Markov跳变系统的单步约束预测控制

Constrained one step predictive control of discrete time Markovian jump linear systems

针对离散Markov跳变系统,研究带输出约束的单步预测控制问题。首先设计基于模态的单步预测控制器,驱动系统状态到达相应的终端不变集内,以此保证约束预测控制系统的稳定性,接着进一步讨论了系统存在峰值有界噪声输入情形。其中终端不变集是通过在预测时域外寻求一个虚拟的带约束的状态反馈控制器以保证系统的随机稳定性来获得,为计算方便,控制器的优化问题转化为SDP问题,并得到以LMI描述的优化问题。最后对Markov跳变系统描述的经济学动力系统的仿真结果说明了本控制器设计方法能够在峰值有界噪声输入下保证系统的稳定性,并且使控制变量满足给定的约束条件。

The one step receding horizon control （RHC） problcm is considered for discrete time Markovian jump linear system, subject to constraints on control inputs. At first, constrained one step receding horizon control low are designed to drive the state trajectory into a terminal invariant set, which guarantees stochastic stability of jump system. Then the situation with peak bounded noise inputs is also studied. And the invariant set depends on the existence of a fictitious state feedback control law, which guarantees stochastic stability of jump system out of the receding horizon. For computational tractability, the controller optimization problem is transformed into a semi-definite programming （SDP） problem which can be easily solved by means of LMI. The sinulation results of an economic dynamic system which described by a Markovian jump linear system demonstrates that the method are valid.