Non‐iterative SOS‐based approach for guaranteed cost control design of polynomial systems with input saturation

Abstract

This study proposes a novel sum of squares (SOS) decomposition-based constrained guaranteed cost function controller for polynomial systems. The sufficient non-linear controller design conditions are derived such that an upper bound of a quadratic cost function subjected to the input amplitude constraint is minimised and asymptotic stability of the polynomial system is guaranteed. First, the constrained optimisation problem is formulated by an alternative unconstrained optimisation problem with the vanishing disturbance input. Then, by considering the S-procedure, the sufficient conditions are derived in terms of SOS decomposition. The main novelty of this study is that the stability issue of input saturated polynomial systems together with the non-linear control law is considered. In addition, the other advantage of this approach over the recently guaranteed cost controller design methods is that the proposed conditions can be solved without any iterative techniques. Finally, to show the effectiveness of the proposed approach, it is applied to a piezoelectrically actuated clamped–clamped micro-beam system and the results are compared with those of existing ones.