Feedback control design using sum of squares optimisation

Applications in many engineering fields require nonlinear modelling and control. However, for nonlinear dynamical systems, designing a control law that makes the system's operating point globally asymptot-ically stable is challenging. In this paper, for systems whose dynamics can be modelled through poly-nomial vector fields, we provide a procedure to design a controller that guarantees global asymptotic stability and a certain cost. To achieve this goal, we use sum of squares programming. In particular, we further develop a previously proposed approach to provide such a control law also for cases where the previous approach failed. The new approach is less restrictive and requires less memory. We apply it to the van der Pol system, the Lorenz system, to a model of a hypersonic flight vehicle, and to satellite attitude control.(c) 2022 European Control Association. Published by Elsevier Ltd. All rights reserved.