2 research outputs found
Constrained nonlinear output regulation using model predictive control -- extended version
We present a model predictive control (MPC) framework to solve the
constrained nonlinear output regulation problem. The main feature of the
proposed framework is that the application does not require the solution to
classical regulator (Francis-Byrnes-Isidori) equations or any other offline
design procedure. In particular, the proposed formulation simply minimizes the
predicted output error, possibly with some input regularization. Instead of
using terminal cost/sets or a positive definite stage cost as is standard in
MPC theory, we build on the theoretical results by Grimm et al. 2005 using a
detectability notion. The proposed formulation is applicable if the constrained
nonlinear regulation problem is (strictly) feasible, the plant is incrementally
stabilizable and incrementally input-output to state stable
(i-IOSS/detectable). We show that for minimum phase systems such a design
ensures exponential stability of the regulator manifold. We also provide a
design procedure in case of unstable zero dynamics using an incremental input
regularization and a nonresonance condition. Inherent robustness properties for
the noisy error/output-feedback case are established under simplifying
assumptions (e.g. no state constraints). The theoretical results are
illustrated with an example involving offset free tracking with noisy error
feedback. The paper also contains novel results for MPC without terminal
constraints with positive semidefinite input/output stage costs that are of
independent interest.Comment: Extended version of accepted paper in Transaction on Automatic
Control, 2021. Contains the following additional results: Exponential bounds
on the suboptimality index using an observability condition and an extension
of the derived theory to the noisy error feedback cas
A nonlinear model predictive control framework using reference generic terminal ingredients -- extended version
In this paper, we present a quasi infinite horizon nonlinear model predictive
control (MPC) scheme for tracking of generic reference trajectories. This
scheme is applicable to nonlinear systems, which are locally incrementally
stabilizable. For such systems, we provide a reference generic offline
procedure to compute an incrementally stabilizing feedback with a continuously
parameterized quadratic quasi infinite horizon terminal cost. As a result we
get a nonlinear reference tracking MPC scheme with a valid terminal cost for
general reachable reference trajectories without increasing the online
computational complexity. As a corollary, the terminal cost can also be used to
design nonlinear MPC schemes that reliably operate under online changing
conditions, including unreachable reference signals. The practicality of this
approach is demonstrated with a benchmark example.
This paper is an extended version of the accepted paper [1], and contains
additional details regarding \textit{robust} trajectory tracking (App.~B),
continuous-time dynamics (App.~C), output tracking stage costs (App.~D) and the
connection to incremental system properties (App.~A).Comment: Extended version of accepted paper in Transaction on Automatic
Control, 2020. Contains additional details in the appendix regarding robust
trajectory tracking, continuous-time dynamics, output tracking stage costs
and incremental system propertie