2 research outputs found
A generalized Bellman-Ford Algorithm for Application in Symbolic Optimal Control
Symbolic controller synthesis is a fully-automated and correct-by-design
synthesis scheme whose limitations are its immense memory and runtime
requirements. A current trend to compensate for this downside is to develop
techniques for parallel execution of the scheme both in mathematical foundation
and in software implementation. In this paper we present a generalized
Bellman-Ford algorithm to be used in the so-called symbolic optimal control,
which is an extension of the aforementioned synthesis scheme. Compared to the
widely used Dijkstra algorithm our algorithm has two advantages. It allows for
cost functions taking arbitrary (e.g. negative) values and for parallel
execution with the ability for trading processing speed for memory consumption.
We motivate the usefulness of negative cost values on a scenario of aerial
firefighting with unmanned aerial vehicles. In addition, this four-dimensional
numerical example, which is rich in detail, demonstrates the great performance
of our algorithm.Comment: This version has been accepted for publication in Proc. European
Control Conference (ECC), 202
Symbolic Optimal Control
We present novel results on the solution of a class of leavable, undiscounted
optimal control problems in the minimax sense for nonlinear, continuous-state,
discrete-time plants. The problem class includes entry-(exit-)time problems as
well as minimum time, pursuit-evasion and reach-avoid games as special cases.
We utilize auxiliary optimal control problems (`abstractions') to compute both
upper bounds of the value function, i.e., of the achievable closed-loop
performance, and symbolic feedback controllers realizing those bounds. The
abstractions are obtained from discretizing the problem data, and we prove that
the computed bounds and the performance of the symbolic controllers converge to
the value function as the discretization parameters approach zero. In
particular, if the optimal control problem is solvable on some compact subset
of the state space, and if the discretization parameters are sufficiently
small, then we obtain a symbolic feedback controller solving the problem on
that subset. These results do not assume the continuity of the value function
or any problem data, and they fully apply in the presence of hard state and
control constraints.Comment: corrected Theorem V.6; simplified definitions of plants, controllers
and closed-loops; references added; full proof of Th VII.3 rather than just a
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