. 2022 Oct 4;9:884669. doi: 10.3389/frobt.2022.884669

TABLE 9.

Double-integrator plant (no transport theorem) with control design based off double-integrator (no transport theorem): quantitative comparative data corresponding to the qualitative display in Figures 3A,B.

Method	State error	Rate error	Cost	Runtime
Classical p + V	0.010115	0.066169	28.1671	3.1012
LQR Optimal PD	0.015015	0.43861	76.3418	2.4597
Time-optimal control	eps	2	2	2.9038
Open loop optimal ^a	eps	Eps	6	2.6086
Real-time optimal (RTOC) ^a	$- 9.1882 \times 10^{- 6}$	0.019289	6.7656	2.7497
Switched RTOC ^a	eps	Eps	6	2.7281

Real-time optimal control ${\bar{u}}^{*} \equiv \hat{a} t + \hat{b}$ (with and without switching) and open-loop optimal control are visually indistinguishable from one another in the graphic depiction.