Accurate Set-Based State Estimation for Nonlinear Discrete-Time Systems Using Differential Inequalities with Model Redundancy

Xuejiao Yang1, Joseph Scott1

  • 1Clemson University

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Regular Session

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10:00 - 12:00 | Mon 17 Dec | Splash 11 | MoA19

Estimation I

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Abstract

This paper presents an efficient recursive algorithm for computing tight enclosures of the set of states consistent with a given nonlinear discrete-time model, an observed output sequence, and given bounds on disturbances and measurement errors. This is commonly called set-based state estimation, and has applications in verification, fault detection, and robust control. The presented algorithm is based on the theory of differential inequalities (DI), which has been extensively developed for nonlinear reachability analysis. Contemporary DI methods make use of redundant model equations to achieve tight reachability bounds at low cost. Here, we extend these methods to set-based state estimation and show very favorable results relative to other recursive algorithms in common use. Notably, however, this approach is only applicable to forward-Euler-discretized systems satisfying a step size bound.

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