On the attainable sets of control systems with \(p\)-integrable controls (Q1771104)

Both linear and nonlinear finite-dimensional control systems with time-varying coefficients are considered. The notion of attainable set is defined and extensively discussed for different sets of so-called admissible controls. The main purpose of the paper is to present the relationships between attainable sets for \(p\)-integrable controls with additional, rather complicated, constraints. Special attention is paid to two-dimensional linear systems with specially constructed controls. The paper contains conditions which show how the attainable sets change when \(p\) changes. Moreover, several illustrative examples are also presented, together with many remarks and comments. Relationships to the results existing in the literature are also mentioned.