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在功能上必须满足性能要求并保持可接受的行为，即使由于随机部件故障或维修、突然的环境扰动、子系统互连的变化、非线性对象运行点的突然变化等引起的动态变化也是如此。具有这种行为的系统可以被建模为混合系统，即在系统理论中通常使用的状态变量的基础上附加一个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跃和不连续的发生。其中最重要的一类混合系统被称为马尔可夫跳跃参数系统，其模式过程是一个在有限集中取值的马尔可夫链。

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.