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We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be nonlinearly parameterized functions of state and time. Reconstruction of state and parameter values is based on the concepts of weakly attracting sets and non-uniform convergence and is subjected to persistency of excitation conditions. In absence of nonlinear parametrization the resulting observers reduce to standard estimation schemes. In this respect, the proposed method constitutes a generalization of the conventional canonical adaptive observer design.
This supplement illustrates application of adaptive observer design from (Tyukin et al, 2013) for systems which are not uniquely identifiable. It also provides an example of adaptive observer design for a magnetic bearings benchmark system (Lin, Knospe, 2000).
Dynamical systems, for instance in model predictive control, often contain unknown parameters, which must be determined during system operation. Online or on-the-fly parameter identification methods are therefore necessary. The challenge of online me
We study the problem of designing interval-valued observers that simultaneously estimate the system state and learn an unknown dynamic model for partially unknown nonlinear systems with dynamic unknown inputs and bounded noise signals. Leveraging aff
Atangana and Baleanu proposed a new fractional derivative with non-local and no-singular Mittag-Leffler kernel to solve some problems proposed by researchers in the field of fractional calculus. This new derivative is better to describe essential asp
This paper studies the extremum seeking control (ESC) problem for a class of constrained nonlinear systems. Specifically, we focus on a family of constraints allowing to reformulate the original nonlinear system in the so-called input-output normal f