We develop a novel model-based hardware-in-the-loop (HIL) framework for optimising energy consumption of embedded software controllers. Controller and plant models are specified as networks of parameterised timed input/output automata and translated into executable code. The controller is encoded into the target embedded hardware, which is connected to a power monitor and interacts with the simulation of the plant model. The framework then generates a power consumption model that maps controller transitions to distributions over power measurements, and is used to optimise the timing parameters of the controller, without compromising a given safety requirement. The novelty of our approach is that we measure the real power consumption of the controller and use thus obtained data for energy optimisation. We employ timed Petri nets as an intermediate representation of the executable specification, which facilitates efficient code generation and fast simulations. Our framework uniquely combines the advantages of rigorous specifications with accurate power measurements and methods for online model estimation, thus enabling automated design of correct and energy-efficient controllers.

In many real-time embedded systems, the choice of values for the timing delays can crucially affect the safety or quantitative characteristics of their execution. We propose a parameter synthesis algorithm that finds optimal timing delays guaranteeing that the system satisfies a given quantitative property. As a modelling framework we consider networks of Timed Input/Output Automata (TIOA) with priorities and parametric guards. To express system properties we extend Metric Temporal Logic (MTL) with counting formulas. We implement the algorithm using constraint solving and Monte Carlo sampling, and demonstrate the feasibility of our approach on a simplified model of a pacemaker. We are able to synthesise timing delays that ensure with high probability that energy usage is minimised, while maintaining the basic safety property of the pacemaker.

We develop a novel hybrid heart model in Simulink that is suitable for quantitative verification of implantable cardiac pacemakers. The heart model is formulated at the level of cardiac cells, can be adapted to patient data, and incorporates stochasticity. It is inspired by the timed and hybrid automata network models of Jiang et al and Ye et al, where probabilistic behaviour is not considered. In contrast to our earlier work, we work directly with action potential signals that the pacemaker sensor inputs from a specific cell, rather than ECG signals. We validate the model by demonstrating that its composition with a pacemaker model can be used to check safety properties by means of approximate probabilistic verification.

This work deals with Markov processes that are defined over an uncountable state space (possibly hybrid) and embedding non-determinism in the shape of a control structure. The contribution looks at the problem of optimization, over the set of allowed controls, of probabilistic specifications defined by automata - in particular, the focus is on deterministic finite-state automata. This problem can be reformulated as an optimization of a probabilistic reachability property over a product process obtained from the model for the specification and the model of the system. Optimizing over automata-based specifications thus leads to maximal or minimal probabilistic reachability properties. For both setups, the contribution shows that these problems can be sufficiently tackled with history-independent Markov policies. This outcome has relevant computational repercussions: in particular, the work develops a discretization procedure leading into standard optimization problems over Markov decision processes. Such procedure is associated with exact error bounds and is experimentally tested on a case study.

Stochastic modelling and algorithmic verification techniques have been proved useful in analysing and detecting unusual trends in performance and energy usage of systems such as power management controllers and wireless sensor devices. Many important properties are dependent on the cumulated time that the device spends in certain states, possibly intermittently. We study the problem of verifying continuous-time Markov Chains (CTMCs) against Linear Duration Properties (LDP), that is, properties stated as conjunctions of linear constraints over the total duration of time spent in states that satisfy a given property. We identify two classes of LDP properties, Eventuality Duration Properties (EDP) and Invariance Duration Properties (IDP), respectively referring to the reachability of a set of goal states, within a time bound; and the continuous satisfaction of a duration property over an execution path. The central question that we address is how to compute the probability of the set of infinite timed paths of the CTMC that satisfy a given LDP. We present algorithms to approximate these probabilities up to a given precision, stating their complexity and error bounds. The algorithms mainly employ an adaptation of uniformisation and the computation of volumes of multidimensional integrals under systems of linear constraints, together with different mechanisms to bound the errors.

