400 research outputs found
Robust Model Predictive Control for Signal Temporal Logic Synthesis
Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
Stability and convergence in discrete convex monotone dynamical systems
We study the stable behaviour of discrete dynamical systems where the map is
convex and monotone with respect to the standard positive cone. The notion of
tangential stability for fixed points and periodic points is introduced, which
is weaker than Lyapunov stability. Among others we show that the set of
tangentially stable fixed points is isomorphic to a convex inf-semilattice, and
a criterion is given for the existence of a unique tangentially stable fixed
point. We also show that periods of tangentially stable periodic points are
orders of permutations on letters, where is the dimension of the
underlying space, and a sufficient condition for global convergence to periodic
orbits is presented.Comment: 36 pages, 1 fugur
On the Convergence of Finite Element Methods for Hamilton-Jacobi-Bellman Equations
In this note we study the convergence of monotone P1 finite element methods
on unstructured meshes for fully non-linear Hamilton-Jacobi-Bellman equations
arising from stochastic optimal control problems with possibly degenerate,
isotropic diffusions. Using elliptic projection operators we treat
discretisations which violate the consistency conditions of the framework by
Barles and Souganidis. We obtain strong uniform convergence of the numerical
solutions and, under non-degeneracy assumptions, strong L2 convergence of the
gradients.Comment: Keywords: Bellman equations, finite element methods, viscosity
solutions, fully nonlinear operators; 18 pages, 1 figur
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