Convex modeling and control of multi-fuel compression ignition engines

Multi-fuel engines are complex machines that operate in varied ambient and operating conditions. For reliable operation of multi-fuel engines in varying operating conditions, proper modeling, and efficient control design for their combustion phasing are required. One of the practically implementable ways this is achieved in practice is by, Gaussian process regression (GPR) models and then designing a feedforward control through look-up tables (LUTs). The main approach of designing LUTs is based on the inversion of GPR models that can be formulated as an optimization problem. Although GPR models have good generalization properties and ensure accuracy with a limited number of data, their usage in optimization problems leads to non-convex costs which are computationally burdensome to solve. To address this problem, this work proposes alternative modeling approaches for multi-fuel engines based on non-parametric convex regression and convex neural networks. First, the experimental data collected from the 4-cylinder diesel engine is exploited to obtain convex models and then, the resulting convex models are used in the LUT design process. To demonstrate the success of the method, we compare the convex models and the GPR model in terms of accuracy, computational time in control design, and control performance, as well as present a comparison in terms of model complexity between the investigated model structures.