Abstract The free piston engine (FPE), considered as a promising alternative to the conventional internal combustion engine, has received more and more attention due to its great potential for efficiency improvement and emission reduction. Such a potential arises from its unique characteristic that the piston motion of the FPE is ultimately free due to the absence of the mechanical crankshaft. With the capability of employing variable piston trajectories, the FPE enables real-time control of the combustion chamber volume and therefore can adjust the in-cylinder gas pressure-temperature history and species concentration prior, during and after the combustion event. Enlightened by this capability, a new control method, namely piston trajectory-based combustion control, is proposed. The objective of this research is to investigate the feasibility and advantages of this advanced control method and realize the fuel-engine co-optimization in real-time. In order to achieve this objective, the entire research is separated into three phases. The first phase of the research focuses on the modeling and analysis of the trajectory-based combustion control in the FPE. A comprehensive model, representing the HCCI combustion process in the FPE along various piston trajectories, is developed, which includes the geometric structure of the FPE, the physics-based model of the FPE operation, and the detailed chemical kinetics of the utilized fuel. Extensive simulation results and the corresponding analysis clearly show that the FPE is able to adjust the entire combustion process by varying the volume of the combustion chamber and therefore altering the in-cylinder gas temperature and pressure traces to increase the indicated output work. In addition, the trajectory-based combustion control can also influence the chemical kinetics of the combustion via manipulating the in-cylinder temperature-pressure history. Specifically, unique asymmetric trajectories are designed that decreases the amount of NOx emission and increases the engine thermal efficiency simultaneously. At last, the analysis of the trajectory-based combustion control is also extended to multiple renewable fuels, e.g. hydrogen, biogas, syngas, ethanol, DME (dimethyl ether), biodiesel, and F-T (Fisher-Tropsch) fuels. It shows that an optimal asymmetric piston trajectory can be designed for each specific renewable fuel, which enables a significant reduction in the NOx emission and an improvement in the thermal efficiency simultaneously. In this way, the trajectory-based combustion control realizes the co-optimization of fuels and engine operation. The second phase of the research is aimed to develop a novel control-oriented model to realize the trajectory-based HCCI combustion control in practice. Intuitively, the comprehensive model from the first phase is not suitable for the control purpose, since the detailed reaction mechanisms usually generate heavy computational burdens. In order to reduce the computational burden and keep sufficient chemical kinetics information for HCCI combustion simulation, in the new control-oriented model, the engine cycle is separated into multiple phases and in each phase, a specific reaction mechanism with the minimal size is applied. With this unique phase separation method, the proposed control-oriented model not only shows a good agreement with the detailed physics-based model but also reduces the computational time significantly. In addition, such a good agreement is sustained at various working conditions, including different CRs, multiple AFRs and various piston motion patterns Ω. The last phase of this dissertation discusses systematic approaches to optimize piston trajectory for the trajectory-based HCCI combustion control. As claimed by the concept of trajectory-based combustion control, the derived optimal piston trajectory is considered as the optimal control signal to the FPE, which provides ultimate engine performance, in terms of maximal engine thermal efficiency and minimal emissions production. In this part, both offline and online optimizations are investigated. For the offline optimization, two approaches are proposed and implemented into the proposed control-oriented model: The first approach represents the piston trajectory as a function of parameter Ω and converts the original problem to a parameters optimization problem. Both optimal symmetric trajectories and asymmetric trajectories are derived at given CR. The advantages of this optimization approach lie on its much lighter computational burden; the second method transforms the trajectory optimization problem into a constrained nonlinear programming and then solves it via the SQP algorithm. By removing the constraints placed by piston motion patterns, this approach enlarges the candidate pool of various piston trajectories. Hence, the derived optimal trajectory further increases the engine output work and sustains the NOx emissions at the same level. For the online optimization, a searching process aimed to determine the optimal piston motion pattern Ω according to variable working conditions is developed. By using the proposed control-oriented model, the designed piston trajectory can be achieved within 0.4s under different working conditions, which enables real time optimal control of HCCI combustion phasing.