Optimality conditions for a linear differential system with a single delay

conference paper

English

In the contribution, linear differential system with a single delay $$\frac{dx(t)}{dt}= A_0x(t) + A_1x(t-\tau) + bu(t), t \geq t_0$$ where A_0, A_1 are $n \times n$ constant matrices, $x \in R^n$, $b \in R^n$, $\tau > 0$, $t_0 \in R$, $u \in R$, is considered. A problem of minimizing (by a suitable control function u(t)) a functional $$I =\int _t_0 ^ \infty (x^T(t)C_{11}x(t) + x^T (t)C_{12}x(t-\tau) + x^T (t-\tau)C_{21}x(t) + ^T (t-\tau)C_{22}x(t-\tau) + du^2(t))dt,$$ where $C_{11}$, $C_{12}$, $C_{21}$, $C_{22}$ are $n \times n$ constant matrices, $d > 0$, and the integrand is a positive-definite quadratic form, is considered. To solve the problem, Malkin’s approach and Lyapunov’s second method are utilized.

delayed differential system, Lyapunov-Krasovskii functional, integral quality criterion, optimal control.

DEMCHENKO, H.; DIBLÍK, J.

15. 6. 2017

Univerzita obrany v Brně

Brno

978-80-7231-417-1

Matematika, informační technologie a aplikované vědy (MITAV 2017)

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http://mitav.unob.cz/