Minimax Input Shaper Design Using Linear Programming

The focus of this paper is on the design of robust input shapers where the maximum value of the cost function over the domain of uncertainty is minimized. This nonlinear programming problem is reformulated as a linear programming problem by approximating a $n$-dimensional hypersphere with multiple hyperplanes (as in a geodesic dome). A recursive technique to approximate a hypersphere to any level of accuracy is developed using barycentric coordinates. The proposed technique is illustrated on the spring-mass-dashpot and the benchmark floating oscillator problem undergoing a rest-to-rest maneuver. It is shown that the results of the linear programming problem are nearly identical to that of the nonlinear programming problem.