不确定噪声下确保连续LQG最优控制目标的扰动界

不确定噪声下确保连续ＬＱＧ最优控制目标的扰动界奚宏生杨孝先（中国科学技术大学自动化系合肥２３００２７）关键词鲁棒ＬＱＧ最优控制,确保控制目标,扰动界收稿日期１９９４－０９－０８１引言具有不确定噪声的随机线性控制系统为ｘ（ｔ）＝Ａｘ（ｔ）＋Ｂｕ（ｔ）＋...     

一种模型参考鲁棒控制的跟踪性能改善

This paper considers the tracking performance problem of a model reference robust control (MRRC) for plants with relative degree greater than one. A new algorithm is proposed based on the earlier research. It is shown that by applying a special transformation to the tracking system, the L1 bound of the tracking error can be achieved even when the high frequency gain is unknown, and both the tracking performance and the control effort can be improved significantly. Furthermore, the strictly positive real (SPR) condition, which is an essential assumption of the earlier design, can be removed.     

New Result on Model Reference Robust Control: Tracking Performance Improvement

This paper considers the tracking performance problem of a model reference robust control (MRRC) for plants with relative degree greater than one. A new algorithm is proposed based on the earlier research. It is shown that by applying a special transformation to the tracking system, the L∞ bound of the tracking error can be achieved even when the high frequency gain is unknown, and both the tracking performance and the control effort can be improved significantly. Furthermore, the strictly positive real (SPR) condition, which is an essential assumption of the earlier design, can be removed.     

The problem of LQG optimal control via a limited capacity communication channel

The paper addresses a LQG optimal control problem involving bit-rate communication capacity constraints. A discrete-time partially observed system perturbed by white noises is studied. Unlike the classic LQG control theory, the control signal must be first encoded, then transmitted to the actuators over a digital communication channel with a given bandwidth, and finally decoded. Both the control law and the algorithms of encoding and decoding should be designed to archive the best performance. The optimal control strategy is obtained. It is shown that where the estimator-coder separation principle holds, the controller-coder one fails to be true.     

Robust output feedback stabilization via risk-sensitive control

We consider a problem of robust linear quadratic Gaussian (LQG) control for discrete-time stochastic uncertain systems with partial state measurements. For a finite-horizon case, the problem was recently introduced by Petersen et al. (IEEE Trans. Automat. Control 45 (2000) 398). In this paper, an infinite horizon extension of the results of Petersen et al. (IEEE Trans. Automat. Control 45 (2000) 398) is discussed. We show that for a broad class of uncertain systems under consideration, a controller constructed in terms of the solution to a specially parameterized risk-sensitive stochastic control problem absolutely stabilizes the stochastic uncertain system.     

An optimal control approach to robust tracking of linear systems

In our early work, we show that one way to solve a robust control problem of an uncertain system is to translate the robust control problem into an optimal control problem. If the system is linear, then the optimal control problem becomes a linear quadratic regulator (LQR) problem, which can be solved by solving an algebraic Riccati equation. In this article, we extend the optimal control approach to robust tracking of linear systems. We assume that the control objective is not simply to drive the state to zero but rather to track a non-zero reference signal. We assume that the reference signal to be tracked is a polynomial function of time. We first investigated the tracking problem under the conditions that all state variables are available for feedback and show that the robust tracking problem can be solved by solving an algebraic Riccati equation. Because the state feedback is not always available in practice, we also investigated the output feedback. We show that if we place the poles of the observer sufficiently left of the imaginary axis, the robust tracking problem can be solved. As in the case of the state feedback, the observer and feedback can be obtained by solving two algebraic Riccati equations.     

Robust stability and performance via fixed-order dynamic compensation with guaranteed cost bounds

A feedback control-design problem involving structured plant parameter uncertainties is considered. Two robust control-design issues are addressed. The Robust Stability Problem involves deterministic bounded structured parameter variations, while the Robust Performance Problem includes, in addition, a quadratic performance criterion averaged over stochastic disturbances and maximized over the admissible parameter variations. The optimal projection approach to fixed-order, dynamic compensation is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design. The principle result is a sufficient condition for characterizing dynamic controllers of fixed dimension which are guaranteed to provide both robust stability and performance. The sufficient conditions involve a system of modified Riccati and Lyapunov equations coupled by an oblique projection and the uncertainty bounds. The full-order result involves a system of two modified Riccati equations and two modified Lyapunov equations coupled by the uncertainty bounds. The coupling illustrates the breakdown of the separation principle for LQG control with structured plant parameter variations. Supported in part by the Air Force Office of Scientific Research under Contract F49620-86-C-0002.     

半主动悬架LQG控制及仿真分析

通过3自由度车辆半主动悬架系统模型的建立,采用LQG理论确定了半主动悬架的控制方法,并在MatLab/Simulink环境中对其进行仿真,并把它与被动悬架作了比较。仿真结果表明,相对被动悬架,具有LQG控制的半主动悬架在降低人体的加速度、改善车辆的乘坐舒适性和平顺性及行驶安全性上有显著的效果。     

内模控制系统鲁棒跟踪控制器的参数化及优化

针对最常用的2自由度内模控制系统,利用基于传递函数互质分解的频域理论,推导了存在模型失配且参考输入和扰动为任意已知函数时,所有能实现稳态无差跟踪的前馈控制器和反馈滤波器的参数化表达式.所得结论同时适用干连续和离散时间系统,并可在参数化基础上实现频域的优化控制.     

