Efficient Energy Distribution in a Smart Grid using Multi-Player Games

Algorithms and models based on game theory have nowadays become prominent techniques for the design of digital controllers for critical systems. Indeed, such techniques enable automatic synthesis: given a model of the environment and a property that the controller must enforce, those techniques automatically produce a correct controller, when it exists. In the present paper, we consider a class of concurrent, weighted, multi-player games that are well-suited to model and study the interactions of several agents who are competing for some measurable resources like energy. We prove that a subclass of those games always admit a Nash equilibrium, i.e. a situation in which all players play in such a way that they have no incentive to deviate. Moreover, the strategies yielding those Nash equilibria have a special structure: when one of the agents deviate from the equilibrium, all the others form a coalition that will enforce a retaliation mechanism that punishes the deviant agent. We apply those results to a real-life case study in which several smart houses that produce their own energy with solar panels, and can share this energy among them in micro-grid, must distribute the use of this energy along the day in order to avoid consuming electricity that must be bought from the global grid. We demonstrate that our theory allows one to synthesise an efficient controller for these houses: using penalties to be paid in the utility bill as an incentive, we force the houses to follow a pre-computed schedule that maximises the proportion of the locally produced energy that is consumed.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017

Formal Design and Verification of Digital PID Gain Scheduling Controllers

The verification process of embedded systems is fundamental for their correct development. Embedded control is a popular choice among the engineering community, making the relationship between control systems and computer science very close. Gain scheduling is a typical approach for safety-critical systems (e.g. jet-engines). It is preferred due to a known route to certification. Nonetheless, stability and performance are hard to prove analytically. Consequently, safety and airworthiness are achieved by extensive testing, and therefore a new way for verification is desirable. Model checking, an exhaustive verification technique, is a part of formal methods. Model checking can aid in detecting ambiguities and collisions in requirements, increasing and improving testing coverage and error detection rate. However, there are still limitations and challenges to model checking. The state-space explosion problem limits its use to realistic dynamic control systems: Computational memory runs out or available data types are not appropriate for modelling. This thesis addresses the formal design and verification of discrete PID gain-scheduled control systems. By the means of a novel abstraction methodology the control problem is resolved in a model checking environment; formally tuning the controller whilst systematically constructing a control schedule. The work in this overcomes typical constraints imposed by model checking. In this manner, the gain-scheduled controller can be efficiently generated and the resulting schedule is correct-by-construction with respect to high level performance requirements. This novel methodology incorporates computer science and control systems tools, proposing an a priori verification approach in contrast to current a posteriori testing activities. By combining computer science and control engineering, the gap between formal methods and control systems is reduced. The next step in this line of research is to analyse the scalability of the approach using more realistic models and design cases; in this manner the state-space explosion problem can be addressed with a divide and conquer approach. Also, a trade-off analysis between benefits and the required effort learning the new approach in a real development cycle must be conducted to assess feasibility and capabilities of the approach