Covering Method for Point-to-Point Control of Constrained Flat Systems

Generation of Achievable Three-Dimensional Trajectories for Autonomous Wheeled Vehicles via Tracking Differentiators

“…The plant for trajectory planning is an unmanned wheeled platform with two driving wheels. Consider a dynamical system that describes the motion of the center of mass of this vehicle in a stationary Cartesian coordinate system Oxy [4,26]:…”

“…To generate motion trajectories with specified velocity and acceleration constraints, it is more appropriate to represent the model of the control plant in canonical form concerning the output variables and their derivatives up to and including second order. In [26], it is shown that the system (1) is differentially flat concerning flat output y 11 = x, y 12 = y. By extending the state space (namely by introducing an auxiliary dynamic variable ξ(t)), System (1) can be represented in the canonical Brunowski form with two inputs and two outputs:…”

The Admissible Control Correction Method in a Nonlinear Terminal Perturbed Problem

“…Theorem 1. Let the vector function F 0 be such function that the system in (2) is flat and u 0 (t) is the open-loop control in problem (2) obtained by means of algorithm [9,10], the regularization parameter α = O(ε k ), where k ≥ 2, F 1 is twice differentiable of all variables, the coordinates u 1,i are found exactly. Then, there is such a perturbation parameter ε 0 > 0 thatfor all 0 < ε ≤ ε 0 1.…”

“…Following the algorithm of the covering method [9,10], we introduce the additional state variable ξ = u 1 = ẏ1 .…”

“…In this paper, we consider a solution in a nonlinear perturbed point-to-point control problem (or problem with fixed ends), where the limiting system is flat [5,9]. We construct the open-loop control for it using the covering method [6,10]. After that, it turns out that the control correction can be found with the help of the solution of regularized incorrectly posed problem obtained from first order asymptotics terms equations.…”