LQG自校正控制器

尽管LQG控制具有很多优点,但由于计算量大,LQG自校正控制仍未能得到成功应用．在本文,提出了一种新的LQG自校正控制器,它是基于最优控制理论和对象的输入输出模型设计的．该算法无需求解Riccati方程或进行谱因子分解,故计算量大为减小,易于实现．系统的闭环特性也在文中作了分析．     

Minimum‐variance control of astronomical adaptive optic systems with actuator dynamics under synchronous and asynchronous sampling

Adaptive optic (AO) systems are now routinely used in ground‐based telescopes to counter the effects of atmospheric turbulence. A deformable mirror (DM) generates a correction wavefront, which is subtracted from the turbulent wavefront using measurements of the residual phase provided by a wavefront sensor (WFS). Minimizing the variance of the residual phase defines a sampled data control problem combining a continuous time minimum‐variance (MV) performance criterion with a discrete‐time controller. For a fairly general class of linear time‐invariant DM and turbulence WFS models, this control problem can be transformed into an equivalent discrete‐time LQ optimization problem involving a set of (discrete‐time) control‐sufficient statistics of the incoming continuous‐time turbulence. This paper shows how to constructively solve this MV problem in the presence of DM's dynamics, starting from continuous‐time models of DM and turbulence. This result is extended to the case of asynchronous DM/WFS sampling. An illustrative application to optimal control of tip‐tilt turbulent modes for the European extremely large telescope in the presence of first‐order DM's dynamics is presented. Copyright © 2010 John Wiley & Sons, Ltd.     

车辆追踪运行的离散模型与最优控制

对车辆追踪运行进行控制,是实现车辆安全、快捷运行的重要手段之一.将车辆追踪运行控制问题归结为“速度差”调节和标准车距跟踪的混合系统进行研究.建立了离散模型,分析了其能控性和能观性,运用最优控制理论求解其反馈控制律,给出了算法步骤.对具体算例进行了仿真实现.     

Optimal Nonlinear Income Taxation with a Two-Dimensional Population; A Computational Approach

We consider the optimal income tax problem when income differences are due to differences in abilities and in preferences between consumption and leisure among individuals. We model this problem as an optimal control problem and develop a numerical method for solving it. The method is based on the expansion of state and control variables in Lagrange series and on a spectral collocation method for approximating state equations. In this way the optimal control problem is reduced to a parameter optimization problem. The problem is difficult to solve, but we managed to do so with some limitations. On the basis of our calculations we conclude that the tax system in the two-dimensional case is more redistributive compared to that obtained from the one-dimensional model.     

基于状态反馈的LQG半主动悬架控制策略研究

随着我国智能电网的建设以及电力市场的逐步推行,传统的集中式大电网供电模式已经无法满足当今社会对电力的需求,分布式电源的引入就成为了未来电网发展的一个新趋势。分布式发电技术的引入不仅可以解决集中式发电投资大、建设周期长、调节不灵活及事故范围大等弊端,还能有效地解决全世界所面临的能源危机和环境污染等问题。由于分布式电源的引入,配电网中将会出现很多新的节点类型,处理这些节点时如果采用传统的潮流算法往往难以达到预期的效果,而潮流计算是开展配电网其它研究工作的基础,因此,研究含分布式电源的配电网潮流计算显得尤为重要。本文详细论述了分布式发电的意义以及国内外对于含分布式电源的配电网潮流算法的研究现状。     

奇异动态经济系统最优跟踪问题

奇异动态经济系统最优跟踪问题阎九喜（山东建筑工程学院济南２５００１４）程兆林（山东大学数学系济南２５０１００）关键词动态经济系统,最优跟踪问题,广义系统,最优控制理论．１）山东省自然科学基金资助项目．本文曾在１９９５年中国控制会议（安徽黄山）上宣读．...     

对象不稳定的内模控制系统的参数优化仿真

内模控制系统的参数优化对提高工业生产效率意义重大.内模控制系统的产生随控制对象的状态变化而发生变化,随着控制过程复杂程度的增加,控制对象的不稳定状态极具增加,控制参数发生不可控突变.传统的参数控制方法采用补偿技术控制参数突变,但是,这种补偿存在较为明显的滞后性,属于后发式控制,容易形成过控制和欠控制等弊端.为解决上述问题,提出一种控制器和稳定器的参数化设计方法,针对对象不稳定的改进内模控制系统,利用基于传递函数互质分解的频域理论,在保证内稳定性及鲁棒无差跟踪一般性结论的基础上,推导得到所有满足条件的控制器和稳定器的参数化表达式,在众多满足一般性结论的控制器集合中找寻最优控制器,进一步实现系统跟踪性能,抗扰性及鲁棒性能上的优化,最后通过Matlab/Simulink仿真平台进行仿真,验证了所得结论的真实性和可靠性.提出的参数化优化方法可进一步应用于其它内模控制系统的扩展中,优化了参数控制过程.     

Robust model predictive control with guaranteed setpoint tracking

In this paper a novel robust model predictive control (RMPC) algorithm is proposed, which is guaranteed to stabilize any linear time-varying system in a given convex uncertainty region while respecting state and input constraints. Moreover, unlike most existing RMPC algorithms, the proposed algorithm is guaranteed to remove steady-state offset in the controlled variables for setpoints (possibly) different from the origin when the system is unknown linear time-invariant. The controller uses a dual-mode paradigm (linear control law plus free control moves to reach an appropriate invariant region), and the key step is the design of a robust linear state feedback controller with integral action and the construction of an appropriate polyhedral invariant region in which this controller is guaranteed to satisfy the process constraints. The proposed algorithm is efficient since the on-line implementation only requires one to solve a convex quadratic program with a number of decision variables that scale linearly with the control horizon. The main features of the new control algorithm are illustrated through an example of the temperature control of an open-loop unstable continuous stirred tank reactor.