361 research outputs found
Reach Control on Simplices by Piecewise Affine Feedback
We study the reach control problem for affine systems on simplices, and the
focus is on cases when it is known that the problem is not solvable by
continuous state feedback. We examine from a geometric viewpoint the structural
properties of the system which make continuous state feedbacks fail. This
structure is encoded by so-called reach control indices, which are defined and
developed in the paper. Based on these indices, we propose a subdivision
algorithm and associated piecewise affine feedback. The method is shown to
solve the reach control problem in all remaining cases, assuming it is solvable
by open-loop controls
Non-linear eigenvalue problems arising from growth maximization of positive linear dynamical systems
We study a growth maximization problem for a continuous time positive linear
system with switches. This is motivated by a problem of mathematical biology
(modeling growth-fragmentation processes and the PMCA protocol). We show that
the growth rate is determined by the non-linear eigenvalue of a max-plus
analogue of the Ruelle-Perron-Frobenius operator, or equivalently, by the
ergodic constant of a Hamilton-Jacobi (HJ) partial differential equation, the
solutions or subsolutions of which yield Barabanov and extremal norms,
respectively. We exploit contraction properties of order preserving flows, with
respect to Hilbert's projective metric, to show that the non-linear eigenvector
of the operator, or the "weak KAM" solution of the HJ equation, does exist. Low
dimensional examples are presented, showing that the optimal control can lead
to a limit cycle.Comment: 8 page
Strategies for coverage and focus on event for robotic swarms with limited sensing capabilities
We consider the problem of coverage in Robotic Networks: developing an efficient algorithm which is able to perform a deployment in static-obstacle-structured environments focusing on events is our main idea. We are interested on the trade-off between local communication and optimal coverage, therefore we are going to present an algorithm based on article: "Sensor Coverage Robot Swarms Using Local Sensing without Metric Information", using its similar scenario types
Convexity Applications in Single and Multi-Agent Control
The focus of this dissertation is in the application of convexity for control problems; specifically, single-agent problems with linear or nonlinear dynamics and multi-agent problems with linear dynamics. A mixture of convex and non-convex constraints for optimal control problems is also considered. The main contributions of this dissertation include: 1) a convexification of single-agent problems with linear dynamics and annular control constraint, 2) a technique for controlling bounded nonlinear single-agent systems, and 3) a technique for solving multi-agent pursuit-evasion games with linear dynamics and convex control and state constraints. The first result shows that for annularly constrained linear systems, controllability is a sufficient condition for a free or fixed time problem to be solvable as a sequence of convex optimization problems. The second result shows that if a nonlinear system is bounded and “ordered”, it is possible to use a convex combination of bounding linear systems to design a control for the nonlinear system. The third result takes advantage of a convex reachable set computation for each agent in solving games using a geometrical approach. Altogether, the theoretical and computational results demonstrate the significance of convex analysis in solving non-convex control problems
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