研究故障条件下子空间预测控制器的设计问题，在推导输出预测估计值后分析残差矢量的统计分布特性
及残差矢量在各个瞬时时刻处的具体形式. 针对含有等式和不等式约束条件的预测控制器最优化问题，通过对偶
运算将较复杂的约束优化转化为无约束优化问题，采用最近邻梯度法即可求得基-对偶优化问题的最优解. 最后以
直升机悬停状态为例，验证控制器设计方法的有效性.
This paper studies design of controllers in subspace predictive control structure under faulty conditions.
Having derived the output predictive estimations, statistic distribution of the residual and the expression
are analyzed. To optimize the prediction controller with equalities and inequalities, dual decomposition is used
to convert the former constrained optimization into unconstrained optimization. The incremental proximal
method is applied to solve the primal-dual optimization problem. With a helicopter as an example, effectiveness
of the proposed control strategy is verified.
[1] CHIUSO A. The role of vector autoregressive modeling in predictor based subspace identification [J]. Automatica, 2007, 43(6): 1034-1048.
[2] CHIUSO A. On the relation between CCA and predictor based subspace identification[J]. IEEE Transactions of Automatic Control, 2007, 52(10): 1795-1811.
[3] 王建宏.子空间预测控制算法在主动噪声振动中的应用[J]. 振动与冲击,2011,30(10): 129-135.
WANG Jianhong, WANG Daobo. Subspace predictive control applied to active noise and vibration control[J]. Journal of Vibration and Shock, 2011, 30(10): 129-135. (in Chinese)
[4] 王建宏.子空间预测控制中的椭球优化及其应用[J]. 应用科学学报，2010,28(4): 424-429.
WANG Jianhong, WANG Daobo. Application of the ellipsoid optimization algorithm in subspace predictive control[J]. Journal of Applied Science, 2010, 28(4): 424-429. (in Chinese)
[5] 王建宏.故障估计下子空间预测控制的快速梯度算法[J]. 上海交通大学学报：自然科学版，2013,47(7)：1015-1021.
Wang Jianhong. Fast gradient algorithm in subspace predictive control under fault estimation[J]. Journal of Shanghai Jiao Tong University: Natural Science Edition. 2013, 47(7): 1015-1021. (in Chinese)
[6] LJUNG L. System identification: theory for the user [M]. [S.l.]: Prentice Hall, 1999.
[7] BOYD S, VANDENBERGHE L. Convex optimization [M]. UK: Cambridge University Press, 2008.
[8] ZEILINGER Melanie. Real time suboptimal model predictive control using a combination of explicit MPC and online optimization [J]. IEEE Transactions of Automatic Control, 2011, 56(7): 1524-1534.
[9] JAKOB K. A design algorithm using external perturbation to improve iterative feedback tuning convergence[J]. Automatica, 2011, 47(2): 2665-2670.
[10] OHLSSON Henrik. Identification of switched linear regression models using sum of norms regularization[J]. Automatica, 2013, 49(4): 1045-1050.
[11] Van Mulders Anne. Identification of systems with localised nonlinearity: from state space to block structured models[J]. Automatica, 2013, 49(5 ): 1392-1396.
[12] FELLER Christian. An improved algorithm for combinatorial multi-parameteric quadratic programming[J]. Automatica, 2013, 49(5 ): 1370-1376.
[13] FIOER Havard. Observers for interconnected nonlinear and linear systems[J]. Automatica, 2012, 48(7 ): 1339-1346.
[14] RAKO Lauret. Identification of switched linear systems via sparse optimization[J]. Automatica, 2011, 47(4 ): 668-677.
[15] Paul M J Vanden Hof. Identification of dynamic models in complex networks with prediction error methods [J]. Automatica, 2013, 49(10): 2994-3006.
