arXiv subjects
Publications and source records attributed to Mario Sassano.
Considering infinite-horizon, discrete-time, linear quadratic, N-player dynamic games with scalar dynamics, a graphical representation of feedback Nash equilibrium solutions is provided. This representation is utilised to derive conditions for the number and properties of different feedback Nash equilibria a game may admit. The results are illustrated via a numerical example.
This paper solves the robust hybrid output regulation problem for arbitrary uncertain hybrid MIMO linear systems with periodic jumps without the restrictive assumptions used in all previous works on the subject. A necessary condition for solving the problem is that the regulator must incorporate an internal model of the flow zero-dynamics, which is typically affected by uncertainties and then unknown. Hence, the proposed regulator consists of three units: a data-driven estimator of the dynamics that are invisible from the regulated output during flows, a flow internal model in charge of achieving regulation during flows, and a jump internal model in charge of imposing a suitable reset of the state at each jump.
This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $Γ_1 \subset Γ_2 \subset \Re^n$, with $Γ_1$ compact, the theorems presented in this paper give conditions under which a qualitative property of $Γ_1$ that holds relative to $Γ_2$ (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set $Γ_1$, then $Γ_1$ is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal.
In this short note we prove a hierarchical stability result that applies to hybrid dynamical systems satisfying the hybrid basic conditions of (Goebel et al., 2012). In particular, we establish sufficient conditions for uniform asymptotic stability of a compact set based on some hierarchical stability assumptions involving two nested closed sets containing such a compact set. Moreover, mimicking the well known result for cascaded systems, we prove that the basin of attraction of such compact set coincides with the largest set from which all solutions are bounded. The result appears to be useful when applied to several recent works involving hierarchical control architectures.