带马尔科夫跳和乘积噪声的随机系统的最优控制
doi: 10.3724/SP.J.1004.2012.01113
Optimal Control of Stochastic System with Markovian Jumping and Multiplicative Noises
-
摘要: 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.Abstract: An optimization problem for a stochastic system of N players is presented. An optimal Pareto controller of the stochastic system with Markovian jumping and multiplicative white noises is designed in infinite time horizon. The optimal Pareto solution is obtained by using the generalized Lyapunov equation approach and solving stochastic generalized Riccati algebraic equations (SGRAEs). It is proved that the controller is a stabilizing feedback control and the solution of SGRAEs is minimal associated with the optimal control.
-
Key words:
- Pareto solution /
- stochastic system /
- Markovian jumping /
- multiplicative noises /
- minimal solution
-
[1] Morozan T. Optimal stationary control for dynamic systems with Markov perburbations. Stochastic Analysis and Applications, 1983, 1(3): 299-325[2] Morozan T. Stability and control for linear systems with jump Markov perburbations. Stochastic Analysis and Applications, 1995, 13(1): 91-110[3] Boukas E K, Liu Z K. Deterministic and Stochastic Time-Delay Systems. New York: Springer-Verlag, 2002. 380-427[4] Costa O L V, Fragoso M D, Marques R P. Discrete-Time Markov Jump Linear Systems. London: Springer-Verlag, 2005. 71-142[5] Kleinman D L. On the stability of linear stochastic systems. IEEE Transactions on Automatic Control, 1969, 14(4): 429-430[6] Willems J L, Willems J C. Feedback stabilizability for stochastic systems with state and control dependent noise. Automatica, 1976, 12(3): 277-283[7] Ghaoui L E. State-feedback control of systems with multiplicative noise via linear matrix inequalities. Systems and Control Letters, 1995, 24(3): 223-228[8] Rami M A, Zhou X Y. Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic control. IEEE Transactions on Automatic Control, 2000, 45(6): 1131-1143[9] Chen B S, Zhang W H. Stochastic H2/H∞ control with state-dependent noise. IEEE Transactions on Automatic Control, 2004, 49(1): 45-57[10] Zhan W H, Huang Y L, Zhang H S. Stochastic H2/H∞ control for discrete-time systems with state and disturbance dependent noise. Automatica, 2007, 43(3): 513-521[11] Zhang W H, Zhang H S, Chen B S. Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion. IEEE Transactions on Automatic Control, 2008, 53(7): 1630-1642[12] Wonham W M. Random differential equations in control theory. Probabilistic Methods in Applied Mathematics. New York: Academic Press, 1970. 131-132[13] Haurie A, Leizarowitz A. Overtaking optimal regulation and tracking of piecewise diffusion linear systems. SIAM Journal on Control and Optimization, 1992, 30(4): 816-837[14] Mao X. Stability of stochastic differential equations with Markovian switching. Stochastic Processes and Their Applications, 1999, 79(1): 45-67[15] Dragan V, Morozan T, Stoica A M. Mathematical Methods in Robust Control of Linear Dtochastic Systems. New York: Springer-Verlag, 2006. 80-151[16] Dragan V, Morozan T. The linear quadratic optimization problems for a class of linear stochastic systems with multiplicative white noise and Markovian jumping. IEEE Transactions on Automatic Control, 2004, 49(5): 665-675[17] Mukaidani H. Soft-constrained stochastic Nash games for weakly coupled large-scale systems. Automatica, 2009, 45(5): 1272-1279[18] Mukaidani H. Robust guaranteed cost control for uncertain stochastic systems with multiple decision makers. Automatica, 2009, 45(7): 1758-1764[19] Lee J H, Won C H, Diersing R W. Two player statistical game with higher order cumulants. In: Proceedings of the American Control Conference. Baltimore, USA: IEEE, 2010. 4857-4862
点击查看大图
计量
- 文章访问数: 1878
- HTML全文浏览量: 78
- PDF下载量: 665
- 被引次数: 0