New approach to optimal controller synthesis via identification

This work aims to propose a new approach for synthesizing an optimal controller of chosen dimension. The proposed approach makes it possible to stay as close as possible to the practical considerations in optimal controller synthesis and thus avoid a quadratic criterion constrained by the choice of weighting matrices. Furthermore, the proposed approach can be generalized to controller synthesis through learning. The proposed solution reduces the constraints associated with nonconvex optimization. Indeed, the non-convexity of the problem makes the result highly dependent on the initial condition. Thus, two problems are formulated: a convex optimization problem with a fixed dimension, potentially yielding a slowly unstable solution, and a nonconvex problem depending on initial stabilizing controller. The latter ensures the stability of the optimal solution.

Therefore, an algorithm is developed, enabling the computation of the optimal controller of a chosen dimension from a given linear time-invariant model and specified references.