In the area of symbolic control, which to be precisely defined I mean using finite abstraction of dynamical systems with verification algorithms to construct provably correct controllers satisfying a temporal logic formula, I am interested in the ways to tackle environment uncertainties like dynamic obstacles.
In the paper Article Control of Probabilistic Systems under Dynamic, Partially Kn...
a method is proposed, but it is assumed that the car model is given in form of a Markov Decision Process(MDP) apriori, While I am interested in researches done combining the problem of finding an abstract model of the system and the problem of handling uncertainties in environment.Is anybody aware of a research which has done so? Or any ideas how one can combine these two problems? I have done a literature review in the field and I have not came up with an idea so far.
Thanks in advance for your help.
Abstraction based controller synthesis solves control problems in three steps:
1. Computing an abstraction of the plant , and an abstract version of the specification, to obtain an auxiliary control problem (pair of abstraction, abstract specification).
2. Solving the abstract control problem, to obtain an abstract controller.
3. Refining the abstract controller to obtain a controller that solves the original control problem.
For details, please see the work
[1] Reissig, Weber and Rungger, Feedback Refinement Relations for the Synthesis of Symbolic Controllers, IEEE Trans Autom Control 2017,
https://www.researchgate.net/publication/273447079
That work assumes a discrete-time control problem and allows for static uncertainties of the environment, by modelling the plant as a difference inclusion,
x(t+1) \in F(x(t),u(t)), t \in \mathbb{Z}_+
If the uncertanties are dynamic, that dynamics must be made part of the plant. Feedback refinement relations have, to the best of my knowledge, not yet extended to that case.
Gunther Reissig Thank you very much for your kind answer.
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