Efficient solution of the diesel-engine optimal control problem by time-domain decomposition

• Time subdivision for optimal control problems with integral inequality constraints.
• Exact and approximate iterative algorithms to solve the high-level problem.
• Sparsity exploitation and parallel computing within the low-level subproblems.
• Practical implementation for the fuel-optimal control problem of diesel engines.
• Speedup factor of 25 achieved for the diesel-engine problem.

Offline solutions of the optimal control problems relating to diesel engines provide implications for causal control strategies and serve as a tool to automate the engine calibration process. However, the numerical solution of these dynamic optimisation problems is challenging. Above all, the model evaluations are expensive, integral and local inequality constraints are present, and the time horizon to be considered is long. Generally, the continuous problem is transcribed into a nonlinear mathematical program, which has a runtime that increases superlinearly with the problem size. In the literature, the time-domain decomposition of unconstrained and control-constrained problems is proposed to alleviate this often prohibiting increase in computational time. This paper extends the decomposition approach to problems with integral inequality constraints by utilising a partially dual formulation to derive equivalence conditions. To achieve these conditions, exact and approximate iteration schemes are proposed. The time-domain decomposition is combined with an iterative mesh refinement and a parallelisation of the model evaluations, which dominate the runtime of the solution process. On a standard personal computer, an overall speedup factor of 25 is achieved for a realistically sized instance of the diesel-engine problem.