Abstract. Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they are less suitable to describe software and hardware interfacing the physical world. For this reason there is a growing interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics, where each "symbol" corresponds to an "aggregate" of states in the continuous model. Since these symbolic models are of the same nature of the models used in computer science to describe software and hardware, they provide a unified language to study problems of control in which software and hardware interact with the physical world. Furthermore the use of symbolic models enables one to leverage techniques from supervisory control and algorithms from game theory for controller synthesis purposes. In this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent (bisimilar) to a symbolic model. The approximation error is a design parameter in the construction of the symbolic model and can be rendered as small as desired. Furthermore if the state space of the control system is bounded the obtained symbolic model is finite. For digital control systems, and under the stronger assumption of incremental input-to-state stability, symbolic models can be constructed through a suitable quantization of the inputs.

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International audienceSwitched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems, the constant evolution of technology demands that we make similar progress with respect to different, and perhaps more complex, objectives. This paper describes one particular approach to address these different objectives based on the construction of approximately equivalent (bisimilar) symbolic models for switched systems. The main contribution of this paper consists in showing that under standard assumptions ensuring incremental stability of a switched system (i.e., existence of a common Lyapunov function, or multiple Lyapunov functions with dwell time), it is possible to construct a finite symbolic model that is approximately bisimilar to the original switched system with a precision that can be chosen a priori. To support the computational merits of the proposed approach, we use symbolic models to synthesize controllers for two examples of switched systems, including the boost dc-dc converter

We derive a new method to quantify the impact of correlated firing on the information transmitted by neuronal populations. This new method considers, in an exact way, the effects of high order spike train statistics, with no approximation involved, and it generalizes our previous work that was valid for short time windows and small populations. The new technique permits one to quantify the information transmitted if each cell were to convey fully independent information separately from the information available in the presence of synergy-redundancy effects. Synergy-redundancy effects are shown to arise from three possible contributions: a redundant contribution due to similarities in the mean response profiles of different cells; a synergistic stimulus-dependent correlational contribution quantifying the information content of changes of correlations with stimulus, and a stimulus-independent correlational contribution term that reflects interactions between the distribution of rates of individual cells and the average level of cross-correlation. We apply the new method to simultaneously recorded data from somatosensory and visual cortices. We demonstrate that it constitutes a reliable tool to determine the role of cross-correlated activity in stimulus coding even when high firing rate data (such as multi-unit recordings) are considered.