期刊名称：International Journal of Applied Mathematics and Computer Science
电子版ISSN：2083-8492
出版年度：2009
卷号：19
期号：3
DOI：10.2478/v10006-009-0035-1
出版社：De Gruyter Open
摘要：Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuous-time dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants
