Consider the problem of reaching the origin in minimum time, for the control system ẋ = F(x) + G(x)u, |u(t)| ≤ 1, assuming F(0) = 0, x ∈ ℝ2. For a generic family of C3 vector fields F,G, we introduce an equivalence relation on the corresponding time-optimal feedback. We describe an algorithm to construct an optimal synthesis and give generic conditions in order to obtain the structural stability of feedbacks.
|Original language||English (US)|
|Number of pages||37|
|Journal||Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm|
|State||Published - Sep 1 1997|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics