Optimal Control of Diesel Engines: Numerical Methods, Applications, and Experimental Validation

Figure 3

Sparsity structure of the Jacobian of the NLP resulting from the transcription of a continuous-time OCP by Radau collocation. Four collocation intervals are used, all with collocation order 1 except for the third interval which is of order 4. Characteristically for Radau collocation, the zeroth point only contributes linearly to the first dynamic constraint of the first interval. The variables at each discretisation point are ordered as (𝐮^𝑇_𝑙,𝐱^𝑇_𝑙)^𝑇.