On mappability of control systems to linear systems with analytic matrices

Invariants of linear control systems with analytic matrices and the linearizability problem

“…We emphasize that, unlike Definition 1, in Definition 2 the target linear system is fixed. This requirement is justified by the theorem on linearizability conditions, originally proposed and proved in [19]. Here we formulate the modification obtained in [21].…”

“…the operator R(t, x) reduces to the derivative on t, i.e., R k g(t, x) = g (k) (t, x), k ≥ 0 (here and below g (k) (t, x) means the k-th derivative on t). In [19], driftless systems (8) were considered as a kind of a canonical form for general affine systems (4). Under the assumptions a(t, x)…”

“…In [19] driftless systems were used in order to obtain conditions for linearizability of nonautonomous nonlinear systems.…”

“…In turn, a method of explicit solving the power Markov moment problem was proposed in [17]; see also [18]. The non-autonomous statement of the linearizability problem mentioned above was proposed in [19], where conditions on mappability of a nonlinear control system to a preassigned linear system (1) with analytic matrices were obtained. In the present paper we solve more general problem: to find conditions under which a nonlinear system is mapped to some linear system with analytic matrices, which is not given in advance.…”

Solving the time-optimal control problem for nonlinear non-autonomous linearizable systems

“…Then, in Subsection 2.2, we recall some recent results on linearizability conditions for non-autonomous systems proposed in [5]. Additionally to linearizability conditions known since [6], [7] and generalized to systems of the class 𝐶 1 in [8], [9], in the non-autonomous case some new conditions arise, see [10] and [11] for further discussion.…”