Abstract
We investigate the use of Hamilton-Jacobi approaches for the purpose of state reconstruction of dynamic systems. First, the classical formulation based on the minimization of an estimation functional is analyzed. Second, the structure of the resulting estimator is taken into account to study the global stability properties of the estimation error by relying on the notion of input-to-state stability. A condition based on the satisfaction of a Hamilton-Jacobi inequality is proposed to construct estimators with input-to-state stable dynamics of the estimation error, where the disturbances affecting such dynamics are regarded as input. Third, the so-developed general framework is applied to the special case of high-gain observers for a class of nonlinear systems.
Highlights
AlessandriWe investigate the use of Hamilton-Jacobi approaches for the purpose of state reconstruction of dynamic systems
This paper investigates the problem of reconstructing the state of nonlinear dynamic systems based on limited output information by using a Hamilton-Jacobi theoretical framework
The state estimation problem is addressed by minimizing a quadratic cost functional in such a way as to find the structure of the estimator, which is a dynamic system forced by the output and able to generate an estimate of the system variables at each time instant
Summary
We investigate the use of Hamilton-Jacobi approaches for the purpose of state reconstruction of dynamic systems. The classical formulation based on the minimization of an estimation functional is analyzed. The structure of the resulting estimator is taken into account to study the global stability properties of the estimation error by relying on the notion of inputto-state stability. A condition based on the satisfaction of a Hamilton-Jacobi inequality is proposed to construct estimators with input-to-state stable dynamics of the estimation error, where the disturbances affecting such dynamics are regarded as input. The so-developed general framework is applied to the special case of high-gain observers for a class of nonlinear systems
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