An iterative approach for the discrete-time dynamic control of Markov jump linear systems with partial information. (English) Zbl 1440.93242
Summary: The \(H_2\), \(H_\infty\) and mixed \(H_2/H_\infty\) dynamic output feedback control of Markov jump linear systems in a partial observation context is studied through an iterative approach. By partial information, we mean that neither the state variable \(x(k)\) nor the Markov chain \(\theta (k)\) are available to the controller. Instead, we assume that the controller relies only on an output \(y(k)\) and a measured variable \(\hat{\theta}(k)\) coming from a detector that provides the only information of the Markov chain \(\theta (k)\). To solve the problem, we resort to an iterative method that starts with a state-feedback controller and solves at each iteration a linear matrix inequality optimization problem. It is shown that this iterative algorithm yields to a nonincreasing sequence of upper bound costs so that it converges to a minimum value. The effectiveness of the iterative procedure is illustrated by means of two examples in which the conservatism between the upper bounds and actual costs is significantly reduced.
MSC:
| 93E03 | Stochastic systems in control theory (general) |
| 93B52 | Feedback control |
| 93C55 | Discrete-time control/observation systems |
| 93B36 | \(H^\infty\)-control |
| 93C05 | Linear systems in control theory |
Keywords:
dynamic output feedback control; linear matrix inequalities; Markov jump linear systems; mixed \(H_2/H_\infty\) controlReferences:
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