Robust output feedback model predictive control using online estimation bounds

Abstract

We present a framework to design nonlinear robust output feedback model predictive control (MPC) schemes that ensure constraint satisfaction under noisy output measurements and disturbances. We provide novel estimation methods to bound the magnitude of the estimation error based on: stability properties of the observer; detectability; set-membership estimation; moving horizon estimation (MHE). Robust constraint satisfaction is guaranteed by suitably incorporating these online validated bounds on the estimation error in a homothetic tube based MPC formulation. In addition, we show how the performance can be further improved by combining MHE and MPC in a single optimization problem. The framework is applicable to a general class of detectable and (incrementally) stabilizable nonlinear systems. While standard output feedback MPC schemes use offline computed worst-case bounds on the estimation error, the proposed framework utilizes online validated bounds, thus reducing conservatism and improving performance. We demonstrate the reduced conservatism of the proposed framework using a nonlinear 10-state quadrotor example.

Ellipsoidal tube‐based output feedback robust MPC for linear systems with bounded disturbances and noises

“…where F f is the feedback controller gain. When the tightened constraint sets U k and X k are computed via Theorem 1, problem ( 32)- (36) in Lemma 1 can be off-line solved to design the terminal constraint set (Q −1 f ) with the terminal controller gain F f and the terminal cost matrix P f for the ellipsoidal tube-based OFRMPC approach. Lemma 1.…”

“…▪ Problem ( 32)-( 36) can be the extension of the state feedback robust MPC optimization in Reference 38, where constraints (33), (34), (35), and (36) are similar to the constraints on robust stability, the current system state, control input and system states in Reference 38, respectively. When the system matrix C = I, the system output constraint (34) in Reference 38 is equivalent to the system state constraints in (36). Differently from the polytopic uncertain system in Reference 38, the constraints in problem ( 32)-( 36) are designed for linear system (31).…”

“…always hold. By further adding the constraints (35) and (36) and linearly searching the minimal scalar 𝜃 f over the interval (0, 1), it is possible to optimize a small set…”

A simple suboptimal moving horizon estimation scheme with guaranteed robust stability

“…Such a characterization of an RGES of observer was previously used in the context of MHE in [13]. Overall, we consider a rather general class of observers in (3), which represents an active area of research.…”

Suboptimal nonlinear moving horizon estimation

“…As a result, solving the NLP initialized using the observer-based candidate solution is in general faster than using the nominal trajectory (especially when using the time-discounted cost function). To examine the influence of larger estimation horizons, we modify the design by choosing N = 10 (20) and T = 15 (30). Based on Table IV, it can be seen that the main observations from before remain qualitatively unchanged.…”