Tracking Controller Design for Polynomial Nonlinear Systems Using Sum of Squares Optimization and Input to State Stability

Roshanravan, S.; Shamaghdari, S.

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Modares Mechanical Engineering

Volume 19, Issue 6 (June 2019) Modares Mechanical Engineering 2019, 19(6): 1375-1384 | Back to browse issues page

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Roshanravan S, Shamaghdari S. Tracking Controller Design for Polynomial Nonlinear Systems Using Sum of Squares Optimization and Input to State Stability. Modares Mechanical Engineering 2019; 19 (6) :1375-1384
URL: http://mme.modares.ac.ir/article-15-20812-en.html

Tracking Controller Design for Polynomial Nonlinear Systems Using Sum of Squares Optimization and Input to State Stability

S. Roshanravan¹

, S. Shamaghdari ^*

1- Control Department, Electrical Engineering Faculty, Iran University of Science & Technology, Tehran, Iran
2- Control Department, Electrical Engineering Faculty, Iran University of Science & Technology, Tehran, Iran , shamaghdari@iust.ac.ir

Abstract: (6951 Views)

This paper presents a new method to design stabilizing and tracking control laws for a class of nonlinear systems whose state space description is in the form of polynomial functions. This method employs the nonlinear model directly in the controller design process without the need for local about an operating point. The approach is based on the sum of squares (SOS) decomposition of multivariate polynomials which is transformed into a convex optimization problem. It is shown that the design problem can be formulated as a sum of squares optimization problem. This method can guarantee of the nonlinear system with less conservatism than based Also, a sum of squares technique is used to evaluate the stability of closed loop system state with respect to exogenous input. The nonlinear dynamic model of air vehicles can usually be expressed by polynomial nonlinear equations. Therefore, the proposed method can be applied to design an air vehicle autopilot. The hardware in the loop (HIL) simulation is an important test for evaluation of the aerospace control system before flight test. The HIL results using designed controller for a supersonic air vehicle are presented. The results from HIL is compared to the software simulation that the appropriate consistency of results shows the efficiency of the proposed method in the air vehicle autopilot control loop.

Keywords: Polynomial nonlinear systems Sum of squares Input tracking Input to state stability Hardware in the loop

Full-Text [PDF 590 kb] (2392 Downloads)

Article Type: Original Research | Subject: Control
Received: 2018/05/13 | Accepted: 2018/12/23 | Published: 2019/06/1

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