Symbolic computation in nonlinear control system analysis & design

Symbolic computation, also known as computer algebra, is a powerful tool in solving tough and intricate problems in applied mathematics. We present a closely tied set of symbolic computation functions, together called the NON~CON package that solves some problems in the analysis and design of nonlinear control system. A model of the system must be available for the computation. The model, in general a set of nonlinear differential and algebraic equations in the state, input, and output of the system, is not required to be affine in the input nor to have a well-defined relative degree. The functions available range from the computation of the zero dynamics of the model to computing invariant manifolds. All functions are based on constructive algorithms and are implemented in MAPLE. The N ON~CON package is successful for low order models that do not contain large intricate expressions. For large order models the package is less successful, due to an intrinsic limitation in MAPLE's handling of objects. Other problems stem from the need to solve sets of nonlinear ((partial) differential) equations. The examples presented use eresting models of mechanical systems, i.e., a string of mass-damper-spring sets and a four-wheel vehicle