Dynamic inversion for nonaffine-in-control systems via time-scale separation: part I

Output regulation of nonaffine nonlinear systems using singular perturbation theory

“…Proof In the following we will show that the assumptions of Tikhonov's theory are all satisfied for Theorem 1, and here we need the assumptions B1 and B2 in [8] for our proof. First, the assumption B1 clearly implies that A1 holds [8], and under the assumption of B2, the systeṁ z(t) =ζ(ξ (t),z(t), ω(t))…”

“…First, the assumption B1 clearly implies that A1 holds [8], and under the assumption of B2, the systeṁ z(t) =ζ(ξ (t),z(t), ω(t))…”

“…In this paper, we show how the result established by [8,10] can be extended to the problem of output tracking for nonaffine nonlinear systems. Based on the method provided by singular perturbation theory, see [4], by defining the resultant control signal as a solution to "fast" dynamics, the original problem can be solved by two models representing the slow and fast dynamics.…”

“…However, many practical applications give rise to nonaffine-in-control nonlinear systems due to the fact that in the latter case an explicit inversion is not possible. As stated in [8], the systeṁ x = u + exp(u) is nonlinear, and for given ν, finding u such that u + exp(u) = ν is not possible. In stabilization problems, the method based on dynamic inversion ( [8∼10]) overcame this drawback by Tikhonov's theorem in singular perturbation.…”

“…In Section 2, the singular perturbation theory is introduced. The result of output regulation extended from [8] is given in Section 3. The simulations illustrate the theoretical results in Section 4, and finally some conclusions are given.…”