317 research outputs found
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
Decibell: A novel approach to the ORM software in Java
DeciBell is an open source and free tool developed to tackle in a uniform and structured way the problem of Java and SQL cooperation (available at http://github.com/hampos/DeciBell). In DeciBell, Java classes are related to relational database entities automatically and in a transparent way as far as the background operations are concerned. So, on one hand, non-expert users can work on Java code exclusively while expert ones are able to focus on more algorithmic aspects of the problem they try to solve rather than be wasted with trivial database management issues. In contrast to the existing O.R.M. programs, DeciBell does not require any configuration files or composite query structures, but only a proper annotation of certain fields of the classes. This annotation is carried out by means of the Java Annotations which is a modern trend in Java programming. Among its supported facilities, DeciBell supports primary keys (single and multiple), foreign keys, constraints, one-to-one, one- to-many, and many-to-many relations and all these using pure Java predicates and no SQL or other Query Languages
Error analysis of coarse-grained kinetic Monte Carlo method
In this paper we investigate the approximation properties of the
coarse-graining procedure applied to kinetic Monte Carlo simulations of lattice
stochastic dynamics. We provide both analytical and numerical evidence that the
hierarchy of the coarse models is built in a systematic way that allows for
error control in both transient and long-time simulations. We demonstrate that
the numerical accuracy of the CGMC algorithm as an approximation of stochastic
lattice spin flip dynamics is of order two in terms of the coarse-graining
ratio and that the natural small parameter is the coarse-graining ratio over
the range of particle/particle interactions. The error estimate is shown to
hold in the weak convergence sense. We employ the derived analytical results to
guide CGMC algorithms and we demonstrate a CPU speed-up in demanding
computational regimes that involve nucleation, phase transitions and
metastability.Comment: 30 page
A Simple and Efficient Algorithm for Nonlinear Model Predictive Control
We present PANOC, a new algorithm for solving optimal control problems
arising in nonlinear model predictive control (NMPC). A usual approach to this
type of problems is sequential quadratic programming (SQP), which requires the
solution of a quadratic program at every iteration and, consequently, inner
iterative procedures. As a result, when the problem is ill-conditioned or the
prediction horizon is large, each outer iteration becomes computationally very
expensive. We propose a line-search algorithm that combines forward-backward
iterations (FB) and Newton-type steps over the recently introduced
forward-backward envelope (FBE), a continuous, real-valued, exact merit
function for the original problem. The curvature information of Newton-type
methods enables asymptotic superlinear rates under mild assumptions at the
limit point, and the proposed algorithm is based on very simple operations:
access to first-order information of the cost and dynamics and low-cost direct
linear algebra. No inner iterative procedure nor Hessian evaluation is
required, making our approach computationally simpler than SQP methods. The
low-memory requirements and simple implementation make our method particularly
suited for embedded NMPC applications
Hybrid deterministic stochastic systems with microscopic look-ahead dynamics
We study the impact of stochastic mechanisms on a coupled hybrid system consisting of a general advection-diffusion-reaction partial differential equation and a spatially distributed stochastic lattice noise model. The stochastic dynamics include both spin-flip and spin-exchange type interparticle interactions. Furthermore, we consider a new, asymmetric, single exclusion pro- cess, studied elsewhere in the context of traffic flow modeling, with an one-sided interaction potential which imposes advective trends on the stochastic dynamics. This look-ahead stochastic mechanism is responsible for rich nonlinear behavior in solutions. Our approach relies heavily on first deriving approximate differential mesoscopic equations. These approximations become exact either in the long range, Kac interaction partial differential equation case, or, given sufficient time separation con- ditions, between the partial differential equation and the stochastic model giving rise to a stochastic averaging partial differential equation. Although these approximations can in some cases be crude, they can still give a first indication, via linearized stability analysis, of the interesting regimes for the stochastic model. Motivated by this linearized stability analysis we choose particular regimes where interacting nonlinear stochastic waves are responsible for phenomena such as random switching, convective instability, and metastability, all driven by stochasticity. Numerical kinetic Monte Carlo simulations of the coarse grained hybrid system are implemented to assist in producing solutions and understanding their behavior
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