chapter  7
Numerical Approach
Pages 82

THIS chapter describes different techniques to solve for the parameters of inputshaper/time-delay filters (IS/TDF) and saturating controllers. Except for a very small class of systems, closed form solutions for IS/TDF and saturating controllers cannot be derived. One has to therefore resort to numerical techniques to determine the optimal control profiles. This chapter describes three techniques to determine the IS/TDF and saturating controllers. The first entails parameterizing the control profile and solving for the optimal parameters via a gradient based constrained optimization algorithm. The second technique exploits the strengths of linear programming in conjunction with a bisection algorithm to determine the optimal IS/TDF and saturating control profiles. The third exploits semidefinite optimization techniques to optimize a linear cost subject to linear matrix inequalities (LMI). All three techniques are illustrated on simple examples. MATLAB program listing which encode the two algorithms are also provided. This chapter deals with input shaper/time-delay filters, saturating controllers, minimax controllers that desensitize the control profile to modeling errors, and also presents results for benchmark examples.