Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems

Table 1

Iteration results 𝑢^(𝑖) for Example 1 when 𝑚=8 and 𝑥₁=−1/8.

𝑥2	𝑢^(0)	𝑢^(1)	𝑢^(2)	𝑢^(3)	𝑢^(4)	𝑢exact
−7/8	1.0000	1.4463	1.3772	1.3786	1.3793	1.3624
−5/8	0.7500	1.0636	1.0114	1.0130	1.0136	1.0089
−3/8	0.5000	0.68889	0.6548	0.6548	0.6550	0.6553
−1/8	0.2500	0.3135	0.3027	0.3017	0.3015	0.3018
1/8	0	−0.0615	−0.0515	−0.0519	−0.0520	−0.0518
3/8	−0.2500	−0.4397	−0.4080	−0.4053	−0.4049	−0.4053
5/8	−0.5000	−0.8137	−0.7584	−0.7571	−0.7572	−0.7589
7/8	−0.7500	−1.1880	−1.1123	−1.1130	−1.1135	−1.1124