Mathematical Problems in Engineering

Research Article

Suboptimal Regulation of a Class of Bilinear Interconnected Systems with Finite-Time Sliding Planning Horizons

Table 1

Matrix entries of the simulated system structure.
𝑖 = 1 , 2 , 3 ; 𝐴 1 ≡ ⎡ ⎢ ⎣ 1 − 0 . 1 5 5 7 𝑇 0 0 1 − 0 . 1 8 0 0 𝑇 ⎤ ⎥ ⎦ ; 𝐵 1 ≡ ⎡ ⎢ ⎣ 0 0 − 0 . 0 1 8 9 𝑇 0 ⎤ ⎥ ⎦
𝐷 1 ≡ ⎡ ⎢ ⎣ 0 0 0 ( − 0 . 0 5 5 7 + 0 . 0 0 4 3 𝑇 ) 𝑇 ( − 0 . 0 5 5 7 + 0 . 0 0 4 3 𝑇 ) 𝑇 0 0 0 0 0 ⎤ ⎥ ⎦ ; 𝑀 1 ≡ ⎡ ⎢ ⎣ 1 − 1 0 0 . 0 0 0 0 𝑇 0 1 3 . 3 3 3 3 𝑇 1 − 8 5 . 8 3 3 3 𝑇 ⎤ ⎥ ⎦ ; 𝑃 1 ≡ ⎡ ⎢ ⎣ 0 ( 8 0 . 0 0 0 0 − 8 0 0 0 . 0 0 0 0 𝑇 ) 𝑇 0 1 0 6 6 . 6 6 4 0 𝑇 ⎤ ⎥ ⎦
𝐿 1 1 ≡ ⎡ ⎢ ⎣ 0 0 ( − 0 . 0 0 6 2 + 0 . 5 3 2 2 𝑇 ) 𝑇 0 ⎤ ⎥ ⎦ ; 𝑀 2 ≡ ⎡ ⎢ ⎢ ⎢ ⎣ 1 − 2 8 . 6 1 4 5 𝑇 1 9 5 0 . 3 2 8 7 𝑇 3 5 . 7 3 3 2 𝑇 1 . 9 5 5 4 𝑇 1 − 2 3 1 . 1 6 5 2 𝑇 − 4 . 1 2 8 1 𝑇 0 . 0 2 6 0 𝑇 − 0 . 0 0 5 6 𝑇 1 + 0 . 1 7 0 6 𝑇 ⎤ ⎥ ⎥ ⎥ ⎦
𝐿 2 1 ≡ ⎡ ⎢ ⎢ ⎢ ⎣ ( 3 5 . 7 3 2 2 − 4 5 3 6 . 9 1 9 9 𝑇 ) 𝑇 0 ( − 4 . 1 2 8 1 + 5 1 2 . 0 8 4 4 𝑇 ) 𝑇 0 ( − 0 . 0 0 5 6 + 0 . 0 5 7 5 𝑇 ) 𝑇 0 ⎤ ⎥ ⎥ ⎥ ⎦ ; 𝑀 3 ≡ ⎡ ⎢ ⎣ 1 − 2 . 0 0 0 0 𝑇 0 6 . 8 5 7 0 𝑇 1 − 7 5 . 2 3 8 0 𝑇 ⎤ ⎥ ⎦