Symbolic abstractions for nonlinear control systems via feedback refinement relation Abstract   This paper studies the construction of symbolic abstractions for nonlinear control systems via feedback refinement relation. Both the delayfree and timedelay cases are addressed. For the delayfree case, to reduce the computational complexity, we propose a new approximation approach for the state and input sets based on a static quantizer, and then a novel symbolic model is constructed such that the original system and the symbolic model satisfy the feedback refinement relation. For the timedelay case, both static and dynamic quantizers are combined to approximate the state and input sets. This leads to a novel dynamic symbolic model for timedelay control systems, and a feedback refinement relation is established between the original system and the symbolic model. Finally, a numerical example is presented to illustrate the obtained results.

Compositional abstractionbased synthesis for networks of stochastic switched systems Abstract   In this paper, we provide a compositional approach for constructing finite abstractions (a.k.a. finite Markov decision processes (MDPs)) of interconnected discretetime stochastic switched systems. The proposed framework is based on a notion of stochastic simulation functions, using which one can employ an abstract system as a substitution of the original one in the controller design process with guaranteed error bounds on their output trajectories. To this end, we first provide probabilistic closeness guarantees between the interconnection of stochastic switched subsystems and that of their finite abstractions via stochastic simulation functions. We then leverage sufficient smallgain type conditions to show compositionality results of this work. Afterwards, we show that under standard assumptions ensuring incremental inputtostate stability of switched systems (i.e., existence of common incremental Lyapunov functions, or multiple incremental Lyapunov functions with dwelltime), one can construct finite MDPs for the general setting of nonlinear stochastic switched systems. We also propose an approach to construct finite MDPs together with their corresponding stochastic simulation functions for a particular class of nonlinear stochastic switched systems. We show that for this class of systems, the aforementioned incremental stability property can be readily checked by matrix inequalities. To demonstrate the effectiveness of our proposed results, we first apply our approaches to a road traffic network in a circular cascade ring composed of 200 cells, and construct compositionally a finite MDP of the network. We employ the constructed finite abstractions as substitutes to compositionally synthesize policies keeping the density of the traffic lower than 20 vehicles per cell. We then apply our proposed techniques to a fully interconnected network of 500 nonlinear subsystems (totally 1000 dimensions), and construct their finite MDPs with guaranteed error bounds. We compare our proposed results with those available in the literature.