Jacob Deleuran Grunnet

Discrete game abstraction for fault tolerant control synthesis

The focus of this paper is on the generation of controllers for fault tolerant control. Active off-line fault tolerant control design relies on a pool of controllers designed to handle different failure modes. Designing this pool of controllers remains a challenge and this paper hence investigates automatic control synthesis for a specific class of systems by abstracting the control problem to a set of combinatorial objects or a state machine. Next, a discrete game is formulated, in which the objective is to reach a goal set representing a desired (reference) state, and faults are treated as moves by a malignant opponent. Assuming that a winning strategy exists for this game, it forms a rule base that determines which control law to use under a given fault condition.

Automated fault tolerant control synthesis based on discrete games

This paper focuses on how fault tolerant controllers can be designed based on discrete game abstractions of piecewise-affine hybrid systems (PAHS). The proposed method aims at automatic generation of the controllers by converting the discrete games to timed games, which can be solved by the UppAal toolbox. Winning strategies to the games are then refined to piecewise-affine control strategies which is a type of gain scheduling. The feasibility of the method is shown through the automated design of a fault tolerant controller for a simple example.

Combinatorial hybrid systems

As initially suggested by E. Sontag, it is possible to approximate an arbitrary nonlinear system by a set of piecewise linear systems. In this work we concentrate on how to control a system given by a set of piecewise linear systems defined on simplices. By using the results of L. Habets and J. van Schuppen, it is possible to find a controller for the system on each of the simplices thus guaranteeing that the system flow on the simplex only will leave the simplex through a subset of its faces. Motivated by R. Forman, on the triangulated state space we define a combinatorial vector field, which indicates for a given face the future simplex. In the suggested definition we allow nondeterminacy in form of splitting and merging of solution trajectories. The combinatorial vector field gives rise to combinatorial counterparts of most concepts from dynamical systems, such as duals to vector fields, flow, flow lines, fixed points and Lyapunov functions. Finally it will be shown how this theory extends to switched dynamical systems and an algorithmic overview of how to do supervisory control will be shown towards the end.