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

Table 1

𝛼	𝐽^1𝛼(𝜑^∗)	𝐽^2𝛼(𝜑^∗)	𝜑^∗
0.5	0.00066463	0.05016802	0.06066266sin(3.14159265𝑥)−0.03734277sin(6.28318530𝑥); +0.00825020sin(9.42477796𝑥)−0.00290788sin(12.5663706𝑥); +0.00130929sin(15.7079632𝑥)−0.00145454sin(18.8495559𝑥); +0.00060179sin(21.9911485𝑥)−0.00037057sin(25.1327412𝑥); +0.00024238sin(28.2743338𝑥)−0.00031746sin(31.4159265𝑥)
0.3	0.00027601	0.05420087	0.06418794sin(3.14159265𝑥)−0.03847726sin(6.28318530𝑥); +0.00841988sin(9.42477796𝑥)−0.00295308sin(12.5663706𝑥); +0.00132564sin(15.7079632𝑥)−0.00146973sin(18.8495559𝑥); +0.00060719sin(21.9911485𝑥)−0.00037348sin(25.1327412𝑥); +0.00024407sin(28.2743338𝑥)−0.00031946sin(31.4159265𝑥)
0.1	0.00005173	0.05881966	0.06814824sin(3.14159265𝑥)−0.03968284sin(6.28318530𝑥); +0.00859668sin(9.42477796𝑥)−0.00299971sin(12.5663706𝑥); +0.00134242sin(15.7079632𝑥)−0.00148524sin(18.8495559𝑥); +0.00061268sin(21.9911485𝑥)−0.00037644sin(25.1327412𝑥); +0.00024579sin(28.2743338𝑥)−0.00032149sin(31.4159265𝑥)
0.03	0.00002314	0.06059838	0.06965236sin(3.14159265𝑥)−0.04012284sin(6.28318530𝑥); +0.00866032sin(9.42477796𝑥)−0.00301638sin(12.5663706𝑥); +0.00134839sin(15.7079632𝑥)−0.00149075sin(18.8495559𝑥); +0.00061463sin(21.9911485𝑥)−0.00037749sin(25.1327412𝑥); +0.00024640sin(28.2743338𝑥)−0.00032220sin(31.4159265𝑥)
0.01	0.00002053	0.06112368	0.06814824sin(3.14159265𝑥)−0.03968284sin(6.28318530𝑥); +0.00859668sin(9.42477796𝑥)−0.00299971sin(12.5663706𝑥); +0.00134242sin(15.7079632𝑥)−0.00148524sin(18.8495559𝑥); +0.00061268sin(21.9911485𝑥)−0.00037644sin(25.1327412𝑥); +0.00024579sin(28.2743338𝑥)−0.00032149sin(31.4159265𝑥)
0.001	0.00002020	0.06133626	0.07029513sin(3.14159265𝑥)−0.04030800sin(6.28318530𝑥); +0.00868697sin(9.42477796𝑥)−0.00302334sin(12.5663706𝑥); +0.00135088sin(15.7079632𝑥)−0.00149304sin(18.8495559𝑥); +0.00061544sin(21.9911485𝑥)−0.00037793sin(25.1327412𝑥); +0.00024665sin(28.2743338𝑥)−0.00032250sin(31.4159265𝑥)