267 research outputs found
New insights on stochastic reachability
In this paper, we give new characterizations of the stochastic reachability problem for stochastic hybrid systems in the language of different theories that can be employed in studying stochastic processes (Markov processes, potential theory, optimal control). These characterizations are further used to obtain the probabilities involved in the context of stochastic reachability as viscosity solutions of some variational inequalities
Abstractions of Stochastic Hybrid Systems
In this paper we define a stochastic bisimulation concept for a very general class of stochastic hybrid systems, which subsumes most classes of stochastic hybrid systems. The definition of this bisimulation builds on the concept of zigzag morphism defined for strong Markov processes.
The main result is that this stochastic bisimulation is indeed an equivalence relation. The secondary result is that this bisimulation relation for the stochastic hybrid system models used in this paper implies the same
kind of bisimulation for their continuous parts and respectively for their jumping structures
Towards a General Theory of Stochastic Hybrid Systems
In this paper we set up a mathematical structure,
called Markov string, to obtaining a very general class of models for stochastic hybrid systems. Markov Strings are, in fact, a class of Markov processes, obtained by a
mixing mechanism of stochastic processes, introduced
by Meyer. We prove that Markov strings are strong Markov processes with the cadlag property. We then show how a very general class of stochastic hybrid processes can be embedded
in the framework of Markov strings. This class, which
is referred to as the General Stochastic Hybrid Systems (GSHS), includes as special cases all the classes of stochastic hybrid processes, proposed in the literature
Abstractions of stochastic hybrid systems
Many control systems have large, infinite state space that can not be easily abstracted. One method to analyse and verify these systems is reachability analysis. It is frequently used for air traffic control and power plants. Because of lack of complete information about the environment or unpredicted changes, the stochastic approach is a viable alternative. In this paper, different ways of introducing rechability under uncertainty are presented. A new concept of stochastic bisimulation is introduced and its connection with the reachability analysis is established. The work is mainly motivated by safety critical situations in air traffic control (like collision detection and avoidance) and formal tools are based on stochastic analysis
Stochastic optimization on continuous domains with finite-time guarantees by Markov chain Monte Carlo methods
We introduce bounds on the finite-time performance of Markov chain Monte
Carlo algorithms in approaching the global solution of stochastic optimization
problems over continuous domains. A comparison with other state-of-the-art
methods having finite-time guarantees for solving stochastic programming
problems is included.Comment: 29 pages, 6 figures. Revised version based on referees repor
Mathematical modeling of genome replication
Peer reviewedPublisher PD
Reachability analysis of discrete-time systems with disturbances
Published versio
Behavioral uncertainty quantification for data-driven control
This paper explores the problem of uncertainty quantification in the
behavioral setting for data-driven control. Building on classical ideas from
robust control, the problem is regarded as that of selecting a metric which is
best suited to a data-based description of uncertainties. Leveraging on
Willems' fundamental lemma, restricted behaviors are viewed as subspaces of
fixed dimension, which may be represented by data matrices. Consequently,
metrics between restricted behaviors are defined as distances between points on
the Grassmannian, i.e., the set of all subspaces of equal dimension in a given
vector space. A new metric is defined on the set of restricted behaviors as a
direct finite-time counterpart of the classical gap metric. The metric is shown
to capture parametric uncertainty for the class of autoregressive (AR) models.
Numerical simulations illustrate the value of the new metric with a data-driven
mode recognition and control case study.Comment: Submitted to the 61st IEEE Conference on Decision and Contro
A randomized approach to stochastic model predictive control
In this paper, we propose a novel randomized approach to Stochastic Model Predictive Control (SMPC) for a linear system affected by a disturbance with unbounded support. As it is common in this setup, we focus on the case where the input/state of the system are subject to probabilistic constraints, i.e., the constraints have to be satisfied for all the disturbance realizations but for a set having probability smaller than a given threshold. This leads to solving at each time t a finite-horizon chance-constrained optimization problem, which is known to be computationally intractable except for few special cases. The key distinguishing feature of our approach is that the solution to this finite-horizon chance-constrained problem is computed by first extracting at random a finite number of disturbance realizations, and then replacing the probabilistic constraints with hard constraints associated with the extracted disturbance realizations only. Despite the apparent naivety of the approach, we show that, if the control policy is suitably parameterized and the number of disturbance realizations is appropriately chosen, then, the obtained solution is guaranteed to satisfy the original probabilistic constraints. Interestingly, the approach does not require any restrictive assumption on the disturbance distribution and has a wide realm of applicability
PGL\u3csub\u3e2\u3c/sub\u3e(F\u3csub\u3el\u3c/sub\u3e) Number Fields with Rational Companion Forms
We give a list of PGL2(Fl) number fields for ℓ ≥ 11 which have rational companion forms. Our list has fifty-three fields and seems likely to be complete. Some of the fields on our list are very lightly ramified for their Galois group
- …