Sensitivity Analysis of Krasovskii Passivity-Based Controllers

In the domain of passivity theory, there were major contributions in the last decade, the most recent notion of passivity being the so-called Krasovskii passivity. This framework offers the possibility of designing a controller which ensures the passivity of the resulting closed-loop system. The current paper proposes a solution to design the parameters of Krasovskii passivity-based controllers (K-PBCs) in order to ensure small sensitivity of the closed-loop systems. As such, after the initial construction of the passivity output, the controller parameters are designed in order to impose the dominant eigenvalues of the Jacobian of the resulting closed-loop system with the smallest deviation around the given forced equilibrium point which is, additionally, smaller than a prescribed stability margin. The resulting optimization problem is non-convex by nature, and a metaheuristic approach is proposed to design these parameters. Moreover, in order to impose an extra set of performances, the control system contains an outer loop where dynamical path planning is used to impose the additional requirements. All mentioned results are developed for processes modeled as bilinear systems. In order to illustrate the proposed control method, a numerical example consisting of a single-ended primary inductor DC-DC converter (SEPIC) process is presented.