This paper introduces predefined-time stable dynamical systems which are a class of fixed-time stable dynamical systems with settling time as an explicit parameter that can be defined in advance. This concept allows for the design of observers and controllers for problems that require to fulfill hard time constraints. An example is encountered in the fault detection and isolation problem, where mode detection in a timely manner needs to be guaranteed in order to apply a recovery action. Furthermore, through the notion of strong predefined-time stability, the approach hereinafter presented permits to overcome the problem of overestimation of the convergence time bound encountered in previous methods for the analysis of finite-time stable systems, where the stabilization time is often an unbounded function of the initial conditions of the system. A Lyapunov analysis is provided together with a detailed discussion of the applications to consensus and first order sliding mode controller design. Finite-time stability, Sliding-mode control, Lyapunov stability, Robust control, Consensus.
This
paper presents a method for the input trajectory design of
dynamical systems with the aim of enhancing state estimation accuracy.
The method is based on the optimization of a modified version of an
index derived from a set-theoretic approach to observability. The
presented technique is applied to a model representing a fed-batch
bioreactor and the results are compared to a traditional method. Applying
the input trajectory obtained from the devised design method results
in a significantly better state estimation performance than the one
found when applying the control actions obtained by the traditional
design approach.
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