Vehicle Sliding Mode Control with Adaptive Upper Bounds: Static versus Dynamic Allocation to Saturated Tire Forces

Pseudocode 1

Pseudocode for interior-point algorithm.

Given A, W , and v

 Compute G, c, and h in (4.2).

 Choose the allocated control input of the previous sample time as the initial value 𝐮_𝟎

 If each entry of 𝐮_𝟎 violates the inequality (3.9), reduce it to satisfy(3.9)

 Compute initial values for 𝐩₀ and𝝀₀.

 Compute the initial value for barrier parameter𝜂.

 Compute residuals 𝐫_𝐜,𝐫_𝐛, and 𝐫_𝐬 given in(4.7)

 Select error tolerance 𝜀 and set𝑘←0.

repeat until 𝐸(𝐮,𝐩,𝝀,0)≤𝜀

 Compute step direction from equation (4.9),

 Compute step size to satisfy nonnegativity conditions using (4.11),

 Update the variables 𝐮,𝐩, and 𝝀 using (4.10),

 Compute affine scaling 𝜂_aff step from (4.13) and 𝜎_𝑘 according to (4.14),

 Update the barrier parameter 𝜂_𝑘+1 based on (4.12),

 Compute residuals 𝐫_𝐜,𝐫_𝐛, and 𝐫_𝐬 from (4.7),

 Set 𝑘←𝑘+1

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