A Sum of Squares Optimization Approach to Robust Control of Bilinear Systems

Nobuyama, Eitaku; Aoyagi, Takahiko; Kami, Yasushi

doi:10.5772/17576

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Control design for discrete‐time bilinear systems using the scalarized Schur complement

Vatani

Hovd

Olaru

2017

Intl J Robust & Nonlinear

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Summary In this paper, controller design for discrete‐time bilinear systems is investigated by using sum of squares programming methods and quadratic Lyapunov functions. The class of rational polynomial controllers is considered, and necessary conditions on the degree of controller polynomials for quadratic stability are derived. Next, a scalarized version of the Schur complement is proposed. For controller design, the Lyapunov difference inequality is converted to a sum of squares problem, and an optimization problem is proposed to design a controller, which maximizes the region of quadratic stability of the bilinear system. Input constraints can also be accounted for. Copyright © 2017 John Wiley & Sons, Ltd.

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Control design for discrete‐time bilinear systems using the scalarized Schur complement

Vatani

Hovd

Olaru

2017

Intl J Robust & Nonlinear

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Control design and analysis for discrete time bilinear systems using Sum of Squares methods

Vatani

Hovd

Olaru

2014

53rd IEEE Conference on Decision and Control

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Abstract-In this paper, stabilization of discrete time bilinear systems is investigated by using Sum of Squares (SOS) programming methods and a quadratic Lyapunov function. Starting from the fact that global asymptotic stability cannot be proven with a quadratic Lyapunov function if the controller is polynomial in the states, the controller is instead proposed to be a ratio of two polynomials of the states. First, a simple one-step optimal controller is designed, and it is found that it is indeed defined as a ratio of two polynomials. However, this simple controller design does not result in any stability guarantees. For stability investigation, the Lyapunov difference inequality is converted to a SOS problem, and an optimization problem is proposed to design a controller which maximizes the region of convergence of the bilinear system. Input constraints can also be accounted for in the optimization problem.

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A Sum of Squares Optimization Approach to Robust Control of Bilinear Systems

Cited by 2 publications

References 7 publications

Control design for discrete‐time bilinear systems using the scalarized Schur complement

Control design for discrete‐time bilinear systems using the scalarized Schur complement

Control design and analysis for discrete time bilinear systems using Sum of Squares methods

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