arXiv subjects

Paolo Zuliani

Publications and source records attributed to Paolo Zuliani.

26 records · Page 2Linked to original sources

arXiv2017

Automated Synthesis of Safe and Robust PID Controllers for Stochastic Hybrid Systems

We present a new method for the automated synthesis of safe and robust Proportional-Integral-Derivative (PID) controllers for stochastic hybrid systems. Despite their widespread use in industry, no automated method currently exists for deriving a PID controller (or any other type of controller, for that matter) with safety and performance guarantees for such a general class of systems. In particular, we consider hybrid systems with nonlinear dynamics (Lipschitz-continuous ordinary differential equations) and random parameters, and we synthesize PID controllers such that the resulting closed-loop systems satisfy safety and performance constraints given as probabilistic bounded reachability properties. Our technique leverages SMT solvers over the reals and nonlinear differential equations to provide formal guarantees that the synthesized controllers satisfy such properties. These controllers are also robust by design since they minimize the probability of reaching an unsafe state in the presence of random disturbances. We apply our approach to the problem of insulin regulation for type 1 diabetes, synthesizing controllers with robust responses to large random meal disturbances, thereby enabling them to maintain blood glucose levels within healthy, safe ranges.

eess.SY↗

arXiv2017

Verifying Quantum Programs: From Quipper to QPMC

In this paper we present a translation from the quantum programming language Quipper to the QPMC model checker, with the main aim of verifying Quipper programs. Quipper is an embedded functional programming language for quantum computation. It is above all a circuit description language, for this reason it uses the vector state formalism and its main purpose is to make circuit implementation easy providing high level operations for circuit manipulation. Quipper provides both an high-level circuit building interface and a simulator. QPMC is a model checker for quantum protocols based on the density matrix formalism. QPMC extends the probabilistic model checker IscasMC allowing to formally verify properties specified in the temporal logic QCTL on Quantum Markov Chains. We implemented and tested our translation on several quantum algorithms, including Grover's quantum search.

cs.LO↗

arXiv2015

Towards Personalized Prostate Cancer Therapy Using Delta-Reachability Analysis

Recent clinical studies suggest that the efficacy of hormone therapy for prostate cancer depends on the characteristics of individual patients. In this paper, we develop a computational framework for identifying patient-specific androgen ablation therapy schedules for postponing the potential cancer relapse. We model the population dynamics of heterogeneous prostate cancer cells in response to androgen suppression as a nonlinear hybrid automaton. We estimate personalized kinetic parameters to characterize patients and employ $δ$-reachability analysis to predict patient-specific therapeutic strategies. The results show that our methods are promising and may lead to a prognostic tool for personalized cancer therapy.

q-bio.QM↗

arXiv2015

Probabilistic bounded reachability for hybrid systems with continuous nondeterministic and probabilistic parameters

We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid systems with continuous dynamics given by solutions of nonlinear ordinary differential equations (with possibly nondeterministic initial conditions and parameters), and probabilistic behaviour given by initial parameters distributed as continuous (with possibly infinite support) and discrete random variables. Our approach is to define an appropriate relaxation of the (undecidable) reachability problem, so that it can be solved by $δ$-complete decision procedures. In particular, for systems with continuous random parameters only, we develop a validated integration procedure which computes an arbitrarily small interval that is guaranteed to contain the reachability probability. In the more general case of systems with both nondeterministic and probabilistic parameters, our procedure computes a guaranteed enclosure for the range of reachability probabilities. We have applied our approach to a number of nonlinear hybrid models and validated the results by comparison with Monte Carlo simulation.

cs.LO↗

arXiv2015

ProbReach: Verified Probabilistic Delta-Reachability for Stochastic Hybrid Systems

We present ProbReach, a tool for verifying probabilistic reachability for stochastic hybrid systems, i.e., computing the probability that the system reaches an unsafe region of the state space. In particular, ProbReach will compute an arbitrarily small interval which is guaranteed to contain the required probability. Standard (non-probabilistic) reachability is undecidable even for linear hybrid systems. In ProbReach we adopt the weaker notion of delta-reachability, in which the unsafe region is overapproximated by a user-defined parameter (delta). This choice leads to false alarms, but also makes the reachability problem decidable for virtually any hybrid system. In ProbReach we have implemented a probabilistic version of delta-reachability that is suited for hybrid systems whose stochastic behaviour is given in terms of random initial conditions. In this paper we introduce the capabilities of ProbReach, give an overview of the parallel implementation, and present results for several benchmarks involving highly non-linear hybrid systems.

cs.LO↗

arXiv2014

SReach: A Bounded Model Checker for Stochastic Hybrid Systems

In this paper we describe a new tool, SReach, which solves probabilistic bounded reachability problems for two classes of stochastic hybrid systems. The first one is (nonlinear) hybrid automata with parametric uncertainty. The second one is probabilistic hybrid automata with additional randomness for both transition probabilities and variable resets. Standard approaches to reachability problems for linear hybrid systems require numerical solutions for large optimization problems, and become infeasible for systems involving both nonlinear dynamics over the reals and stochasticity. Our approach encodes stochastic information by using random variables, and combines the randomized sampling, a $δ$-complete decision procedure, and statistical tests. SReach utilizes the $δ$-complete decision procedure to solve reachability problems in a sound manner, i.e., it always decides correctly if, for a given assignment to all random variables, the system actually reaches the unsafe region. The statistical tests adapted guarantee arbitrary small error bounds between probabilities estimated by SReach and real ones. Compared to standard simulation-based methods, our approach supports non-deterministic branching, increases the coverage of simulation, and avoids the zero-crossing problem. We demonstrate our method's feasibility by applying SReach to three representative biological models and to additional benchmarks for nonlinear hybrid systems with multiple probabilistic system parameters.

cs.FL↗

arXiv2014

Parameter Synthesis for Cardiac Cell Hybrid Models Using Delta-Decisions

A central problem in systems biology is to identify parameter values such that a biological model satisfies some behavioral constraints (\eg, time series). In this paper we focus on parameter synthesis for hybrid (continuous/discrete) models, as many biological systems can possess multiple operational modes with specific continuous dynamics in each mode. These biological systems are naturally modeled as hybrid automata, most often with nonlinear continuous dynamics. However, hybrid automata are notoriously hard to analyze --- even simple reachability for hybrid systems with linear differential dynamics is an undecidable problem. In this paper we present a parameter synthesis framework based on $δ$-complete decision procedures that sidesteps undecidability. We demonstrate our method on two highly nonlinear hybrid models of the cardiac cell action potential. The results show that our parameter synthesis framework is convenient and efficient, and it enabled us to select a suitable model to study and identify crucial parameter ranges related to cardiac disorders.

cs.LO↗

arXiv2014

Statistical Model Checking for Biological Applications

In this paper we survey recent work on the use of statistical model checking techniques for biological applications. We begin with an overview of the basic modelling techniques for biochemical reactions and their corresponding stochastic simulation algorithm - the Gillespie algorithm. We continue by giving a brief description of the relation between stochastic models and continuous (ordinary differential equation) models. Next we present a literature survey, divided in two general areas. In the first area we focus on works addressing verification of biological models, while in the second area we focus on papers tackling the parameter synthesis problem. We conclude with some open problems and directions for further research.

cs.LO↗