Minimizing Running Costs in Consumption Systems

A standard approach to optimizing long-run running costs of discrete systems is based on minimizing the mean-payoff, i.e., the long-run average amount of resources ("energy") consumed per transition. However, this approach inherently assumes that the energy source has an unbounded capacity, which is not always realistic. For example, an autonomous robotic device has a battery of finite capacity that has to be recharged periodically, and the total amount of energy consumed between two successive charging cycles is bounded by the capacity. Hence, a controller minimizing the mean-payoff must obey this restriction. In this paper we study the controller synthesis problem for consumption systems with a finite battery capacity, where the task of the controller is to minimize the mean-payoff while preserving the functionality of the system encoded by a given linear-time property. We show that an optimal controller always exists, and it may either need only finite memory or require infinite memory (it is decidable in polynomial time which of the two cases holds). Further, we show how to compute an effective description of an optimal controller in polynomial time. Finally, we consider the limit values achievable by larger and larger battery capacity, show that these values are computable in polynomial time, and we also analyze the corresponding rate of convergence. To the best of our knowledge, these are the first results about optimizing the long-run running costs in systems with bounded energy stores.Comment: 32 pages, corrections of typos and minor omission

Quantitative multi-objective verification for probabilistic systems

We present a verification framework for analysing multiple quantitative objectives of systems that exhibit both nondeterministic and stochastic behaviour. These systems are modelled as probabilistic automata, enriched with cost or reward structures that capture, for example, energy usage or performance metrics. Quantitative properties of these models are expressed in a specification language that incorporates probabilistic safety and liveness properties, expected total cost or reward, and supports multiple objectives of these types. We propose and implement an efficient verification framework for such properties and then present two distinct applications of it: firstly, controller synthesis subject to multiple quantitative objectives; and, secondly, quantitative compositional verification. The practical applicability of both approaches is illustrated with experimental results from several large case studies

Decidability Results for Multi-objective Stochastic Games

We study stochastic two-player turn-based games in which the objective of one player is to ensure several infinite-horizon total reward objectives, while the other player attempts to spoil at least one of the objectives. The games have previously been shown not to be determined, and an approximation algorithm for computing a Pareto curve has been given. The major drawback of the existing algorithm is that it needs to compute Pareto curves for finite horizon objectives (for increasing length of the horizon), and the size of these Pareto curves can grow unboundedly, even when the infinite-horizon Pareto curve is small. By adapting existing results, we first give an algorithm that computes the Pareto curve for determined games. Then, as the main result of the paper, we show that for the natural class of stopping games and when there are two reward objectives, the problem of deciding whether a player can ensure satisfaction of the objectives with given thresholds is decidable. The result relies on intricate and novel proof which shows that the Pareto curves contain only finitely many points. As a consequence, we get that the two-objective discounted-reward problem for unrestricted class of stochastic games is decidable.Comment: 35 page

Value Iteration for Long-run Average Reward in Markov Decision Processes

Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI) is one of the simplest and most efficient algorithmic approaches to MDPs with other properties, such as reachability objectives. Unfortunately, a naive extension of VI does not work for MDPs with long-run average rewards, as there is no known stopping criterion. In this work our contributions are threefold. (1) We refute a conjecture related to stopping criteria for MDPs with long-run average rewards. (2) We present two practical algorithms for MDPs with long-run average rewards based on VI. First, we show that a combination of applying VI locally for each maximal end-component (MEC) and VI for reachability objectives can provide approximation guarantees. Second, extending the above approach with a simulation-guided on-demand variant of VI, we present an anytime algorithm that is able to deal with very large models. (3) Finally, we present experimental results showing that our methods significantly outperform the standard approaches on several benchmarks

Percentile Queries in Multi-Dimensional Markov Decision Processes

Markov decision processes (MDPs) with multi-dimensional weights are useful to analyze systems with multiple objectives that may be conflicting and require the analysis of trade-offs. We study the complexity of percentile queries in such MDPs and give algorithms to synthesize strategies that enforce such constraints. Given a multi-dimensional weighted MDP and a quantitative payoff function $f$, thresholds $v_i$ (one per dimension), and probability thresholds $\alpha_i$, we show how to compute a single strategy to enforce that for all dimensions $i$, the probability of outcomes $\rho$ satisfying $f_i(\rho) \geq v_i$ is at least $\alpha_i$. We consider classical quantitative payoffs from the literature (sup, inf, lim sup, lim inf, mean-payoff, truncated sum, discounted sum). Our work extends to the quantitative case the multi-objective model checking problem studied by Etessami et al. in unweighted MDPs.Comment: Extended version of CAV 2015 pape

