Learning-based Symbolic Abstractions for Nonlinear Control Systems

Symbolic models or abstractions are known to be powerful tools towards the control design of cyber-physical systems (CPSs) with logic specifications. In this paper, we investigate a novel learning-based approach towards the construction of symbolic models for nonlinear control systems. In particular, the symbolic model is constructed based on learning the un-modeled part of the dynamics from training data based on state-space exploration, and the concept of an alternating simulation relation that represents behavioral relationships with respect to the original control system. Moreover, we aim at achieving safe exploration, meaning that the trajectory of the system is guaranteed to be in a safe region for all times while collecting the training data. In addition, we provide some techniques to reduce the computational load of constructing the symbolic models and the safety controller synthesis, so as to make our approach practical. Finally, a numerical simulation illustrates the effectiveness of the proposed approach

Safety controller design for incrementally stable switched systems using event-based symbolic models

International audienceIn this paper, we investigate the problem of lazy safety controllers synthesis for event-based symbolic models of incrementally stable switched systems with aperiodic time sampling. First of all, we provide a novel event-based scheme for symbolic models design. The obtained symbolic models are computed while considering all transitions of different durations satisfying a triggering condition. In addition, they are related to the original switched system by a feedback refinement relation and thus useful for control applications. Then, using the particular structure of the obtained event-based symbolic model, a lazy safety controller is designed while choosing transitions of longest durations. Secondly, for the same state sampling parameter and desired precision, we show that the obtained event-based symbolic model is related by a feedback refinement relation to the classical symbolic model designed for incrementally stable switched systems with periodic time sampling. Based on this relationship, we prove analytically that the size of the set of controllable states obtained with the lazy safety controller designed for an event-based symbolic model is larger than the one obtained with a safety controller designed for the classical symbolic model. Finally, an illustrative example is proposed in order to show the efficiency of the proposed method and simulations are performed for a Boost DC-DC converter structure