On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System

Table 2

𝛼	𝐽^1𝛼(𝜑^∗)	𝐽^2𝛼(𝜑^∗)	𝜑^∗
0.9	5.78860382	8.69671794	0.02889657sin(8.37758041𝑥)+0.04493685sin(7.33038285𝑥); +0.24991184sin(1.04719755𝑥)+0.52713734sin(2.09439510𝑥); +0.45790546sin(3.14159265𝑥)+0.26256973sin(4.18879020𝑥); +0.15223865sin(5.23598775𝑥)+0.09116834sin(6.28318530𝑥); +0.02580495sin(9.42477796𝑥)+0.01946190sin(10.4719755𝑥)
0.6	3.70770920	11.9063673	0.32482219sin(1.04719755𝑥)+0.03043404sin(8.37758041𝑥); +0.04796407sin(7.33038285𝑥)+0.65182517sin(2.09439510𝑥); +0.54263121sin(3.14159265𝑥)+0.30032478sin(4.18879020𝑥); +0.16919357sin(5.23598775𝑥)+0.02014690sin(10.4719755𝑥); +0.02690906sin(9.42477796𝑥)+0.09904027sin(6.28318530𝑥)
0.2	0.73684310	20.7888427	0.02815886sin(9.42477796𝑥)+0.71530518sin(3.14159265𝑥); +0.60922355sin(1.04719755𝑥)+0.99053011sin(2.09439510𝑥); +0.36120182sin(4.18879020𝑥)+0.19210117sin(5.23598775𝑥); +0.02095115sin(10.4719755𝑥)+0.10849356sin(6.28318530𝑥); +0.05138069sin(7.33038285𝑥)+0.03214310sin(8.37758041𝑥)
0.04	0.26519950	25.3541218	0.03275462sin(8.37758041𝑥)+0.92069918sin(1.04719755𝑥); +0.05250012sin(7.33038285𝑥)+1.14670525sin(2.09439510𝑥); +0.02863498sin(9.42477796𝑥)+0.19820000sin(5.23598775𝑥); +0.11127608sin(6.28318530𝑥)+0.02127006sin(10.4719755𝑥); +0.76666431sin(3.14159265𝑥)+0.37689906sin(4.18879020𝑥)
0.02	0.25964159	25.7401337	0.05264297sin(7.33038285𝑥)+0.02869561sin(9.42477796𝑥); +0.93896719sin(1.04719755𝑥)+1.15756155sin(2.09439510𝑥); +0.77151420sin(3.14159265𝑥)+0.02131060sin(10.4719755𝑥); +0.37869007sin(4.18879020𝑥)+0.03283263sin(8.37758041𝑥); +0.19895419sin(5.23598775𝑥)+0.11162916sin(6.28318530𝑥)
0.002	0.25769444	26.0957452	0.95568491sin(1.04719755𝑥)+0.02875041sin(9.42477796𝑥); +0.02134722sin(10.4719755𝑥)+0.19963788sin(5.23598775𝑥); +0.11194885sin(6.28318530𝑥)+0.05277220sin(7.33038285𝑥); +0.03290315sin(8.37758041𝑥)+0.77593184sin(3.14159265𝑥); +1.16750459sin(2.09439510𝑥)+0.38031659sin(4.18879020𝑥)