Unconstrained Moving Horizon Estimation and Simultaneous Model Predictive Control by Multi-Parametric Programming

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

“…Previous work has been performed on reformulating the MHE with the filtered arrival cost [83] and with the smoothed update of the arrival cost [349].…”

Simultaneous constrained Moving Horizon state Estimation and Model Predictive Control by multi-parametric programming

“…The proposed method consists of three main steps ( [9], [10], [11]): i) first the Karush-Kuhn-Tucker (KKT) conditions for (9) are formed, ii) the error dynamics for the estimation error at time T −N are obtained, and iii) the error dynamics at time T , which is the current time of the estimation, are obtained.…”

“…A method for obtaining an RPI set bounding the estimation error was presented for the case of unconstrained state estimation (Luenberger observer [8] and unconstrained MHE [10], [11]), where the error dynamics are described by a single linear time invariant (LTI) system, i.e. A err,i = A err and D i = D.…”

“…The methodology proposed here addresses this problem by 1. formulating the dynamics that govern the estimation error, 2. using these dynamics to find the set that bounds the error, and then 3. incorporating the bounding set into the constraints of the MPC thus robustifying against the estimation error [8]. This methodology has previously been applied using the Luenberger observer [8] and the unconstrained MHE [9], [10], [11]. In [9] the error dynamics and bounds were obtained for the unconstrained MHE, however for a formulation of MHE not including the estimation of the process noise.…”

“…In [9] the error dynamics and bounds were obtained for the unconstrained MHE, however for a formulation of MHE not including the estimation of the process noise. In [11] we have recently extended this work to the slightly more common formulation of MHE that includes the estimation of this noise. For reasons of optimality, these additional estimates can only improve the estimation result.…”