2018/03/28 by Franco Blanchini, Blanchini, Franco, Filippo Fabiani +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Adaptive Dynamic Programming Control #Advanced Control Systems Optimization #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1803.10689
openalex publication_date 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Merging two Control Lyapunov Functions (CLFs) means creating a single "new-born" CLF by starting from two parents functions. Specifically, given a "father" function, shaped by the state constraints, and a "mother" function, designed with some optimality criterion, the merging CLF should be similar to the father close to the constraints and similar to the mother close to the origin. To successfully merge two CLFs, the control-sharing condition is crucial: the two functions must have a common control law that makes both Lyapunov derivatives simultaneously negative. Unfortunately, it is difficult to guarantee this property a-priori, i.e., while computing the two parents functions. In this paper, we propose a technique to create a constraint-shaped "father" function that has the control-sharing property with the "mother" function. To this end, we introduce a partial control-sharing, namely, the control-sharing only in the regions where the constraints are active. We show that imposing partial control-sharing is a convex optimization problem. Finally, we show how to apply the partial control-sharing for merging constraint-shaped functions and the Riccati-optimal functions, thus generating a CLF with bounded complexity that solves the constrained linear-quadratic stabilization problem with local optimality.