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

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...

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Bibliographic Details
Published in:Circuits, systems, and signal processing systems, and signal processing, 2020-04, Vol.39 (4), p.1831-1852
Main Author: Aliyu, M. D. S.
Format: Article
Language:English
Subjects:
Circuits and Systems
Control systems
Differential games
Economic models
Electrical Engineering
Electronics and Microelectronics
Engineering
Feedback control
Instrumentation
Nonlinear control
Nonlinear systems
Output feedback
Signal,Image and Speech Processing
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Summary: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.
ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-019-01229-4