Synthesizing Switching Controllers for Hybrid Systems by Continuous Invariant Generation

We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials. This is achieved by combining a QE (quantifier elimination)-based method for generating continuous invariants with a qualitative approach for predefining templates. Our synthesis method is relatively complete with regard to a given family of predefined templates. Using qualitative analysis, we discuss heuristics to reduce the numbers of parameters appearing in the templates. To avoid too much human interaction in choosing templates as well as the high computational complexity caused by QE, we further investigate applications of the SOS (sum-of-squares) relaxation approach and the template polyhedra approach in continuous invariant generation, which are both well supported by efficient numerical solvers

Experimental study of a counter-flow regenerative evaporative cooler

This paper aims to investigate the operational performance and impact factors of a counter-flow regenerative evaporative cooler (REC). This was undertaken through a dedicated experimental process. Temperature, humidity and flow rate of the air flows at the inlet, outlet and exhaust opening of the cooler were tested under various operational conditions, i.e., different inlet air conditions, feed water temperature and evaporation rate were also correspondingly measured. It was found that the wet-bulb effectiveness of the presented cooler ranged from 0.55 to 1.06 with Energy Efficiency Ratio (EER) rated from 2.8 to 15.5. The major experimental results were summarised below: 1) the wet-bulb effectiveness was significantly enhanced through either ways of increasing inlet wet-bulb depression or reducing intake air velocity, or alternatively by increasing working-to-intake air ratio; 2) the cooling capacity and EER of cooler was rapidly increased by means of increasing inlet wet-bulb depression or increasing intake air velocity, or reducing working-to-intake air ratio instead; 3) the effectiveness reduced by less 5% while feed water temperature increased from 18.9 to 23.1°C; 4) apparent acceleration in water evaporation rate was gained from increasing inlet wet-bulb depression or air velocity. The presented cooler showed 31% increase in wet-bulb effectiveness and 40% growth in EER compared to conventional indirect evaporative cooler. The research helped identifying the performance of a new REC with enhanced performance and thus contributed to development of energy efficient air conditioning technologies, which eventually lead to significant energy saving and carbon emissions reduction in air conditioning sector

Abstraction of Elementary Hybrid Systems by Variable Transformation

Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in practice, especially in safety-critical domains. Due to the non-polynomial expressions which lead to undecidable arithmetic, verification of EHSs is very hard. Existing approaches based on partition of state space or over-approximation of reachable sets suffer from state explosion or inflation of numerical errors. In this paper, we propose a symbolic abstraction approach that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all non-polynomial terms with newly introduced variables. Thus the verification of EHSs is reduced to the one of PHSs, enabling us to apply all the well-established verification techniques and tools for PHSs to EHSs. In this way, it is possible to avoid the limitations of many existing methods. We illustrate the abstraction approach and its application in safety verification of EHSs by several real world examples