不确定随机系统LQG对偶控制

基金项目: 高等学校博士学科点专项科研基金资助项目（20060700007）；陕西省自然科学基金资助项目（2005F15）

详细信息

LQG Dual Control on Uncertain Stochastic Systems

School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China

摘要: 针对不确定性模型为多胞型的随机系统进行了对偶控制的研究．首先，假定多胞型不确定参数存在于状态空间模型的系统矩阵、输入矩阵和量测矩阵中．其次，将此不确定性模型通过不确定参数的后验概率加权，得到其增广系统．然后，使用动态规划得到增广系统的次优控制律．最后，通过仿真验证了本文方法的可行性和有效性．
- 模型不确定性 /
- 多胞型 /
- 对偶控制 /
- 随机系统
Abstract: The problem of dual control is studied for the stochastic system of which the uncertainty model is polytopic.First,it is assumed that the polytope exists in the system matrix,input matrix and measure matrix of the state space model.Second,with the posterior probability weighting of the uncertain parameters,an augmented system is obtained for the uncertainty model.Then,the suboptimal control law is achieved using the dynamic programming principle.Finally,the feasibility and effectiveness of the presented approach are verified with simulation.
- model uncertainty /
- polytopic /
- dual control /
- stochastic system

[1]	Deshpande J G,Upadhyay T N,Lainiotis D G.Adaptive control of linear stochastic systems[J].Automatica,1973,9(1):107～115.
[2]	Milito R,Padilla C S,Padilla R A,et al.Innovations approach to dual control[J].IEEE Transactions on Automatic Control,1982,AC-27(1):132～137.
[3]	Li D,Qian F C,Fu P L.Variance minimization approach for a class of dual control problems[J].IEEE Transactions on Automatic Control,2002,47(12):2010～2020.
[4]	Li D,Qian F C.Closed-loop optimal control law for discrete time LQG problems with a mean-variance objective[A].Proceedings of the IEEE Conference on Decision and Control[C].Piscataway,NJ,USA:IEEE,2004.2291～2296.
[5]	Fu P L,Li D,Qian F C.Active dual control for linear-quadratic Gaussian system with unknown parameters[A].Proceedings of the 15th World Congress of IFAC[C].San Francisco,USA:IFAC,2002.
[6]	钱富才,刘丁,李云霞.基于两级算法的对偶控制[J].控制理论与应用,2004,21(1):89～93.
[7]	Li D,Qian F C,Fu P L.Research on dual control[J].Acta Automatica Sinica,2005,31 (1):32～42.
[8]	钱富才,宋俐,陈晓可.基于滚动优化的对偶控制策略[J].控制理论与应用,2005,22(6):855～861.