Designing nonpolynomial controllers for polynomial systems with input constraints using convex optimization and passivity

In this paper, a computational approach for controller design for polynomial systems with input constraints is proposed. The design is formulated as a convex optimization problem and capable of dealing with asymmetric input constraints. The idea of the method is to combine the recently introduced notion of virtual inputs and the notion of feedback passivity to obtain an optimization problem with polynomial constraints. The optimization problem is relaxed using the method of sum of squares which finally results in an LMI problem. The resulting state feedback controllers are non-polynomial. The approach contains some conservatism arising when formulating the design as a convex optimization problem. The introduction of slack variables and a postprocessing step reduces this conservatism. The applicability of the method is demonstrated by a controller design for a jet engine compressor.