OPTIMALITY CONDITIONS FOR SCALAR LINEAR DIFFERENTIAL SYSTEM

OPTIMALITY CONDITIONS FOR SCALAR LINEAR DIFFERENTIAL SYSTEM

Paper in proceedings (conference paper)

In the contribution, for scalar linear differential system $$\frac{dx(t)}{dt}= Ax(t) +Bu(t),$$ where $A \in R^{n×n}$, $B \in R^{n×m}$, $x(t) \in R^n$ and $u(t) \in R^m$ is a control function, a problem of minimizing a function $$I[x(t),u(t)] =\int _t_0 ^ \infty (x^T(t)Cx(t) + u^T(t)Du(t))dt,$$ where $C \in R^{n×n}$ is a symmetric, positive definite matrix and $D$ is a diagonal control matrix, $D = diag{d_j}$, $d_j > 0$, $j = 1,...,m$, is considered. To solve the problem, Malkin’s approach and Lyapunov’s second method are utilized.

In the contribution, for scalar linear differential system $$\frac{dx(t)}{dt}= Ax(t) +Bu(t),$$ where $A \in R^{n×n}$, $B \in R^{n×m}$, $x(t) \in R^n$ and $u(t) \in R^m$ is a control function, a problem of minimizing a function $$I[x(t),u(t)] =\int _t_0 ^ \infty (x^T(t)Cx(t) + u^T(t)Du(t))dt,$$ where $C \in R^{n×n}$ is a symmetric, positive definite matrix and $D$ is a diagonal control matrix, $D = diag{d_j}$, $d_j > 0$, $j = 1,...,m$, is considered. To solve the problem, Malkin’s approach and Lyapunov’s second method are utilized.

optimization problem, control function, Lyapunov function.

optimization problem, control function, Lyapunov function.

DEMCHENKO, H.

2018

27.04.2017

Vysoké učení technické v Brně, Fakulta elektrotechniky a komunikačních technologií

Brno

978-80-214-5496-5

Proceedings of the 23nd Conference STUDENT EEICT 2017

629

633

5

http://eeict.feec.vutbr.cz/2017/sbornik/EEICT_2017-sbornik-komplet-2.pdf