72 research outputs found
Probably Approximately Correct MDP Learning and Control With Temporal Logic Constraints
We consider synthesis of control policies that maximize the probability of
satisfying given temporal logic specifications in unknown, stochastic
environments. We model the interaction between the system and its environment
as a Markov decision process (MDP) with initially unknown transition
probabilities. The solution we develop builds on the so-called model-based
probably approximately correct Markov decision process (PAC-MDP) methodology.
The algorithm attains an -approximately optimal policy with
probability using samples (i.e. observations), time and space that
grow polynomially with the size of the MDP, the size of the automaton
expressing the temporal logic specification, ,
and a finite time horizon. In this approach, the system
maintains a model of the initially unknown MDP, and constructs a product MDP
based on its learned model and the specification automaton that expresses the
temporal logic constraints. During execution, the policy is iteratively updated
using observation of the transitions taken by the system. The iteration
terminates in finitely many steps. With high probability, the resulting policy
is such that, for any state, the difference between the probability of
satisfying the specification under this policy and the optimal one is within a
predefined bound.Comment: 9 pages, 5 figures, Accepted by 2014 Robotics: Science and Systems
(RSS
Model Checking the Quantitative mu-Calculus on Linear Hybrid Systems
We study the model-checking problem for a quantitative extension of the modal
mu-calculus on a class of hybrid systems. Qualitative model checking has been
proved decidable and implemented for several classes of systems, but this is
not the case for quantitative questions that arise naturally in this context.
Recently, quantitative formalisms that subsume classical temporal logics and
allow the measurement of interesting quantitative phenomena were introduced. We
show how a powerful quantitative logic, the quantitative mu-calculus, can be
model checked with arbitrary precision on initialised linear hybrid systems. To
this end, we develop new techniques for the discretisation of continuous state
spaces based on a special class of strategies in model-checking games and
present a reduction to a class of counter parity games.Comment: LMCS submissio
On Robustness Computation and Optimization in BIOCHAM-4
Long version with appendicesInternational audienceBIOCHAM-4 is a tool for modeling, analyzing and synthesizing biochemical reaction networks with respect to some formal, yet possibly imprecise, specification of their behavior. We focus here on one new capability of this tool to optimize the robustness of a parametric model with respect to a specification of its dynamics in quantitative temporal logic. More precisely, we present two complementary notions of robustness: the statistical notion of model robustness to parameter perturbations, defined as its mean functionality, and a metric notion of formula satisfaction robustness, defined as the penetration depth in the validity domain of the temporal logic constraints. We show how the formula robustness can be used in BIOCHAM-4 with no extra cost as an objective function in the parameter optimization procedure, to actually improve the model robustness. We illustrate these unique features with a classical example of the hybrid systems community and provide some performance figures on a model of MAPK signalling with 37 parameters
A Skin Microbiome Model with AMP interactions and Analysis of Quasi-Stability vs Stability in Population Dynamics
The skin microbiome plays an important role in the maintenance of a healthy
skin. It is an ecosystem, composed of several species, competing for resources
and interacting with the skin cells. Imbalance in the cutaneous microbiome,
also called dysbiosis, has been correlated with several skin conditions,
including acne and atopic dermatitis. Generally, dysbiosis is linked to
colonization of the skin by a population of opportunistic pathogenic bacteria.
Treatments consisting in non-specific elimination of cutaneous microflora have
shown conflicting results. In this article, we introduce a mathematical model
based on ordinary differential equations, with 2 types of bacteria populations
(skin commensals and opportunistic pathogens) and including the production of
antimicrobial peptides to study the mechanisms driving the dominance of one
population over the other. By using published experimental data, assumed to
correspond to the observation of stable states in our model, we reduce the
number of parameters of the model from 13 to 5. We then use a formal
specification in quantitative temporal logic to calibrate our model by global
parameter optimization and perform sensitivity analyses. On the time scale of 2
days of the experiments, the model predicts that certain changes of the
environment, like the elevation of skin surface pH, create favorable conditions
for the emergence and colonization of the skin by the opportunistic pathogen
population, while the production of human AMPs has non-linear effect on the
balance between pathogens and commensals. Surprisingly, simulations on longer
time scales reveal that the equilibrium reached around 2 days can in fact be a
quasi-stable state followed by the reaching of a reversed stable state after 12
days or more. We analyse the conditions of quasi-stability observed in this
model using tropical algebraic methods, and show their non-generic character in
contrast to slow-fast systems. These conditions are then generalized to a large
class of population dynamics models over any number of species.Comment: arXiv admin note: substantial text overlap with arXiv:2206.1022
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