Moving Horizon Estimation Scheme Research Articles

Moving horizon state estimation for nonlinear systems with bounded uncertainties

In this work, a robust moving horizon estimation scheme augmented by an auxiliary nonlinear observer is proposed for nonlinear systems with bounded model uncertainties. Specifically, an auxiliary deterministic nonlinear observer that asymptotically tracks nominal system state is taken advantage of to calculate a confidence region that contains the actual system state taking into account the effects of bounded model uncertainties at every sampling time. This region is then used to design a constraint on the state estimates in the proposed moving horizon estimation. The proposed design brings together deterministic and optimization-based observer design techniques. First, the proposed moving horizon estimation scheme is proved to give bounded estimation errors in the case of bounded model uncertainties. Second, the proposed approach provides another option to compromise the effects of errors in arrival cost approximations and can be used together with different arrival cost approximation techniques to further improve the state estimate. The applicability and effectiveness of the proposed approach is demonstrated through the application to two chemical process examples.

Multi-objective model-based control for an automotive catalyst

A model-based feedforward/feedback air fuel ratio controller that optimizes the oxygen storage capacity of the three-way catalyst in automotive emission control systems is presented. This work incorporates a simplified dynamic catalyst model that describes the physical behavior of oxygen chemisorption and reversible deactivation in the catalyst system. A novel aspect of this work is the use of the oxygen storage capability of the catalyst not only to minimize vehicle emissions but also to optimize engine performance and fuel economy during transient engine demand. The feedback/feedforward controller is a nonlinear model predictive controller that incorporates catalyst, engine air fuel ratio controller, and fuel system models to determine the optimal air fuel ratio target trajectory. Feedback is provided by a nonlinear moving horizon estimation strategy for the determination of the oxygen storage level of the catalyst based on air fuel ratio sensors.

EXPLICIT SOLUTION TO CONSTRAINED LINEAR ESTIMATION

This paper investigates the structure present in constrained linear state estimation problems formulated as a quadratic optimization program subject to linear inequality constraints. Polyhedral constraints on the system disturbance, the measurement noise, and the initial state are considered. The result interprets the measurement data and prior estimate as parameters and the parameter space is partitioned into multiple regions. Within each region the state estimate can be calculated as a piece-wise affine function of the measurement data and prior estimate. The parameterized regions and coefficients of the piece-wise affine function can be precomputed offline allowing a simplified approach in implementing a moving horizon estimation scheme.

Moving horizon estimation for hybrid systems

We propose a state-smoothing algorithm for hybrid systems based on moving-horizon estimation (MHE) by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems. We provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the MHE scheme. Moreover, we propose two practical algorithms for the computation of penalties that allow us to implement MHE by solving a mixed-integer quadratic program.