A scalable iterative convex design for nonlinear systems

A recently developed control scheme for approximately optimal control of nonlinear systems is the so-called Convex Control Design (ConvCD) methodology, that transforms the control problem of generic nonlinear systems into a convex optimization problem. The ConvCD approach constructs a polynomial controller approximating the optimal control law: such design does not provide a scalable controller as it requires the use of a polynomial controller, which is not scalable, especially in large-scale applications. This problem is overcome in this paper by modifying the ConvCD formulation so that the optimal control law is approximated with a Multi-Controller with Mixing: that is, the polynomial controller is substituted by linear control elements plus mixing signals that are responsible for smoothly switching from one linear element to another. The stability properties of the Multi-Controller with Mixing are analyzed and an iterative approach is proposed to solve the resulting optimization problem. The resulting procedure aims at the development of a scalable and modular architecture for nonlinear systems, in order to allow for easier implementation and re-configurability. A numerical example is used to show the effectiveness of the method.