Performance Analysis of Maximum Power Point Tracking Algorithms Under Varying Irradiation

Photovoltaic (PV) system is one of the reliable alternative sources of energy and its contribution in energy sector is growing rapidly. The performance of PV system depends upon the solar insolation, which will be varying throughout the day, season and year. The biggest challenge is to obtain the maximum power from PV array at varying insolation levels. The maximum power point tracking (MPPT) controller, in association with tracking algorithm will act as a principal element in driving the PV system at maximum power point (MPP). In this paper, the simulation model has been developed and the results were compared for perturb and observe, incremental conductance, extremum seeking control and fuzzy logic controller based MPPT algorithms at different irradiation levels on a 10 KW PV array. The results obtained were analysed in terms of convergence rate and their efficiency to track the MPP.Keywords: Photovoltaic system, MPPT algorithms, perturb and observe, incremental conductance, scalar gradient extremum seeking control, fuzzy logic controller.Article History: Received 3rd Oct 2016; Received in revised form 6th January 2017; Accepted 10th February 2017; Available onlineHow to Cite This Article: Naick, B. K., Chatterjee, T. K. & Chatterjee, K. (2017) Performance Analysis of Maximum Power Point Tracking Algorithms Under Varying Irradiation. Int Journal of Renewable Energy Development, 6(1), 65-74.http://dx.doi.org/10.14710/ijred.6.1.65-7

Robust Multidimensional Mean-Payoff Games are Undecidable

Mean-payoff games play a central role in quantitative synthesis and verification. In a single-dimensional game a weight is assigned to every transition and the objective of the protagonist is to assure a non-negative limit-average weight. In the multidimensional setting, a weight vector is assigned to every transition and the objective of the protagonist is to satisfy a boolean condition over the limit-average weight of each dimension, e.g., \LimAvg(x_1) \leq 0 \vee \LimAvg(x_2)\geq 0 \wedge \LimAvg(x_3) \geq 0. We recently proved that when one of the players is restricted to finite-memory strategies then the decidability of determining the winner is inter-reducible with Hilbert's Tenth problem over rationals (a fundamental long-standing open problem). In this work we allow arbitrary (infinite-memory) strategies for both players and we show that the problem is undecidable

IN VITRO ANTIOXIDANT ACTIVITIES OF THE FRACTIONS OF COCCINIA GRANDIS L. LEAF EXTRACT

The present study was aimed at investigating the antioxidant activities of the various fractions of the hydromethanolic extract of the leaves of Coccinia grandis L. Voigt. (Cucurbitaceae). The antioxidant activities of the fractions have been evaluated by using nine in vitro assays and were compared to standard antioxidants such as ascorbic acid, α-tocopherol, curcumin and butylated hydroxyl toluene (BHT). All the fractions showed effective H-donor activity, reducing power, free radical scavenging activity, metal chelating ability and inhibition of β-carotene bleaching. None of the fractions exerted an obvious pro-oxidant activity. The antioxidant property depends upon concentration and increased with increasing amount of the fractions. The free radical scavenging and antioxidant activities may be attributed to the presence of phenolic and flavonoid compounds present in the fractions. The results obtained in the present study indicate that the leaves of C. grandis are a potential source of natural antioxidant

Games on graphs with a public signal monitoring

We study pure Nash equilibria in games on graphs with an imperfect monitoring based on a public signal. In such games, deviations and players responsible for those deviations can be hard to detect and track. We propose a generic epistemic game abstraction, which conveniently allows to represent the knowledge of the players about these deviations, and give a characterization of Nash equilibria in terms of winning strategies in the abstraction. We then use the abstraction to develop algorithms for some payoff functions.Comment: 28 page

Soft Breakdown of Zener Diode

Zener diodes are found to show breakdown properties at much lower bias voltages compared to the so called Zener breakdown voltages. The soft breakdown becomes conspicuous from the occurrence of a point of inflexion near the origin of the I-V characteristics. The phenomenon has been explained by interband tunneling of carriers taking place under small reverse bias voltages