Lyapunov‐based MPC with robust moving horizon estimation and its triggered implementation

In this work, we consider moving horizon state estimation (MHE)‐based model predictive control (MPC) of nonlinear systems. Specifically, we consider the Lyapunov‐based MPC (LMPC) developed in (Mhaskar et al., IEEE Trans Autom Control. 2005;50:1670–1680; Syst Control Lett. 2006;55:650–659) and the robust MHE (RMHE) developed in (Liu J, Chem Eng Sci. 2013;93:376–386). First, we focus on the case that the RMHE and the LMPC are evaluated every sampling time. An estimate of the stability region of the output control system is first established; and then sufficient conditions under which the closed‐loop system is guaranteed to be stable are derived. Subsequently, we propose a triggered implementation strategy for the RMHE‐based LMPC to reduce its computational load. The triggering condition is designed based on measurements of the output and its time derivatives. To ensure the closed‐loop stability, the formulations of the RMHE and the LMPC are also modified accordingly to account for the potential open‐loop operation. A chemical process is used to illustrate the proposed approaches. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4273–4286, 2013     

A real-time algorithm for moving horizon state and parameter estimation

A moving horizon estimation (MHE) approach to simultaneously estimate states and parameters is revisited. Two different noise models are considered, one with measurement noise and one with additional state noise. The contribution of this article is twofold. First, we transfer the real-time iteration approach, developed in Diehl et al. (2002) for nonlinear model predictive control, to the MHE approach to render it real-time feasible. The scheme reduces the computational burden to one iteration per measurement sample and separates each iteration into a preparation and an estimation phase. This drastically reduces the time between measurements and computed estimates. Secondly, we derive a numerically efficient arrival cost update scheme based on one single QR-factorization. The MHE algorithm is demonstrated on two chemical engineering problems, a thermally coupled distillation column and the Tennessee Eastman benchmark problem, and compared against an Extended Kalman Filter. The CPU times demonstrate the real-time applicability of the suggested approach.     

Nonstationary fault detection and diagnosis for multimode processes

Fault isolation based on data‐driven approaches usually assume the abnormal event data will be formed into a new operating region, measuring the differences between normal and faulty states to identify the faulty variables. In practice, operators intervene in processes when they are aware of abnormalities occurring. The process behavior is nonstationary, whereas the operators are trying to bring it back to normal states. Therefore, the faulty variables have to be located in the first place when the process leaves its normal operating regions. For an industrial process, multiple normal operations are common. On the basis of the assumption that the operating data follow a Gaussian distribution within an operating region, the Gaussian mixture model is employed to extract a series of operating modes from the historical process data. The local statistic T² and its normalized contribution chart have been derived for detecting abnormalities early and isolating faulty variables in this article. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

High‐frequency sampling and kernel estimation for continuous‐time moving average processes

Interest in continuous‐time processes has increased rapidly in recent years, largely because of high‐frequency data available in many applications. We develop a method for estimating the kernel function g of a second‐order stationary Lévy‐driven continuous‐time moving average (CMA) process Y based on observations of the discrete‐time process Y^Δ obtained by sampling Y at Δ, 2Δ, …, nΔ for small Δ. We approximate g by g^Δ based on the Wold representation and prove its pointwise convergence to g as Δ → 0 for continuous‐time autoregressive moving average (CARMA) processes. Two non‐parametric estimators of g^Δ, on the basis of the innovations algorithm and the Durbin–Levinson algorithm, are proposed to estimate g. For a Gaussian CARMA process, we give conditions on the sample size n and the grid spacing Δ(n) under which the innovations estimator is consistent and asymptotically normal as n → ∞. The estimators can be calculated from sampled observations of any CMA process, and simulations suggest that they perform well even outside the class of CARMA processes. We illustrate their performance for simulated data and apply them to the Brookhaven turbulent wind speed data. Finally, we extend results of Brockwell et al. (2012) for sampled CARMA processes to a much wider class of CMA processes.