Dynamic equivalence of control systems via infinite prolongation

Abstract

Abstract. In this paper, we put the issue of dynamic equivalence of control systems in the context of pullbacks of coframings on infinite jet bundles over the state manifolds. While much attention has been given to differentially flat systems, i.e. systems dynamically equivalent to linear control systems, the advantage of this approach is that it allowed us to consider control affine systems as well. Through this context we are able to classify all control affine systems of three states and two controls under dynamic equivalence of the type (x, u) → y(x, u).

Automorphisms of Ordinary Differential Equations

“…. , ), we have already obtained the equation = 0 and then identities = 0 easily follow by applying the common rule ( ) = 0 together with (26). This concludes the proof.…”

“…It may be regarded as a mere formally adapted individual subcase of the theory of underdetermined systems of ordinary differential equations. However, the exceptional role of the independent variable (the change of notation), the state variables , and the control is emphasized in applications; see [24][25][26] and references therein. In particular, only the -preserving and moreover -independent symmetries of the system (344) are accepted.…”

Dynamic Equivalence of Control Systems and Infinite Permutation Matrices

“…, ω p+k and similarly for (3.2). For more details of these proofs, see [14]. 5 To prove P3, note that there exists an n 2 × m 2 matrix F such that…”

“…Let (M, C M ), (N, C N ), ω i , η i , A, B be as above. In [14], it is proved that there exist transformations …”

“…In [14], the author considered all control-affine systems with 3 states and 2 controls, proving that three statically non-equivalent systems are pairwise dynamically equivalent at height (1,1). In addition, he introduced a new method of studying dynamic equivalences of two control systems.…”