Stability of a truncated infinite constrained receding horizon scheme: the general discrete nonlinear case

Stability proof for nonlinear MPC design using monotonically increasing weighting profiles without terminal constraints

“…On the other hand, it has been shown quite early [4] that provable stability can be obtained without terminal stability-related constraint by using sufficiently long prediction horizon [6,9]. More recent results followed, [see [8,7,5] and the references therein] where deeper analysis is obtained regarding this fact.…”

Stability and Robustness of Nonlinear Receding Horizon Control

“…Consider the time-invariant nonlinear discrete-time system x(k + 1) = f(x(k), u(k)), x(t) = X, k~t (1) where x(k) E Rn is the state, u(k) E R m is the input, f(·,·) is a C 2 function of its arguments, and f(O, 0) = 0 (the origin is an equilibrium point). The state and input vectors are subject to the constraints…”

“…The most direct way is to take into account explicitly both nonlinearity and constraints in the minimization of (4). Along this direction, the IH (Infinite Horizon) nonlinear optimal controller is obtained by minimizing (4) subject to (1) and (2) (10) which stabilizes the origin, see e.g. [21].…”

Model Predictive Control for Biped Walking Motion Generation

“…Many variants have been proposed [20], but two extremes are particularly significant in the case of walking robots, either considering only an integral cost function, without any terminal constraint [2], or the opposite, only a terminal constraint, without any cost function [3]. These two control designs can be proven to lead to stable behaviors under mild technical conditions.…”