Stochastic modeling and algorithmic verification techniques have been proved useful in analyzing and detecting unusual trends in performance and energy usage of systems such as power management controllers and wireless sensor devices. Many important properties are dependent on the cumulated time that the device spends in certain states, possibly intermittently. We study the problem of verifying continuous-time Markov chains (CTMCs) against linear duration properties (LDP), i.e. properties stated as conjunctions of linear constraints over the total duration of time spent in states that satisfy a given property. We identify two classes of LDP properties, eventuality duration properties (EDP) and invariance duration properties (IDP), respectively referring to the reachability of a set of goal states, within a time bound; and the continuous satisfaction of a duration property over an execution path. The central question that we address is how to compute the probability of the set of infinite timed paths of the CTMC that satisfy a given LDP. We present algorithms to approximate these probabilities up to a given precision, stating their complexity and error bounds. The algorithms mainly employ an adaptation of uniformization and the computation of volumes of multi-dimensional integrals under systems of linear constraints, together with different mechanisms to bound the errors.

Implantable medical devices, such as cardiac pacemakers, must be designed and programmed to the highest levels of safety and reliability. Recently, errors in embedded software have led to a substantial increase in safety alerts, costly device recalls or even patient death. To address such issues, we propose a model-based framework for quantitative, automated verification of pacemaker software. We adapt the electrocardiogram model of Clifford et al, which generates realistic normal and abnormal heart beat behaviours, with probabilistic transitions between them, to produce a timed sequence of action potential signals that serve as pacemaker input. Working with the timed automata model of the pacemaker by Jiang et al, we develop a methodology for deriving the composition of the heart and the pacemaker, based on discretisation. The main correctness properties we consider include checking that the pacemaker corrects Bradycardia (slow heart beat) and does not induce Tachycardia (fast heart beat), for a range of realistic heart behaviours. We also analyse under sensing, through considering noise on sensor readings, and energy usage. We implement the framework using the probabilistic model checker PRISM and MATLAB and demonstrate encouraging experimental results. Our approach can be adapted to individual patients and is applicable to other pacemaker models.

This paper considers the quantitative verification of discrete-time stochastic hybrid systems (DTSHS) against linear time objectives. The central question is to determine the likelihood of all the trajectories in a DTSHS that are accepted by an automaton on finite or infinite words. This verification covers regular and ω-regular properties, and thus comprises the linear temporal logic LTL. This work shows that these quantitative verification problems can be reduced to computing reachability probabilities over the product of an automaton and the DTSHS under study. The computation of reachability probabilities can be performed in a backward-recursive manner, and quantitatively approximated by procedures over discrete-time Markov chains. A case study shows the feasibility of the approach.

The use of mobile devices is often limited by the battery lifetime. Some devices have the option to connect an extra battery, or to use smart battery-packs with multiple cells to extend the lifetime. In these cases, scheduling the batteries or battery cells over the load to exploit the recovery properties of the batteries helps to extend the overall systems lifetime. Straightforward scheduling schemes, like round-robin or choosing the best battery available, already provide a big improvement compared to a sequential discharge of the batteries. In this paper, we compare these scheduling schemes with the optimal scheduling scheme produced with two different modeling approaches: an approach based on a priced-timed automaton model (implemented and evaluated in Uppaal Cora), as well as an analytical approach (partly formulated as nonlinear optimization problem) for a slightly adapted scheduling problem. We show that in some cases the results of the simple scheduling schemes (round-robin, and best-first) are close to optimal. However, the optimal schedules, computed according to both methods, also clearly show that in a variety of scenarios, the simple schedules are far from optimal.

We study the following problem: given a continuous-time Markov chain (CTMC) C, and a linear real-time property provided as a deterministic timed automaton (DTA) A, what is the probability of the set of paths of C that are accepted by A (C satisfies A)? It is shown that this set of paths is measurable and computing its probability can be reduced to computing the reachability probability in a piecewise deterministic Markov process (PDP). The reachability probability is characterized as the least solution of a system of integral equations and is shown to be approximated by solving a system of partial differential equations. For the special case of single-clock DTA, the system of integral equations can be transformed into a system of linear equations where the coefficients are solutions of ordinary differential equations.

This paper proposes a technique to synthesize parametric rate values in continuous-time Markov chains that ensure the validity of bounded reachability properties. Rate expressions over variables indicate the average speed of state changes and are expressed using the polynomials over reals. The key contribution is an algorithm that approximates the set of parameter values for which the stochastic real-time system guarantees the validity of bounded reachability properties. This algorithm is based on discretizing parameter ranges together with a refinement technique. This paper describes the algorithm, analyzes its time complexity, and shows its applicability by deriving parameter constraints for a real-time storage system with probabilistic error checking facilities.