30,915 research outputs found
Controlling Chaos Faster
Predictive Feedback Control is an easy-to-implement method to stabilize
unknown unstable periodic orbits in chaotic dynamical systems. Predictive
Feedback Control is severely limited because asymptotic convergence speed
decreases with stronger instabilities which in turn are typical for larger
target periods, rendering it harder to effectively stabilize periodic orbits of
large period. Here, we study stalled chaos control, where the application of
control is stalled to make use of the chaotic, uncontrolled dynamics, and
introduce an adaptation paradigm to overcome this limitation and speed up
convergence. This modified control scheme is not only capable of stabilizing
more periodic orbits than the original Predictive Feedback Control but also
speeds up convergence for typical chaotic maps, as illustrated in both theory
and application. The proposed adaptation scheme provides a way to tune
parameters online, yielding a broadly applicable, fast chaos control that
converges reliably, even for periodic orbits of large period
Shaping of molecular weight distribution using b-spline based predictive probability density function control
Issues of modelling and control of molecular weight distributions (MWDs) of polymerization products have been studied under the recently developed framework of stochastic distribution control, where the purpose is to design the required control inputs that can effectively shape the output probability density functions (PDFs) of the dynamic stochastic systems. The B-spline Neural Network has been implemented to approximate the function of MWDs provided by the mechanism model, based on which a new predictive PDF control strategy has been developed. A simulation study of MWD control of a pilot-plant styrene polymerization process has been given to demonstrate the effectiveness of the algorithms
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
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