Stochastic control: theory and applications

实际系统大多是随机的、非线性的。这种类型的动态系统必须在其功能中满足性能要求，并且即使在由于随机部件故障或修理、突然的环境干扰、子系统互连的变化、非线性设备的操作点的突然变化等而导致的动态中存在突然变化时也保持可接受的行为。具有这种行为的系统可以被建模为混合系统，即，通常在系统理论中使用的状态变量，被附加称为模式或状态的离散随机变量。该模式描述了系统参数的随机跳变和不连续性的发生。马尔可夫跳变参数系统是一类重要的混合系统，其模态过程是取值于有限集的马尔可夫链。

Most of practical systems are stochastic and nonlinear. Dynamical systems of this type must in their functioning meet performance requirements and maintain acceptable behavior even in the presence of abrupt changes in their dynamics due, to random component failures or repairs, abrupt environmental disturbances, changes in subsystems interconnections, abrupt changes in the operating point of nonlinear plant, etc. Systems with this behavior may be modeled as hybrid ones, that is, to the state variable usually used in system theory, a discrete random variable called the mode, or regime is appended. The mode describes the random jumps of the systems parameters and the occurrence of the discontinuities. One of the most important hybrid class of systems is the one called systems with Markovian jumping parameters, in which the mode-process is a Markov chain taking values in a finite set.