模型参数辨识器;应用相关函数对描述衰减观测现象的随机变量的数学期望和方差...     

Optimal state estimation for stochastic systems: an informationtheoretic approach

In this paper, we examine the problem of optimal state estimation or filtering in stochastic systems using an approach based on information theoretic measures. In this setting, the traditional minimum mean-square measure is compared with information theoretic measures, Kalman filtering theory is reexamined, and some new interpretations are offered. We show that for a linear Gaussian system, the Kalman filter is the optimal filter not only for the mean-square error measure, but for several information theoretic measures which are introduced in this work. For nonlinear systems, these same measures generally are in conflict with each other, and the feedback control policy has a dual role with regard to regulation and estimation. For linear stochastic systems with general noise processes, a lower bound on the achievable mutual information between the estimation error and the observation are derived. The properties of an optimal (probing) control law and the associated optimal filter, which achieve this lower bound, and their relationships are investigated. It is shown that for a linear stochastic system with an affine linear filter for the homogeneous system, under some reachability and observability conditions, zero mutual information between estimation error and observations can be achieved only when the system is Gaussian     

基于模型参考自适应方法的对偶控制方法研究

针对未知参数随机系统，基于模型参考自适应方法和双准则函数，设计了具有控制和学习作用的对偶控制器．通过控制器的学习作用提高了控制精度，有效地减少了启动时的超调．仿真结果表明，设计的控制器能够具有较好的跟踪性能．     

A multiple model adaptive dual control algorithm for stochastic systems with unknown parameters

An adaptive dual control algorithm is presented for linear stochastic systems with constant but unknown parameters. The system parameters are assumed to belong to a finite set on which a prior probability distribution is available. The tool used to derive the algorithm is preposterior analysis: a probabilistic characterization of the future adaptation process allows the controller to take advantage of the dual effect. The resulting actively adaptive control called model adaptive dual (MAD) control is compared to two passively adaptive control algorithms-the heuristic certainty equivalence (HCE) and the Deshpande-Upadhyay-Lainiotis (DUL) model-weighted controllers. An analysis technique developed for the comparison of different controllers is used to show statistically significant improvement in the performance of the MAD algorithm over those of the HCE and DUL.     

A GRADIENT BASED ADAPTIVE CONTROL ALGORITHM FOR DUAL‐RATE SYSTEMS

In this paper, using a polynomial transformation technique, we derive a mathematical model for dual‐rate systems. Based on this model, we use a stochastic gradient algorithm to estimate unknown parameters directly from the dual‐rate input‐output data, and then establish an adaptive control algorithm for dual‐rate systems. We prove that the parameter estimation error converges to zero under persistent excitation, and the parameter estimation based control algorithm can achieve virtually asymptotically optimal control and ensure the closed‐loop systems to be stable and globally convergent. The simulation results are included.     

Adaptive sampled-data based linear quadratic optimal control of stochastic systems

The problem of sampled-data (SD) based adaptive linear quadratic (LQ) optimal control is considered for linear stochastic continuous-time systems with unknown parameters and disturbances. To overcome the difficulties caused by the unknown parameters and incompleteness of the state information, and to probe into the influence of sample size on system performance, a cost-biased parameter estimator and an adaptive control design method are presented. Under the assumption that the unknown parameter belongs to a known finite set, some sufficient conditions ensuring the convergence of the parameter estimate are obtained. It is shown that when the sample step size is small, the SD-based adaptive control is LQ optimal for the corresponding discretized system, and sub-optimal compared with that of the case where the parameter is known and the information is complete.     

Optimal control of unknown parameter systems

The problem is discussed of finding a cost functional for which an adaptive control law is optimal. The system under consideration is a partially observed linear stochastic system with unknown parameters. It is well known that an optimal finite-dimensional filter for this problem can be derived when the parameters belong to a finite set. Since the optimal filter involves the evaluation of a finite set of a posteriori probabilities for each of the parameter values given the observations, a natural adaptive control scheme is: (i) develop the optimal linear feedback law given each parameter; (ii) use the a posteriori probabilities to form the weighted average (convex combination) of the individual control policies; and (iii) use the weighted average as the control law. A quadratic cost functional is devised for which this strategy is optimal, in a general case, and it is shown that the probing effect identified with dual control problems is inherent in the standard linear-quadratic-Gaussian problem with parameter uncertainty     

An actively adaptive control for linear systems with random parameters via the dual control approach

A new method is presented for controlling a discrete-time linear system with possibly time-varying random parameters in the presence of input and output noise. The cost is assumed to be quadratic in the state and control. Previous algorithms for the above problem when the system had both zeros and poles unknown were of the open-loop feedback type, i.e., they did not take into account that future observations will be made. Therefore, even though these schemes were adaptive, their learning was "accidental." In contrast to this, the new approach uses an expression of the optimal cost-to-go that exhibits the dual purpose of the control, i.e., learning and control. The effect of the present control on the future estimation ("learning") appears explicitly in the cost used in the stochastic dynamic programming equation. The resulting sequence of controls, which is of the closed-loop type, is shown via simulations to appropriately divide its energy between the learning and the control purposes. Therefore, this control is called actively adaptive because it regulates the speed and amount of learning as required by the performance index. The simulations on a third-order system with six unknown parameters also demonstrate the computational feasibility of the proposed algorithm.