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A New Hamilton–Jacobi Differential Game Framework for Nonlinear Estimation and Output Feedback Control

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Abstract

In this paper, we develop a new framework for designing state estimators/filters and output measurement feedback controllers for affine nonlinear systems in state space. The problems are formulated as zero-sum differential games, and sufficient conditions for their solvability are given in terms of Hamilton–Jacobi–Isaacs equations (HJIEs). These HJIEs are new, in the sense that they are both state-dependent and measurement output dependent. This allows for the filter and observer gains to be optimized over all possible nonlinear gains. Examples and simulation results are also presented to support the theory.

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Notes

  1. \(T^{*}{\mathcal X}\), \(T{\mathcal Y}\) represent the cotangent and tangent bundles of \({\mathcal X}\) and \({\mathcal Y}\) with coordinates \((\hat{x},\hat{p}_{1})\), \((y,\dot{y})\), respectively.

  2. Where \({\mathcal L}_{f}(.)\) is the Lie-derivative operator along f.

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Authors and Affiliations

  1. Department of Electrical Engineering, King Faisal University, P. O. Box 400, Al-Ahsa, 31982, Saudi Arabia

    M. D. S. Aliyu

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Aliyu, M.D.S. A New Hamilton–Jacobi Differential Game Framework for Nonlinear Estimation and Output Feedback Control. Circuits Syst Signal Process 39, 1831–1852 (2020). https://doi.org/10.1007/s00034-019-01229-4

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  • DOI: https://doi.org/10.1007/s00034-019-01229-4

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