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Adaptive Experiment Design for Nonlinear System Identification with Operational Constraints

Jingwei Hu, Dave Zachariah, Torbjörn Wigren, Petre Stoica

TL;DR

The paper tackles joint online experiment design and parameter estimation for discrete-time nonlinear systems under operational constraints. It introduces a receding-horizon adaptive input design criterion based on a Fisher information bound, along with a tractable relaxation and an online estimator that uses blockwise ML and the unscented Kalman filter. A practical adaptive design workflow uses a transformed unconstrained input space, automatic differentiation for optimization, and a hybrid global-local search. Numerical experiments on a nonlinear pendulum show improved parameter accuracy, reduced constraint violations, and safer online experimentation.

Abstract

We consider the joint problem of online experiment design and parameter estimation for identifying nonlinear system models, while adhering to system constraints. We utilize a receding horizon approach and propose a new adaptive input design criterion, which is tailored to continuously updated parameter estimates, along with a new sequential estimator. We demonstrate the ability of the method to design informative experiments online, while steering the system within operational constraints.

Adaptive Experiment Design for Nonlinear System Identification with Operational Constraints

TL;DR

The paper tackles joint online experiment design and parameter estimation for discrete-time nonlinear systems under operational constraints. It introduces a receding-horizon adaptive input design criterion based on a Fisher information bound, along with a tractable relaxation and an online estimator that uses blockwise ML and the unscented Kalman filter. A practical adaptive design workflow uses a transformed unconstrained input space, automatic differentiation for optimization, and a hybrid global-local search. Numerical experiments on a nonlinear pendulum show improved parameter accuracy, reduced constraint violations, and safer online experimentation.

Abstract

We consider the joint problem of online experiment design and parameter estimation for identifying nonlinear system models, while adhering to system constraints. We utilize a receding horizon approach and propose a new adaptive input design criterion, which is tailored to continuously updated parameter estimates, along with a new sequential estimator. We demonstrate the ability of the method to design informative experiments online, while steering the system within operational constraints.

Paper Structure

This paper contains 9 sections, 29 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Method
  4. Adaptive design criterion
  5. Relaxation
  6. Online estimator
  7. Adaptive design method
  8. Numerical Experiments
  9. Conclusion

Figures (3)

  • Figure 1: Example realization of pendulum system. Angle $x_t^{(1)}$ when applying two different prbs inputs and the adaptive design that steers the angle within the interval $[-45^\circ, 45^\circ]$.
  • Figure 2: Relative violation of operational constraint \ref{['eq:stateconstraints']}, evaluated using 100 Monte Carlo runs.
  • Figure 3: Mean-square errors of parameter estimator along with (approximate) Cramér-Rao bounds. The estimation errors for prbs2 were too large to be included in the plot. Results are based on 100 Monte Carlo runs.