Stochastic Optimal Tracking with Preview for Linear Discrete Time Markovian Jump Systems

Abstract

It is well known that, for the design of tracking control systems, preview information of reference signals is very useful for improving performance of the systems, and recently much work has been done for preview control systems [Cohen & Shaked (1997); Gershon et al. (2004a); Gershon et al. (2004b); Nakura (2008a); Nakura (2008b); Nakura (2008c); Nakura (2008d); Nakura (2008e); Nakura (2009); Nakura (2010); Sawada (2008); Shaked & Souza (1995); Takaba (2000)]. Especially, in order to design tracking control systems for a class of systems with rapid or abrupt changes, it is effective in improving the tracking performance to construct tracking control systems considering future information of reference signals. Shaked et al. have constructed the H∞ tracking control theory with preview for continuousand discrete-time linear time-varying systems by a game theoretic approach [Cohen & Shaked (1997); Shaked & Souza (1995)]. Recently the author has extended their theory to linear impulsive systems [Nakura (2008b); Nakura (2008c)]. It is also very important to consider the effects of stochastic noise or uncertainties for tracking control systems. By Gershon et al., the theory of stochastic H∞ tracking with preview has been presented for linear continuousand discrete-time systems [Gershon et al. (2004a); Gershon et al. (2004b)]. The H∞ tracking theory by the game theoretic approach can be restricted to the optimal or stochastic optimal tracking theory and also extended to the stochastic H∞ tracking control theory. While some command generators of reference signals are needed in the papers [Sawada (2008); Takaba (2000)], a priori knowledge of any dynamic models for reference signals is not assumed on the game theoretic approach. Also notice that all these works have been studied for the systems with no mode transitions, i.e., the single mode systems. Tracking problems with preview for systems with some mode transitions are also very important issues to research. Markovian jump systems [Boukas (2006); Costa & Tuesta (2003); Costa et al. (2005); Dragan & Morozan (2004); Fragoso (1989); Fragoso (1995); Lee & Khargonekar (2008); Mariton (1990); Souza & Fragoso (1993); Sworder (1969); Sworder (1972)] have abrupt random mode changes in their dynamics. The mode changes follow Markov processes. Such systems may be found in the area of mechanical systems, power systems, manufacturing systems, communications, aerospace systems, financial engineering and so on. Such systems are classified into continuous-time [Boukas (2006); Dragan & Morozan (2004); Mariton (1990);