Permissive Controller Synthesis for Probabilistic Systems
Faculty of Informatics, Masaryk University（马萨里克大学信息学院）；EECS, Queen Mary, University of London（伦敦大学玛丽女王学院电气电子与计算机科学与工程系）；Department of Computer Science, University of Oxford（牛津大学计算机科学系）；School of Computer Science, University of Birmingham（伯明翰大学计算机科学学院）
Klaus Drager, Vojtech Forejt, Marta Kwiatkowska, David Parker, Mateusz Ujma
We propose novel controller synthesis techniques for probabilistic systems modelled using stochastic two-player games: one player acts as a controller, the second represents its environment, and probability is used to capture uncertainty arising due to, for example, unreliable sensors or faulty system components. Our aim is to generate robust controllers that are resilient to unexpected system changes at runtime, and flexible enough to be adapted if additional constraints need to be imposed. We develop a permissive controller synthesis framework, which generates multi-strategies for the controller, offering a choice of control actions to take at each time step. We formalise the notion of permissivity using penalties, which are incurred each time a possible control action is disallowed by a multi-strategy. Permissive controller synthesis aims to generate a multi-strategy that minimises these penalties, whilst guaranteeing the satisfaction of a specified system property. We establish several key results about the optimality of multi-strategies and the complexity of synthesising them. Then, we develop methods to perform permissive controller synthesis using mixed integer linear programming and illustrate their effectiveness on a selection of case studies.
The synthesis of maximally-permissive controllers in infinite-state systems has many practical applications. Such controllers directly correspond to maximal winning strategies in logically specified infinite-state two-player games. In this paper, we introduce a tool called GenSys which is a fixed-point engine for computing maximal winning strategies for players in infinite-state safety games. A key feature of GenSys is that it leverages the capabilities of existing off-the-shelf solvers to implement its fixed point engine. GenSys outperforms state-of-the-art tools in this space by a significan…
In this paper, we present a controller synthesis approach for wind turbine generators (WTG) and energy storage systems with metric temporal logic (MTL) specifications, with provable probabilistic guarantees in the stochastic environment of wind power generation. The MTL specifications are requirements for the grid frequency deviations, WTG rotor speed variations and the power flow constraints at different lines. We present the stochastic control bisimulation function, which bounds the divergence of the trajectories of a switched stochastic control system and the switched nominal control system…
Two-player zero-sum games are a well-established model for synthesising controllers that optimise some performance criterion. In such games one player represents the controller, while the other describes the (adversarial) environment, and controller synthesis corresponds to computing the optimal strategies of the controller for a given criterion. Asarin and Maler initiated the study of quantitative games on (non-probabilistic) timed automata by synthesising controllers which optimise the time to reach a final state. The correctness and termination of their approach was dependent on exploiting …
Verification and Control of Partially Observable Probabilistic Real-Time Systems
School of Computing Science, University of Glasgow（格拉斯哥大学计算科学学院）；School of Computer Science, University of Birmingham（伯明翰大学计算机学院）；Department of Computer Science, University of York（约克大学计算机科学系）
Automated Synthesis of Safe and Robust PID Controllers for Stochastic Hybrid Systems
School of Computing, Newcastle University（纽卡斯尔大学计算机学院）；Department of Computer Science, Stony Brook University（石溪大学计算机科学系）；Faculty of Informatics, TU Wien（维也纳工业大学信息学院）；Department of Electrical and Computer Engineering, Stony Brook University（石溪大学电气与计算机工程系）
Multi-objective probabilistic model checking provides a way to verify several, possibly conflicting, quantitative properties of a stochastic system. It has useful applications in controller synthesis and compositional probabilistic verification. However, existing methods are based on linear programming, which limits the scale of systems that can be analysed and makes verification of time-bounded properties very difficult. We present a novel approach that addresses both of these shortcomings, based on the generation of successive approximations of the Pareto curve for a multi-objective model ch…
Quantitative verification techniques have been developed for the formal analysis of a variety of probabilistic models, such as Markov chains, Markov decision process and their variants. They can be used to produce guarantees on quantitative aspects of system behaviour, for example safety, reliability and performance, or to help synthesise controllers that ensure such guarantees are met. We propose the model of turn-based probabilistic timed multi-player games, which incorporates probabilistic choice, real-time clocks and nondeterministic behaviour across multiple players. Building on the digit…
Quantitative extensions of temporal logics have recently attracted significant attention. In this work, we study frequency LTL (fLTL), an extension of LTL which allows to speak about frequencies of events along an execution. Such an extension is particularly useful for probabilistic systems that often cannot fulfil strict qualitative guarantees on the behaviour. It has been recently shown that controller synthesis for Markov decision processes and fLTL is decidable when all the bounds on frequencies are 1. As a step towards a complete quantitative solution, we show that the problem is decidabl…
Consumption Markov Decision Processes (CMDPs) are probabilistic decision-making models of resource-constrained systems. In a CMDP, the controller possesses a certain amount of a critical resource, such as electric power. Each action of the controller can consume some amount of the resource. Resource replenishment is only possible in special reload states, in which the resource level can be reloaded up to the full capacity of the system. The task of the controller is to prevent resource exhaustion, i.e. ensure that the available amount of the resource stays non-negative, while ensuring an addit…
Brno University of Technology（布尔诺理工大学）；University of California, Berkeley（加州大学伯克利分校）；RWTH Aachen University（亚琛工业大学）
This paper presents a novel method for the automated synthesis of probabilistic programs. The starting point is a program sketch representing a finite family of finite-state Markov chains with related but distinct topologies, and a PCTL specification. The method builds on a novel inductive oracle that greedily generates counter-examples (CEs) for violating programs and uses them to prune the family. These CEs leverage the semantics of the family in the form of bounds on its best- and worst-case behaviour provided by a deductive oracle using an MDP abstraction. The method further monitors the p…
