Symbolic computation in nonlinear control system modeling and analysis

Abstract

The paper discusses the use of symbolic computation for model formulation, model integration, model checking, and model analysis. The zero dynamics plays an important role in the areas of modeling, analysis, and control of linear and nonlinear systems. The zero dynamics gives additional insight in the structure of the model employed and is an aid in modifying a model to satisfy some needs of the modeler. For nonlinear systems the analytical calculations to get the zero dynamics by paper and pencil may be quite involved. Symbolic computation has been used to overcome this difficulty. For a reasonable class of systems the computation can be performed without human aid or intervention, making the zero dynamics procedure a feasible and valuable addition to the toolbox of the modeler, analyst, or control system designer. For system models that are more than moderately complex symbolic computation cannot be fully enjoyed due to the complexity of parts of the algorithms that is (double) exponential in some measure of the problem size, or due to expression swell that cannot be easily eliminated. This implies that symbolic computation will not replace other tools, like those based on numerics, but will complement them.