Dynamic output feedback control for continuous-time Markov jump linear systems with hidden Markov models. (English) Zbl 1485.93626
Summary: In this work, we study the design of dynamic output feedback controllers for continuous-time Markov jump linear systems in the worst-case scenario of partial observation of both, the Markov chain and the state, through an iterative method. We assume that the controller has only access to the output of a fault-detection and isolation device and present design conditions for the \(\mathcal{H}_2\), \(\mathcal{H}_\infty\), and mixed \(\mathcal{H}_2 / \mathcal{H}_\infty\) controller that switches according only to the detector. As a by-product of our formulation, we are also able to design mode-dependent and independent controllers, and briefly discuss the design of filters depending on the detector. The results are given in terms of bilinear matrix inequalities that allow for an iterative separation procedure method in which in each step, we solve a linear matrix inequality problem. We also present an illustrative example in the context of systems subject to faults.
MSC:
| 93E20 | Optimal stochastic control |
| 93B36 | \(H^\infty\)-control |
| 93B52 | Feedback control |
| 93C05 | Linear systems in control theory |
Keywords:
optimal control; \(H_\infty\) control; dynamic output feedback; stochastic jump processes; Markov modelsReferences:
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