Nonlinear L1 and L∞ identifications for continuous systems with applications to class 1 robot manipulator and complex chemical equilibrium computations

This paper presents the nonlinear L₁ and L_∞ programming methods in the identifications of nonlinear continuous systems with successful applications in estimating the dynamic parameters of class 1 manipulator and in solving the complex chemical equilibrium problems. Reaction by injecting methane gas at 300°K into air surroundings at 700°K is used to illustrate the applicability of the nonlinear L_∞-simplex identification in complex chemical equilibrium problems. The nonlinear L _∞-simplex minimization technique is proposed to determine a good approximated set of moles of dominant species by minimizing the maximum error of linear and nonlinear physical constraints due to equilibrium reaction. Eight dynamic parameters of the three-link class 1 robot manipulator are estimated by using the nonlinear L_∞-simplex optimization method with observation data obtained by simulating the robot dynamics motion due to zero applied torques on all three joints. The estimated dynamic parameters agree extremely well with the true nominal values provided the parameters are fully or at least identifiable in nature