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This paper presents a sum of squares (SOS) approach to stability analysis of polynomial fuzzy systems. Our SOS approach provides two innovative and extensive results for the existing LMI approaches to Takagi-Sugeno fuzzy systems. First, we propose a polynomial fuzzy model that is a more general representation of the well-known Takagi-Sugeno fuzzy model. Second, we derive stability conditions based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, stability analysis discussed in this paper is more general than that based on the existing LMI approaches to Takagi-Sugeno fuzzy systems. The stability conditions in the proposed approach can be represented in terms of SOS and are numerically (partially symbolically) solved via the recent developed SOSTOOLS. To illustrate the validity and applicability of the proposed approach, two analytical examples are provided. The first example shows that our approach provides more relaxed stability results than both the existing LMI approaches and a polynomial system approach. The second example illustrates the utility of our approach in comparison with a piecewise Lyapunov function approach.

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Here, we report a case study on inverse design of quantum dot optical spectra using a deep reinforcement learning algorithm for the desired target optical property of semiconductor Cd xSe yTe x− y quantum dots. Machine learning models were trained to predict the optical absorption and emission spectra by using the training dataset by time dependent density functional theory simulation. We show that the trained deep deterministic policy gradient inverse design agent can infer the molecular structure with an accuracy of less than 1 Å at a fixed computational time of milliseconds and up to 100–1000 times faster than the conventional heuristic particle swam optimization method. Most of the effective inverse design problems based on the surrogate machine learning and reinforcement learning model have been focused on the field of nano-photonics. Few attempts have been made in the field of quantum optical system in a similar manner. For the first time, our results, to our knowledge, provide concrete evidence that for computationally challenging tasks, a well-trained deep reinforcement learning agent can replace the existing quantum simulation and heuristics optimization tool, enabling fast and scalable simulations of the optical property of nanometer sized semiconductor quantum dots.