Nonlinear stabilization and parametric optimization in the benchmark nonlinear control design problem

Several control design techniques are applied to the benchmark nonlinear control design problem, resulting in families of stabilizing controllers. The controllers thus obtained depend on free parameters, which are selected so as to optimize measures of performance. The control techniques employed include the following: feedback stabilization methods for critical nonlinear systems, linear feedback stabilization, partial stabilization, vibrational control, and a technique for design of deadbeat controllers. The optimization phase of the work involves numerical optimization, and, in the case of linear feedback design, the use of linear matrix inequalities (LMIs). This paper provides a general discussion of the work, with specific results and comparisons provided in the conference presentation