12,041 research outputs found
Performance Regulation and Tracking via Lookahead Simulation: Preliminary Results and Validation
This paper presents an approach to target tracking that is based on a
variable-gain integrator and the Newton-Raphson method for finding zeros of a
function. Its underscoring idea is the determination of the feedback law by
measurements of the system's output and estimation of its future state via
lookahead simulation. The resulting feedback law is generally nonlinear. We
first apply the proposed approach to tracking a constant reference by the
output of nonlinear memoryless plants. Then we extend it in a number of
directions, including the tracking of time-varying reference signals by
dynamic, possibly unstable systems. The approach is new hence its analysis is
preliminary, and theoretical results are derived for nonlinear memoryless
plants and linear dynamic plants. However, the setting for the controller does
not require the plant-system to be either linear or stable, and this is
verified by simulation of an inverted pendulum tracking a time-varying signal.
We also demonstrate results of laboratory experiments of controlling a platoon
of mobile robots.Comment: A modified version will appear in Proc. 56th IEEE Conf. on Decision
and Control, 201
Structurally robust biological networks
Background:
The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation.
Results:
In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature.
Conclusions:
The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters
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