Sampling-based Approximations with Quantitative Performance for the Probabilistic Reach-Avoid Problem over General Markov Processes

This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which can be selected to affect the probabilistic dynamics. We address the computation of maximal reach-avoid specifications, together with the synthesis of the corresponding optimal controllers. The reach-avoid specification deals with assessing the likelihood that any finite-horizon trajectory of the model enters a given goal set, while avoiding a given set of undesired states. This article newly provides an approximate computational scheme for the reach-avoid specification based on the Fitted Value Iteration algorithm, which hinges on random sample extractions, and gives a-priori computable formal probabilistic bounds on the error made by the approximation algorithm: as such, the output of the numerical scheme is quantitatively assessed and thus meaningful for safety-critical applications. Furthermore, we provide tighter probabilistic error bounds that are sample-based. The overall computational scheme is put in relationship with alternative approximation algorithms in the literature, and finally its performance is practically assessed over a benchmark case study

Automated Experiment Design for Data-Efficient Verification of Parametric Markov Decision Processes

We present a new method for statistical verification of quantitative properties over a partially unknown system with actions, utilising a parameterised model (in this work, a parametric Markov decision process) and data collected from experiments performed on the underlying system. We obtain the confidence that the underlying system satisfies a given property, and show that the method uses data efficiently and thus is robust to the amount of data available. These characteristics are achieved by firstly exploiting parameter synthesis to establish a feasible set of parameters for which the underlying system will satisfy the property; secondly, by actively synthesising experiments to increase amount of information in the collected data that is relevant to the property; and finally propagating this information over the model parameters, obtaining a confidence that reflects our belief whether or not the system parameters lie in the feasible set, thereby solving the verification problem.Comment: QEST 2017, 18 pages, 7 figure

Control refinement for discrete-time descriptor systems: a behavioural approach via simulation relations

The analysis of industrial processes, modelled as descriptor systems, is often computationally hard due to the presence of both algebraic couplings and difference equations of high order. In this paper, we introduce a control refinement notion for these descriptor systems that enables analysis and control design over related reduced-order systems. Utilising the behavioural framework, we extend upon the standard hierarchical control refinement for ordinary systems and allow for algebraic couplings inherent to descriptor systems.Comment: 8 pages, 3 figure

Modularized Control Synthesis for Complex Signal Temporal Logic Specifications

The control synthesis of a dynamic system subject to signal temporal logic (STL) specifications is commonly formulated as a mixed-integer linear programming (MILP) problem. Solving a MILP problem is computationally expensive when the STL formulas are long and complex. In this paper, we propose a framework to transform a long and complex STL formula into a syntactically separate form, i.e., the logical combination of a series of short and simple subformulas with non-overlapping timing intervals. Using this framework, one can easily modularize the synthesis of a complex formula using the synthesis solutions of the subformulas, which improves the efficiency of solving a MILP problem. Specifically, we propose a group of separation principles to guarantee the syntactic equivalence between the original formula and its syntactically separate counterpart. Then, we propose novel methods to solve the largest satisfaction region and the open-loop controller of the specification in a modularized manner. The efficacy of the methods is validated with a robot monitoring case study in simulation. Our work is promising to promote the efficiency of control synthesis for systems with complicated specifications

Data-driven and Model-based Verification: a Bayesian Identification Approach

This work develops a measurement-driven and model-based formal verification approach, applicable to systems with partly unknown dynamics. We provide a principled method, grounded on reachability analysis and on Bayesian inference, to compute the confidence that a physical system driven by external inputs and accessed under noisy measurements, verifies a temporal logic property. A case study is discussed, where we investigate the bounded- and unbounded-time safety of a partly unknown linear time invariant system

Exploration of essential oils as alternatives to conventional fungicides in lupin cultivation

