State-space adaptive control through a modified bootstrap algorithm for parameter and state estimation

1989 ◽  
Vol 136 (5) ◽  
pp. 215 ◽  
Author(s):  
M.S. Ahmed ◽  
N. Sait
Keyword(s):  
Adaptive Control ◽  
State Estimation ◽  
State Space ◽  
Bootstrap Algorithm

scholarly journals Bayesian Joint Input-State Estimation for Nonlinear Systems

Vibration ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 281-303
Author(s):  
Timothy J. Rogers ◽  
Keith Worden ◽  
Elizabeth J. Cross
Keyword(s):  
Nonlinear Systems ◽  
Gaussian Process ◽  
State Estimation ◽  
State Space ◽  
Mean Squared Error ◽  
Duffing Oscillator ◽  
State Space Model ◽  
Input State ◽  
Force Model ◽  
Internal States

This work suggests a solution for joint input-state estimation for nonlinear systems. The task is to recover the internal states of a nonlinear oscillator, the displacement and velocity of the system, and the unmeasured external forces applied. To do this, a Gaussian process latent force model is developed for nonlinear systems. The model places a Gaussian process prior over the unknown input forces for the system, converts this into a state-space form and then augments the nonlinear system with these additional hidden states. To perform inference over this nonlinear state-space model a particle Gibbs approach is used combining a “Particle Gibbs with Ancestor Sampling” Markov kernel for the states and a Metropolis-Hastings update for the hyperparameters of the Gaussian process. This approach is shown to be effective in a numerical case study on a Duffing oscillator where the internal states and the unknown forcing are recovered, each with a normalised mean-squared error less than 0.5%. It is also shown how this Bayesian approach allows uncertainty quantification of the estimates of the states and inputs which can be invaluable in further engineering analyses.

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