%0 Journal Article
%T A Novel Method for Optimal Control of Piecewise Affine Systems Using Semi-Definite Programming
%J 𝕴𝖓𝖙𝖊𝖗𝖓𝖆𝖙𝖎𝖔𝖓𝖆𝖑 𝕵𝖔𝖚𝖗𝖓𝖆𝖑 𝖔𝖋 𝕴𝖓𝖉𝖚𝖘𝖙𝖗𝖎𝖆𝖑 𝕰𝖑𝖊𝖈𝖙𝖗𝖔𝖓𝖎𝖈𝖘, 𝕮𝖔𝖓𝖙𝖗𝖔𝖑 𝖆𝖓𝖉 𝕺𝖕𝖙𝖎𝖒𝖎𝖟𝖆𝖙𝖎𝖔𝖓
%I University of Sistan and Baluchestan
%Z 2645-3517
%A Akbarian, Majid
%A Eghbal, Najmeh
%A Pariz, Naser
%D 2020
%\ 01/01/2020
%V 3
%N 1
%P 59-68
%! A Novel Method for Optimal Control of Piecewise Affine Systems Using Semi-Definite Programming
%K Piecewise affine systems
%K state-feedback
%K discontinues quadratic Lyapunov function
%K continuous quadratic Lyapunov functions
%R 10.22111/ieco.2019.26629.1082
%X : In this paper, a novel optimal control design method by discontinuous quadratic Lyapunov function and continuous quadratic Lyapunov function for 2-dimensional piecewise affine systems via semi-definite programming and LMI constraints is proposed.In fact, for designing optimal control we use from two different criteria. At the first, an upper bound for a quadratic cost function for a stable closed-system is obtained. Then after, considering a state-feedback control approach, not only sufficient conditions for the stability of the closed-loop system but also the upper bound of the cost function are obtained. The optimization problem is formulated as a semi-definite programming with bilinear constraints (BMI). Some variables in BMIs are searched by genetic algorithm, so the bilinear constraints are converted to linear constraints and the controller coefficients are calculated. The effectiveness of the proposed method is verified by numerical examples. The simulation results show that discontinuous quadratic lyapunov functions are more efficient that continuous quadratic lyapunov functions.
%U https://ieco.usb.ac.ir/article_4978_7dd2b2eadb7771bf1cebdfee43a3cd61.pdf