Lupin (Lupinus L.) has the potential to become a true alternative for soybean as protein source, especially in the more temperate regions in the world. However, diseases such as anthracnose (Colletotrichum lupini), gray mold (Botrytis cinerea), and root rot or brown spot (Pleiochaeta setosa) are important threats for lupin production, leading to yield and quality losses. Although conventional fungicides offer a solution to these problems, there is a growing interest in the use of alternative (biological) treatments. In this research, the applicability of four pure plant essential oils (clove oil, juniper oil, tea tree oil, and thyme essential oil) and timbor® (a Thymus vulgaris-derived plant extract) as alternatives for synthetic fungicides towards the lupin pathogens—C. lupini, B. cinerea, and P. setosa—was investigated. The anti-fungal effect of juniper oil was limited, whereas the other oils and timbor® clearly suppressed the growth and spore germination of all fungi. The in vitro experiments revealed that thyme essential oil and timbor® were most effective to inhibit conidial germination and mycelium growth. Furthermore, the results of the pot experiments demonstrated that these Thymus-derived compounds were able to suppress P. setosa brown spot and root rot symptoms. Additional trials are necessary to evaluate the effect of these compounds under field conditions. However, based on these in vitro and pot experiments, it can be concluded that pure essential oils and Thymus-derived plant extracts are promising anti-fungal agents, having the potential to become true alternatives for conventional fungicides in lupin cultivation. To the best of our knowledge, this is the first study demonstrating the potential of plant-derived compounds to treat the main diseases affecting lupin production

Observer-based correct-by-design controller synthesis

Current state-of-the-art correct-by-design controllers are designed for full-state measurable systems. This work first extends the applicability of correct-by-design controllers to partially observable LTI systems. Leveraging 2nd order bounds we give a design method that has a quantifiable robustness to probabilistic disturbances on state transitions and on output measurements. In a case study from smart buildings we evaluate the new output-based correct-by-design controller on a physical system with limited sensor information

Cautious Planning with Incremental Symbolic Perception: Designing Verified Reactive Driving Maneuvers

This work presents a step towards utilizing incrementally-improving symbolic perception knowledge of the robot's surroundings for provably correct reactive control synthesis applied to an autonomous driving problem. Combining abstract models of motion control and information gathering, we show that assume-guarantee specifications (a subclass of Linear Temporal Logic) can be used to define and resolve traffic rules for cautious planning. We propose a novel representation called symbolic refinement tree for perception that captures the incremental knowledge about the environment and embodies the relationships between various symbolic perception inputs. The incremental knowledge is leveraged for synthesizing verified reactive plans for the robot. The case studies demonstrate the efficacy of the proposed approach in synthesizing control inputs even in case of partially occluded environments

Energy-Constrained Active Exploration Under Incremental-Resolution Symbolic Perception

In this work, we consider the problem of autonomous exploration in search of targets while respecting a fixed energy budget. The robot is equipped with an incremental-resolution symbolic perception module wherein the perception of targets in the environment improves as the robot's distance from targets decreases. We assume no prior information about the total number of targets, their locations as well as their possible distribution within the environment. This work proposes a novel decision-making framework for the resulting constrained sequential decision-making problem by first converting it into a reward maximization problem on a product graph computed offline. It is then solved online as a Mixed-Integer Linear Program (MILP) where the knowledge about the environment is updated at each step, combining automata-based and MILP-based techniques. We demonstrate the efficacy of our approach with the help of a case study and present empirical evaluation in terms of expected regret. Furthermore, the runtime performance shows that online planning can be efficiently performed for moderately-sized grid environments

Automated Formation Control Synthesis from Temporal Logic Specifications

In this paper, we propose a novel framework using formal methods to synthesize a navigation control strategy for a multi-robot swarm system with automated formation. The main objective of the problem is to navigate the robot swarm toward a goal position while passing a series of waypoints. The formation of the robot swarm should be changed according to the terrain restrictions around the corresponding waypoint. Also, the motion of the robots should always satisfy certain runtime safety requirements, such as avoiding collision with other robots and obstacles. We prescribe the desired waypoints and formation for the robot swarm using a temporal logic (TL) specification. Then, we formulate the transition of the waypoints and the formation as a deterministic finite transition system (DFTS) and synthesize a control strategy subject to the TL specification. Meanwhile, the runtime safety requirements are encoded using control barrier functions, and fixed-time control Lyapunov functions ensure fixed-time convergence. A quadratic program (QP) problem is solved to refine the DFTS control strategy to generate the control inputs for the robots, such that both TL specifications and runtime safety requirements are satisfied simultaneously. This work enlights a novel solution for multi-robot systems with complicated task specifications. The efficacy of the proposed framework is validated with a simulation study