Abstract
Problems of feedback terminal target control for linear uncertain systems are considered. We continue the development of polyhedral control synthesis using polyhedral (parallelotope-valued) solvability tubes. New control strategies, which can be calculated on the base of these tubes, are proposed. The cases without uncertainties, with additive parallelotope-valued uncertainties, and also with a bilinear uncertainty (interval uncertainties in coefficients of the system) are considered. Ordinary differential equations, which describe the mentioned tubes, are presented for each of these cases. Numerical results are presented.
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Notes
- 1.
The normality condition \(\Vert p^i \Vert _2 = 1\) may be omitted to simplify formulas.
- 2.
Here the class \(U^c_\mathcal{R}\) of feasible control strategies is taken to consist of all convex compact-valued multifunctions \(\mathcal{U}(t,x)\) that are measurable in \(t\), upper semi-continuous in \(x\), being restricted by \(\mathcal{U}(t, x) \subseteq \mathcal{R}(t)\), \(t \in T\). The condition \(\mathcal{U}(\cdot , \cdot ) \in U^c_\mathcal{R}\) ensures that the corresponding differential inclusion does have a solution.
- 3.
This is possible because our strategies will be continuous and even linear with respect to \(x\). Moreover, they will be constructed in an explicit form.
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Acknowledgments
The research was supported by the Program of the Presidium of the Russian Academy of Sciences “Dynamic Systems and Control Theory” under support of the Ural Branch of RAS (Project 12-P-1-1019) and by the Russian Foundation for Basic Research (Grants 12-01-00043,13-01-90419).
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Kostousova, E.K. (2014). On Control Synthesis for Uncertain Differential Systems Using a Polyhedral Technique. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_10
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DOI: https://doi.org/10.1007/978-3-662-43880-0_10
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