4,272 research outputs found
Receding Horizon Temporal Logic Control for Finite Deterministic Systems
This paper considers receding horizon control of finite deterministic
systems, which must satisfy a high level, rich specification expressed as a
linear temporal logic formula. Under the assumption that time-varying rewards
are associated with states of the system and they can be observed in real-time,
the control objective is to maximize the collected reward while satisfying the
high level task specification. In order to properly react to the changing
rewards, a controller synthesis framework inspired by model predictive control
is proposed, where the rewards are locally optimized at each time-step over a
finite horizon, and the immediate optimal control is applied. By enforcing
appropriate constraints, the infinite trajectory produced by the controller is
guaranteed to satisfy the desired temporal logic formula. Simulation results
demonstrate the effectiveness of the approach.Comment: Technical report accompanying a paper to be presented at ACC 201
Formal Synthesis of Control Strategies for Positive Monotone Systems
We design controllers from formal specifications for positive discrete-time
monotone systems that are subject to bounded disturbances. Such systems are
widely used to model the dynamics of transportation and biological networks.
The specifications are described using signal temporal logic (STL), which can
express a broad range of temporal properties. We formulate the problem as a
mixed-integer linear program (MILP) and show that under the assumptions made in
this paper, which are not restrictive for traffic applications, the existence
of open-loop control policies is sufficient and almost necessary to ensure the
satisfaction of STL formulas. We establish a relation between satisfaction of
STL formulas in infinite time and set-invariance theories and provide an
efficient method to compute robust control invariant sets in high dimensions.
We also develop a robust model predictive framework to plan controls optimally
while ensuring the satisfaction of the specification. Illustrative examples and
a traffic management case study are included.Comment: To appear in IEEE Transactions on Automatic Control (TAC) (2018), 16
pages, double colum
Minimal time control of fed-batch processes with growth functions having several maxima
We address the issue of minimal time optimal control of fedbatch reactor in
presence of complex non monotonic kinetics, that can be typically characterized
by the combination of two Haldane models. The optimal synthesis may present
several singular arcs. Global optimal trajectory results are provided on the
basis of a numerical approach that considers an approximation method with
smooth control inputs
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In this issue of IEEE Control Systems Magazine, Andy Packard and friends respond to a query on determining the region of attraction using sum-of-squares methods
Switching Quantum Dynamics for Fast Stabilization
Control strategies for dissipative preparation of target quantum states, both
pure and mixed, and subspaces are obtained by switching between a set of
available semigroup generators. We show that the class of problems of interest
can be recast, from a control--theoretic perspective, into a
switched-stabilization problem for linear dynamics. This is attained by a
suitable affine transformation of the coherence-vector representation. In
particular, we propose and compare stabilizing time-based and state-based
switching rules for entangled state preparation, showing that the latter not
only ensure faster convergence with respect to non-switching methods, but can
designed so that they retain robustness with respect to initialization, as long
as the target is a pure state or a subspace.Comment: 15 pages, 4 figure
Time-Minimal Control of Dissipative Two-level Quantum Systems: the Generic Case
The objective of this article is to complete preliminary results concerning
the time-minimal control of dissipative two-level quantum systems whose
dynamics is governed by Lindblad equations. The extremal system is described by
a 3D-Hamiltonian depending upon three parameters. We combine geometric
techniques with numerical simulations to deduce the optimal solutions.Comment: 24 pages, 16 figures. submitted to IEEE transactions on automatic
contro
Nonisotropic 3-level Quantum Systems: Complete Solutions for Minimum Time and Minimum Energy
We apply techniques of subriemannian geometry on Lie groups and of optimal
synthesis on 2-D manifolds to the population transfer problem in a three-level
quantum system driven by two laser pulses, of arbitrary shape and frequency. In
the rotating wave approximation, we consider a nonisotropic model i.e. a model
in which the two coupling constants of the lasers are different. The aim is to
induce transitions from the first to the third level, minimizing 1) the time of
the transition (with bounded laser amplitudes),
2) the energy of lasers (with fixed final time). After reducing the problem
to real variables, for the purpose 1) we develop a theory of time optimal
syntheses for distributional problem on 2-D-manifolds, while for the purpose 2)
we use techniques of subriemannian geometry on 3-D Lie groups. The complete
optimal syntheses are computed.Comment: 29 pages, 6 figure
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