Suboptimality bounds for linear quadratic problems in hybrid linear systems

Abstract

A method for computation of lower and upper bounds for the linear quadratic cost function associated to a class of hybrid linear systems is proposed. The optimization problem involves state space constraints and switches between the continuous and discrete dynamics at fixed time instances on the boundaries of the flow and jump sets. Our approach computes a quadratic suboptimal cost parameterized by initial and end state variables of all time intervals. Then, the unknown parameters are determined via solving constrained quadratic programming problems.

Measurement dynamic feedback output regulation in hybrid linear systems with state jumps

“…First, note that (7), where is replaced by ′ given by (49) andV is replaced byV ′ given by (52), holds with L = A E , by virtue of (16), (29), (30), and (33). Moreover, (8), whereĴ andV are respectively replaced byĴ ′ andV ′ given by (50) and (52), holds with L̂J = J E , by virtue of (16), (29), and (38). Thus, it is proven that  is an ℋ -invariant subspace ofΣ.…”

“…This class of hybrid dynamical systems has attracted noticeable interest in the last decade, owing to its effectiveness in modeling the special way some real systems, present in several fields of engineering and science, behave. [1][2][3] Classic control problems recently extended to linear impulsive systems are stabilization by state or output feedback, [4][5][6] state estimation, 7 linear quadratic control, 8,9 disturbance decoupling, [10][11][12] and output regulation. [13][14][15][16][17][18][19][20][21] Less typical formulations of some of these problems have also been investigated for hybrid linear systems: see, eg, the work of Yuan and Wu 22 on almost output regulation and the works of Amato et al 23,24 on finite-time stabilization and control.…”

Disturbance decoupling by state feedback for uncertain impulsive linear systems

“…For this reason, impulsive linear systems have recently attracted the interest of many researchers in relation to a number of control problems. By extending to the framework of impulsive linear systems approaches and techniques previously developed for linear systems, solvability conditions have been obtained for stabilization problems, [4][5][6] linear quadratic control problems, 7,8 disturbance decoupling problems, [9][10][11][12] output regulation problems, [13][14][15][16][17][18][19][20][21] and observation problems. [22][23][24][25] Structural geometric methods obtained by extending the classical geometric approach of Basile and Marro 26 and of Wonham 27 have been shown to be particularly effective to deal with the mentioned problems for this class of systems.…”

A geometric approach to structural model matching by output feedback in linear impulsive systems

“…Concerning the state of the art of the methodologies developed to handle this class of dynamical systems, it has to be acknowledged that, nowadays, several control and observation problems have already been formulated and studied in the context of linear impulsive systems. More specifically, problems that have recently been tackled concern state estimation (Medina and Lawrence, 2009;Conte et al, 2017), linear quadratic control (Kouhi et al, 2013;Carnevale et al, 2014b), disturbance decoupling (Conte et al, 2015a;Perdon et al, 2016b), output regulation (Medina and Lawrence, 2006;Zattoni et al, 2015;2017b;2017a;Carnevale et al, 2016), and model matching (Zattoni,26 E. Zattoni 2016b). Nevertheless, the analysis of several aspects of the problems mentioned above remains to be deepened further and, therefore, the research in the field is still truly active.…”