Markov 系统矩阵未知情况下的控制器设计

针对Markov 系统矩阵参数未知的实际情况, 提出一种基于状态反馈控制与自适应控制相结合的控制方法. 基于线性矩阵不等式技术给出相应控制器参数的求解条件. 与现有大多数自适应控制方法相比, 所提方法不仅使估计误差几乎处处有界, 而且原系统的系统状态几乎处处渐近稳定, 具有较好的收敛特性. 在所得结果的基础上, 进一步讨论了转移速率部分未知时的相关控制问题. 数值算例验证了所提出的设计方法的有效性.

Stabilization of Markovian jump systems with unknown system matrices

For the stabilization problem of Markovian jump systems, whose system matrices are unknown, a kind of controller containing state feedback control and adaptive control simultaneously is proposed. Based on the linear inequality matrix technique, the corresponding parameters needed in the designed controller can be solved easily. Compared with some existing adaptive methods, not only the estimated errors are bounded almost surely, but also the states of the resulting closed-loop system are asymptotically stable almost surely. In this sense, the adaptive control method has a better convergence performance in terms of system states asymptotically stable in probability. Furthermore, more extension on the transition rate matrix being partially unknown is considered. A numerical example is given to illustrate the effectiveness of the proposed method.