Pol Jané-Soneira

Pol Jane-Soneira, Gösta Stomberg, Ognjen Stanojev et al.

This article studies the stability of feedback interconnections of linear time-invariant systems based on frequency-dependent passivity indices. Using these frequency-dependent passivity indices, we show that the feedback interconnection of two systems can be certified to be stable even if both systems have a lack of passivity in terms of their scalar passivity indices. The main contribution of this paper is a new stability theorem based on frequency-dependent passivity indices. Moreover, we discuss the connection of the proposed feedback stability theorem to prior results based on scalar passivity indices. A numerical case study showcases the advantages of frequency-dependent passivity indices over scalar indices for feedback interconnections of linear systems.

Armin Gießler, Pol Jané-Soneira, Sören Hohmann

This paper studies the data-driven synthesis of linear quadratic integral (LQI) controllers for continuous-time systems. The objective is to achieve optimal state-feedback control with integral action for reference tracking using only measured data. To this end, we derive a data-driven closed-loop parameterization of the augmented dynamics that incorporates the integral state while relying solely on input-state-output measurements of the underlying system. Based on this parameterization, a data-driven convex optimization problem is formulated whose solution yields the optimal linear quadratic regulator (LQR) feedback gain for the augmented system without explicit knowledge of the system matrices. In addition, a policy gradient flow is derived to compute the optimal controller within the space of stabilizing gains. The proposed approach enables data-driven optimal tracking control while avoiding explicit state augmentation in the data collection phase. The effectiveness of the method is demonstrated through a numerical example involving a distributed generation unit (DGU) in a DC microgrid.

Armin Gießler, Pol Jané-Soneira, Sören Hohmann

We study state-feedback design for continuous-time LTI systems with a control input and an external input-output pair. Our objective is to determine feedback gains that render the closed-loop system (strictly) passive with respect to the external port while minimizing the standard LQR cost in the disturbance-free case. The resulting constrained optimization problem is intractable due to bilinear matrix inequalities. We analyze the set of passivating gains, showing it is unbounded, possibly nonconvex, path-connected, and contractible. We propose an indirect approach, in which the set of passivating feedback gains is inner-approximated by a compact, convex polytope. A projected gradient flow is employed to compute a gain within this polytope that minimizes the LQR cost. Numerical examples illustrate the effectiveness of the method.