Stabilization of jump linear gaussian systems without mode observations

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Abstract
Systems, such as those subject to abrupt changes (including failure) or those with uncertain dynamic model (or more than one possible model), can be naturally modelled as jump linear (JL) systems. Because of their applications in fields such as tracking, fault-tolerant control, manufacturing process and robots, JL systems have drawn extensive attention. The optimal control and stabilization problem for JL systems, when the mode (system model) is not assumed to be directly and perfectly observed, a realistic assumption in many applications, is nonlinear and prohibitive both analytically and computationally because of the dual effect. The main contribution of this work is the sufficient condition for stabilization for a class of adaptive controllers when the mode is not directly observed. We first present the optimal controller under an assumption of a certain type of mode availability. Using this optimal feedback gain, we derive a condition that ensures the stabilizing property for a class of adaptive controllers without direct knowledge of the mode. Two specific adaptive controllers (maximum a posteriori and averaging) are examined in detail and their stabilizing property is proved. An algorithm to compute the optimal feedback gain and its convergence are presented. Examples show that the performance of the adaptive controllers without mode observations derived here is very close to that of the optimal controller with known modes.

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