Catastrophe Control Technique in High Dimension System

Catastrophe control was discussed in high-dimensional nonlinear systems without getting eigenvalues. Using the coefficients of characteristic equations, the linear control gains for catastrophe critical conditions were determined. The nonlinear gains were chosen by utilizing the center manifold theory and normal form reduction to assure the stability of limit cycle. Applications were illustrated for submarine motion model to create a catastrophe with preferred properties at a desired location. This convenient and effective control algorithm has a bright future in nonlinear control system design.