Tesi di dottorato di ricerca
Composite control Lyapunov functions for robust stabilization of constrained uncertain dynamical systems
Settore scientifico disciplinare
Corso di studi
tutor Prof. Caiti, Andrea
- sistemi dinamici
Data inizio appello
This work presents innovative scientific results on the robust stabilization of constrained uncertain dynamical systems via Lyapunov-based state feedback control.<br><br>Given two control Lyapunov functions, a novel class of smooth composite control Lyapunov functions is presented. This class, which is based on the R-functions theory, is universal for the stabilizability of linear differential inclusions and has the following property. Once a desired controlled invariant set is fixed, the shape of the inner level sets can be made arbitrary close to any given ones, in a smooth and non-homothetic way. This procedure is an example of ``merging'' two control Lyapunov functions.<br><br>In general, a merging function consists in a control Lyapunov function whose gradient is a continuous combination of the gradients of the two parents control Lyapunov functions. <br>The problem of merging two control Lyapunov functions, for instance a global control Lyapunov function with a large controlled domain of attraction and a local one with a guaranteed local performance, is considered important for several control applications. The main reason is that when simultaneously concerning constraints, robustness and optimality, a single Lyapunov function is usually suitable for just one of these goals, but ineffective for the others.<br><br>For nonlinear control-affine systems, both equations and inclusions, some equivalence properties are shown between the control-sharing property, namely the existence of a single control law which makes simultaneously negative the Lyapunov derivatives of the two given control Lyapunov functions, and the existence of merging control Lyapunov functions. <br><br>Even for linear systems, the control-sharing property does not always hold, with the remarkable exception of planar systems. <br><br>For the class of linear differential inclusions, linear programs and linear matrix inequalities conditions are given for the the control-sharing property to hold. <br><br>The proposed Lyapunov-based control laws are illustrated and simulated on benchmark case studies, with positive numerical results.