17,169 research outputs found
Stabilising Model Predictive Control for Discrete-time Fractional-order Systems
In this paper we propose a model predictive control scheme for constrained
fractional-order discrete-time systems. We prove that all constraints are
satisfied at all time instants and we prescribe conditions for the origin to be
an asymptotically stable equilibrium point of the controlled system. We employ
a finite-dimensional approximation of the original infinite-dimensional
dynamics for which the approximation error can become arbitrarily small. We use
the approximate dynamics to design a tube-based model predictive controller
which steers the system state to a neighbourhood of the origin of controlled
size. We finally derive stability conditions for the MPC-controlled system
which are computationally tractable and account for the infinite dimensional
nature of the fractional-order system and the state and input constraints. The
proposed control methodology guarantees asymptotic stability of the
discrete-time fractional order system, satisfaction of the prescribed
constraints and recursive feasibility
A survey on fractional order control techniques for unmanned aerial and ground vehicles
In recent years, numerous applications of science and engineering for modeling and control of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) systems based on fractional calculus have been realized. The extra fractional order derivative terms allow to optimizing the performance of the systems. The review presented in this paper focuses on the control problems of the UAVs and UGVs that have been addressed by the fractional order techniques over the last decade
From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples
Linear parameter-varying (LPV) models form a powerful model class to analyze
and control a (nonlinear) system of interest. Identifying a LPV model of a
nonlinear system can be challenging due to the difficulty of selecting the
scheduling variable(s) a priori, which is quite challenging in case a first
principles based understanding of the system is unavailable.
This paper presents a systematic LPV embedding approach starting from
nonlinear fractional representation models. A nonlinear system is identified
first using a nonlinear block-oriented linear fractional representation (LFR)
model. This nonlinear LFR model class is embedded into the LPV model class by
factorization of the static nonlinear block present in the model. As a result
of the factorization a LPV-LFR or a LPV state-space model with an affine
dependency results. This approach facilitates the selection of the scheduling
variable from a data-driven perspective. Furthermore the estimation is not
affected by measurement noise on the scheduling variables, which is often left
untreated by LPV model identification methods.
The proposed approach is illustrated on two well-established nonlinear
modeling benchmark examples
Fractionally Predictive Spiking Neurons
Recent experimental work has suggested that the neural firing rate can be
interpreted as a fractional derivative, at least when signal variation induces
neural adaptation. Here, we show that the actual neural spike-train itself can
be considered as the fractional derivative, provided that the neural signal is
approximated by a sum of power-law kernels. A simple standard thresholding
spiking neuron suffices to carry out such an approximation, given a suitable
refractory response. Empirically, we find that the online approximation of
signals with a sum of power-law kernels is beneficial for encoding signals with
slowly varying components, like long-memory self-similar signals. For such
signals, the online power-law kernel approximation typically required less than
half the number of spikes for similar SNR as compared to sums of similar but
exponentially decaying kernels. As power-law kernels can be accurately
approximated using sums or cascades of weighted exponentials, we demonstrate
that the corresponding decoding of spike-trains by a receiving neuron allows
for natural and transparent temporal signal filtering by tuning the weights of
the decoding kernel.Comment: 13 pages, 5 figures, in Advances in Neural Information Processing
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