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

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Roshanravan s.; Shamghadri s.

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Journal: Modares Mechanical Engineering Year:2019 | Volume:19 | Issue:6 Page(s): 1375-1384

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Information Journal Paper

Title

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

Author(s)

Roshanravan s. | Shamghadri s. | Issue Writer Certificate

Keywords

Polynomial Nonlinear SystemsQ1

Sum of SquaresQ1

Input TrackingQ1

Input to State StabilityQ1

Hardware in the LoopQ1

Abstract

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 linearization 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 globally exponential stability of the nonlinear system with less conservatism than other linearization based methods. 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.

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APA: Copy

Roshanravan, s., & Shamghadri, s.. (2019). Tracking Controller Design for Polynomial Nonlinear Systems Using Sum of Squares Optimization and Input to State Stability. MODARES MECHANICAL ENGINEERING, 19(6 ), 1375-1384. SID. https://sid.ir/paper/178640/en

Vancouver: Copy

Roshanravan s., Shamghadri s.. Tracking Controller Design for Polynomial Nonlinear Systems Using Sum of Squares Optimization and Input to State Stability. MODARES MECHANICAL ENGINEERING[Internet]. 2019;19(6 ):1375-1384. Available from: https://sid.ir/paper/178640/en

IEEE: Copy

s. Roshanravan, and s. Shamghadri, “Tracking Controller Design for Polynomial Nonlinear Systems Using Sum of Squares Optimization and Input to State Stability,” MODARES MECHANICAL ENGINEERING, vol. 19, no. 6 , pp. 1375–1384, 2019, [Online]. Available: https://sid.ir/paper/178640/en

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