2,938 research outputs found
Data-driven computation of invariant sets of discrete time-invariant black-box systems
We consider the problem of computing the maximal invariant set of
discrete-time black-box nonlinear systems without analytic dynamical models.
Under the assumption that the system is asymptotically stable, the maximal
invariant set coincides with the domain of attraction. A data-driven framework
relying on the observation of trajectories is proposed to compute
almost-invariant sets, which are invariant almost everywhere except a small
subset. Based on these observations, scenario optimization problems are
formulated and solved. We show that probabilistic invariance guarantees on the
almost-invariant sets can be established. To get explicit expressions of such
sets, a set identification procedure is designed with a verification step that
provides inner and outer approximations in a probabilistic sense. The proposed
data-driven framework is illustrated by several numerical examples.Comment: A shorter version with the title "Scenario-based set invariance
verification for black-box nonlinear systems" is published in the IEEE
Control Systems Letters (L-CSS
Route Swarm: Wireless Network Optimization through Mobility
In this paper, we demonstrate a novel hybrid architecture for coordinating
networked robots in sensing and information routing applications. The proposed
INformation and Sensing driven PhysIcally REconfigurable robotic network
(INSPIRE), consists of a Physical Control Plane (PCP) which commands agent
position, and an Information Control Plane (ICP) which regulates information
flow towards communication/sensing objectives. We describe an instantiation
where a mobile robotic network is dynamically reconfigured to ensure high
quality routes between static wireless nodes, which act as source/destination
pairs for information flow. The ICP commands the robots towards evenly
distributed inter-flow allocations, with intra-flow configurations that
maximize route quality. The PCP then guides the robots via potential-based
control to reconfigure according to ICP commands. This formulation, deemed
Route Swarm, decouples information flow and physical control, generating a
feedback between routing and sensing needs and robotic configuration. We
demonstrate our propositions through simulation under a realistic wireless
network regime.Comment: 9 pages, 4 figures, submitted to the IEEE International Conference on
Intelligent Robots and Systems (IROS) 201
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
Control of stochastic and induced switching in biophysical networks
Noise caused by fluctuations at the molecular level is a fundamental part of
intracellular processes. While the response of biological systems to noise has
been studied extensively, there has been limited understanding of how to
exploit it to induce a desired cell state. Here we present a scalable,
quantitative method based on the Freidlin-Wentzell action to predict and
control noise-induced switching between different states in genetic networks
that, conveniently, can also control transitions between stable states in the
absence of noise. We apply this methodology to models of cell differentiation
and show how predicted manipulations of tunable factors can induce lineage
changes, and further utilize it to identify new candidate strategies for cancer
therapy in a cell death pathway model. This framework offers a systems approach
to identifying the key factors for rationally manipulating biophysical
dynamics, and should also find use in controlling other classes of noisy
complex networks.Comment: A ready-to-use code package implementing the method described here is
available from the authors upon reques
Robust estimations of the Region of Attraction using invariant sets
The Region of Attraction of an equilibrium point is the set of initial conditions whose trajectories converge to it asymptotically. This article, building on a recent work on positively invariant sets, deals with inner estimates of the ROA of polynomial nonlinear dynamics. The problem is solved numerically by means of Sum Of Squares relaxations, which allow set containment conditions to be enforced. Numerical issues related to the ensuing optimization are discussed and strategies to tackle them are proposed. These range from the adoption of different iterative methods to the reduction of the polynomial variables involved in the optimization. The main contribution of the work is an algorithm to perform the ROA calculation for systems subject to modeling uncertainties, and its applicability is showcased with two case studies of increasing complexity. Results, for both nominal and uncertain systems, are compared with a standard algorithm from the literature based on Lyapunov function level sets. They confirm the advantages in adopting the invariant sets approach, and show that as the size of the system and the number of uncertainty increase, the proposed heuristics ameliorate the commented numerical issues.This work has received funding from the Horizon 2020 research and innovation programme
under grant agreement No 636307, project FLEXOP.
The authors would like to thank Prof. Pete Seiler for helpful discussions about ROA and
SOS
Review on computational methods for Lyapunov functions
Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function
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