Robust State Estimation

In this study, we develop algorithms for robust estimation and fault detection and identification for a class of hybrid systems called the stochastic linear hybrid system (SLHS). 

Robust Hybrid Estimation Algorithm

The authors propose a robust hybrid estimation algorithm that estimates the continuous state and the discrete state of an SLHS with unknown fault inputs. 

• The algorithm decouples the unknown fault input from the estimation error dynamics for each discrete state of the hybrid system to guarantee the convergence of the estimation error. 

• The robust hybrid estimation algorithm is designed for two kinds of discrete state transition models: 

  • the Markov-jump transition model whose discrete transition probabilities are constant (i.e. independent of the continuous state) and 

  • the state-dependent transition model whose discrete state transitions are determined by some guard conditions (i.e. dependent on the continuous state). 

Fault Detection and Identification

The proposed residual generation algorithm computes residuals to facilitate fault detection and isolation. The residuals have the properties that they can reconstruct (in the mean sense) the unknown fault input vector. 

Simulations

The authors also demonstrate the performance of the proposed algorithm with a vertical take-off and landing (VTOL) aircraft example. The figures below represent the flight mode transition of a VTOL aircraft (left) and its corresponding transition model of the hybrid system (right). Please find the detailed results in the paper below.

Related Publication

• W. Liu and I. Hwang, "Robust Estimation and Fault Detection and Isolation Algorithms for Stochastic Linear Hybrid Systems with Unknown Fault Input," IET Control Theory & Applications, Vol. 5(12), pp.1353 – 1368, August 2011