Persistently exciting tube MPC

Abstract

Abstract-This paper presents a new approach to deal with the dual problem of system identification and regulation. The main feature consists of breaking the control input to the system into a regulator part and a persistently exciting part. The former is used to regulate the plant using a robust MPC formulation, in which the latter is treated as a bounded additive disturbance. The identification process is executed by a simple recursive least squares algorithm. In order to guarantee sufficient excitation for the identification, an additional nonconvex constraint is enforced over the persistently exciting part.

Stabilizing predictive control with persistence of excitation for constrained linear systems

“…Since I has row rank m, O o has full row rank, and u(i) is reachable fromŵ(i). The McMillan degree of system (20) is n, and the exciting sequence {ŵ(i)} is SPE of order 2n + m + 1, thus Lemma 1 ensures that the input sequence {u(i)} is SPE of order n + m. According to Corollary 1, this guarantees that the corresponding regressor sequence {φ(i)} is SPE of order 1.…”

“…Constraints (18d) and (18e) need access to the past values ofŵ(i) over a time period of l − 1 steps. This implies that a buffer sequence is required to initialize {ŵ(i)} [14,20]. Notice also that only the lower bound of (6a) is included in the definition of the PE measure (16), this is because the upper bound is trivially met given thatŵ(i) is bounded [13].…”

“…A preliminary version of this approach appeared in [20]. Several modifications and additional contributions have been included in this paper, amongst them (i) the required excitation is guaranteed to be transmitted from the exciting part to the whole input; (ii) sufficient conditions for the existence of a stable linear feedback gain for the true plant are given instead of assumed; and (iii) the problem of prediction model update is tackled by a set of a-posteriori (online) redesign approaches, instead of an overly robustified initial design.…”

Real-time algorithm for self-reflective model predictive control

“…Similar extensions of MPC with learning terms have been proposed in [14,15], which augment the nominal MPC objective with optimal experiment design objectives that penalize the predicted variance of the system parameters. In recent years there have appeared a number of articles on persistently exciting MPC [16,25,31,39,44], which all discuss different ways to excite model predictive controllers in order to improve the accuracy of future state and parameter estimates. An even more recent trend is to extend the concept of application oriented optimal experiment design [17] by associated terms in the objective or constraints of an MPC problem [22,23].…”

Self-Reflective Model Predictive Control

“…Another recent article [43] on online experiment design suggests to use a modified experiment design framework for generating "least costly" excitations, which try to avoid perturbation of the nominal plant operation as much as possible. Other approaches for persistently exciting closed loop MPC can be found in [27,39,51,58].…”