7,238 research outputs found
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems
Development of robust dynamical systems and networks such as autonomous
aircraft systems capable of accomplishing complex missions faces challenges due
to the dynamically evolving uncertainties coming from model uncertainties,
necessity to operate in a hostile cluttered urban environment, and the
distributed and dynamic nature of the communication and computation resources.
Model-based robust design is difficult because of the complexity of the hybrid
dynamic models including continuous vehicle dynamics, the discrete models of
computations and communications, and the size of the problem. We will overview
recent advances in methodology and tools to model, analyze, and design robust
autonomous aerospace systems operating in uncertain environment, with stress on
efficient uncertainty quantification and robust design using the case studies
of the mission including model-based target tracking and search, and trajectory
planning in uncertain urban environment. To show that the methodology is
generally applicable to uncertain dynamical systems, we will also show examples
of application of the new methods to efficient uncertainty quantification of
energy usage in buildings, and stability assessment of interconnected power
networks
On the Hybrid Minimum Principle On Lie Groups and the Exponential Gradient HMP Algorithm
This paper provides a geometrical derivation of the Hybrid Minimum Principle
(HMP) for autonomous hybrid systems whose state manifolds constitute Lie groups
which are left invariant under the controlled dynamics of the
system, and whose switching manifolds are defined as smooth embedded time
invariant submanifolds of . The analysis is expressed in terms of extremal
(i.e. optimal) trajectories on the cotangent bundle of the state manifold .
The Hybrid Maximum Principle (HMP) algorithm introduced in \cite{Shaikh} is
extended to the so-called Exponential Gradient algorithm. The convergence
analysis for the algorithm is based upon the LaSalle Invariance Principle and
simulation results illustrate their efficacy
Model-Based Reinforcement Learning for Stochastic Hybrid Systems
Optimal control of general nonlinear systems is a central challenge in
automation. Enabled by powerful function approximators, data-driven approaches
to control have recently successfully tackled challenging robotic applications.
However, such methods often obscure the structure of dynamics and control
behind black-box over-parameterized representations, thus limiting our ability
to understand closed-loop behavior. This paper adopts a hybrid-system view of
nonlinear modeling and control that lends an explicit hierarchical structure to
the problem and breaks down complex dynamics into simpler localized units. We
consider a sequence modeling paradigm that captures the temporal structure of
the data and derive an expectation-maximization (EM) algorithm that
automatically decomposes nonlinear dynamics into stochastic piecewise affine
dynamical systems with nonlinear boundaries. Furthermore, we show that these
time-series models naturally admit a closed-loop extension that we use to
extract local polynomial feedback controllers from nonlinear experts via
behavioral cloning. Finally, we introduce a novel hybrid relative entropy
policy search (Hb-REPS) technique that incorporates the hierarchical nature of
hybrid systems and optimizes a set of time-invariant local feedback controllers
derived from a local polynomial approximation of a global state-value function
WavePacket: A Matlab package for numerical quantum dynamics. III: Quantum-classical simulations and surface hopping trajectories
WavePacket is an open-source program package for numerical simulations in
quantum dynamics. Building on the previous Part I [Comp. Phys. Comm. 213,
223-234 (2017)] and Part II [Comp. Phys. Comm. 228, 229-244 (2018)] which dealt
with quantum dynamics of closed and open systems, respectively, the present
Part III adds fully classical and mixed quantum-classical propagations to
WavePacket. In those simulations classical phase-space densities are sampled by
trajectories which follow (diabatic or adiabatic) potential energy surfaces. In
the vicinity of (genuine or avoided) intersections of those surfaces
trajectories may switch between surfaces. To model these transitions, two
classes of stochastic algorithms have been implemented: (1) J. C. Tully's
fewest switches surface hopping and (2) Landau-Zener based single switch
surface hopping. The latter one offers the advantage of being based on
adiabatic energy gaps only, thus not requiring non-adiabatic coupling
information any more.
The present work describes the MATLAB version of WavePacket 6.0.2 which is
essentially an object-oriented rewrite of previous versions, allowing to
perform fully classical, quantum-classical and quantum-mechanical simulations
on an equal footing, i.e., for the same physical system described by the same
WavePacket input. The software package is hosted and further developed at the
Sourceforge platform, where also extensive Wiki-documentation as well as
numerous worked-out demonstration examples with animated graphics are
available
- …