Mode-independent control of singular Markovian jump systems: a stochastic optimization viewpoint. (English) Zbl 1410.93116
Summary: In this paper, the mode-independent control problem of singular Markovian jump systems is firstly studied by exploiting a stochastic optimization viewpoint. A new kind of mode-independent \(H_\infty\) controller satisfying a minimum variance approximation is constructed, whose gain is composed of some mode-dependent control gains. The available probability of system mode is described by the Bernoulli variable and taken into account. It shows that such a probability plays an important role in system analysis and associates mode-independent controller with mode-dependent controllers. When the probability is unknown, a kind of adaptive controller is proposed such that the resulting closed-loop system is robust stochastically admissible with an \(H_\infty\) performance. All the proposed conditions are given in terms of linear matrix inequalities. Two numerical examples are used to demonstrate the effectiveness of the proposed methods.
MSC:
| 93E03 | Stochastic systems in control theory (general) |
| 49L20 | Dynamic programming in optimal control and differential games |
| 60J27 | Continuous-time Markov processes on discrete state spaces |
| 93B36 | \(H^\infty\)-control |
Keywords:
singular Markovian jump systems; mode-independent control; adaptive control; stochastic optimization; linear matrix inequalities (LMIs)References:
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