Decentralized Model Predictive Control for Cooperative Multiple Vehicles Subject to Communication Loss

Algorithm 2

DC-DMPC.

Given 𝜇, 𝔼 and initial condition of vehicle i, do:

 (1) 𝑘←0.

 (2) Measure 𝐱^𝑖(𝑘), calculate delay from leader and update the delayed information vector of (10).

 (3) Calculate the tube of all leaders:

   For  ∀𝑗∈𝕍 where (𝑖,𝑗)∈𝔼

   (i) Calculate 𝜷^𝐣(⋅,𝝁,𝑑) from (25).

   (ii) Calculate 𝜶_𝑘^𝑗,𝑖(⋅) from the data provided by offline solution of Problem 2.

   (iii) Update 𝐫^𝑖,𝑗(⋅)←𝐫^𝑖,𝑗(⋅)+sign(𝐫^𝑖,𝑗(⋅))⋅𝜶_𝑘^𝑗,𝑖(⋅) and update 𝐫^𝑖,𝑗 in the cost function (12).

   END

 (4) Solve 𝒫^𝑖_DC(𝐤) and calculate the control action 𝐮^𝑖_𝑘(⋅) and 𝐱^𝑖_𝑘(⋅).

 (5) Send the state trajectory 𝐱^𝑖_𝑘(⋅) to the followers where(𝑗,𝑖)∈𝔼.

 (6) Apply the control action 𝐮^𝑖_𝑘(0) to individual vehicle 𝑖.

 (7) Receive 𝐱^𝑗_𝑘−𝑑(⋅) from leaders where(𝑖,𝑗)∈𝔼.

 (8) 𝑘←𝑘+1. Goto step  2.