TABLE 12.

Double-integrator plant (with transport theorem) with control design based off double-integrator with transport theorem and noisy, mixed sensors (state and rate): sub-displays the quantitative comparative data corresponding to the qualitative display in sub-Figure 6.

Method	State error	Rate error	Cost	Runtime
Classical p + V	−0.0066807	0.03828	27.0755	2.3988
LQR Optimal PD	−0.0047636	0.56965	76.8806	2.4667
Time-optimal control	0.16546	1.2693	2.7286	2.4837
Open loop optimal a	0.0018665	−0.0018665	7.0286	2.5816
Real-time optimal (RTOC) a	0.06463	−171.6553	41,436,948	2.469
Switched RTOC a	0.0018665	−0.0018665	7.0286	2.6125

^aReal-time optimal control ${\text{u}}_{\text{total}}^{\text{*}}=\widehat{a}t+\widehat{b}+{\overline{\omega }}^{\ast }\times \overline{\overline{J}}{\overline{\omega }}^{\ast }$ (with and without switching) and open-loop optimal control are visually indistinguishable from one another in the graphic depiction.