Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine

The numerical solution of optimal control problems by direct collocation is a widely used approach. Quasi-Newton approximations of the Hessian of the Lagrangian of the resulting nonlinear program are also common practice. We illustrate that the transcribed problem is separable with respect to the primal variables and propose the application of dense quasi-Newton updates to the small diagonal blocks of the Hessian. This approach resolves memory limitations, preserves the correct sparsity pattern, and generates more accurate curvature information. The effectiveness of this improvement when applied to engineering problems is demonstrated. As an example, the fuel-optimal and emission-constrained control of a turbocharged diesel engine is considered. First results indicate a significantly faster convergence of the nonlinear program solver when the method proposed is used instead of the standard quasi-Newton approximation

Direct Optimal Motion Planning for Omni-directional Mobile Robots under Limitation on Velocity and Acceleration

This paper describes a low computational direct approach for optimal motion planning and obstacle avoidance of Omni-directional mobile robots within velocity and acceleration constraints on the robot motion. The main purpose of this problem is the minimization of a quadratic cost function while limitation on velocity and acceleration of robot is considered and collision with any obstacle in the robot workspace is avoided. This problem can be formulated as a constraint nonlinear optimal control problem. To solve this problem, a direct method is utilized which employs polynomials functions for parameterization of trajectories. By this transforming, the main optimal control problem can be rewritten as a nonlinear programming problem (NLP) with lower complexity. To solve the resulted NLP and obtain optimal trajectories, a new approach with very small run time is used. Finally, the performance and effectiveness of the proposed method are tested in simulations and some performance indexes are computed for better assessment. Furthermore, a comparison between proposed method and another direct method is done to verify the low computational cost and better performance of the proposed method

Model-based real-time optimisation of a fed-batch cyanobacterial hydrogen production process using economic model predictive control strategy

Hydrogen produced by microorganisms has been considered as a potential solution for sustainable hydrogen production for the future. In the current study, an advanced real-time optimisation methodology is developed to maximise the productivity of a 21-day fed-batch cyanobacterial hydrogen production process, which to the best of our knowledge has not been addressed before. This methodology consists of an economic model predictive control formulation used to predict the future experimental performance and identify the future optimal control actions, and a finite-data window least-squares procedure to re-estimate model parameter values of the on-going process and ensure the high accuracy of the dynamic model. To explore the efficiency of the current optimisation methodology, effects of its essential factors including control position, prediction horizon length, estimation window length, model synchronising frequency, terminal region and terminal cost on hydrogen production have been analysed. Finally, by implementing the proposed optimisation strategy into the current computational fed-batch experiment, a significant increase of 28.7% on hydrogen productivity is achieved compared to the previous study.E. A. del Rio-Chanona is funded by CONACyT scholarship No. 522530 and from the Secretariat of Public Education and the Mexican government.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.ces.2015.11.04

Bio-inspired, Varying Manifold Based Method With Enhanced Initial Guess Strategies For Single Vehicle\u27s Optimal Trajectory Planning

Trajectory planning is important in many applications involving unmanned aerial vehicles, underwater vehicles, spacecraft, and industrial manipulators. It is still a challenging task to rapidly find an optimal trajectory while taking into account dynamic and environmental constraints. In this dissertation, a unified, varying manifold based optimal trajectory planning method inspired by several predator-prey relationships is investigated to tackle this challenging problem. Biological species, such as hoverflies, ants, and bats, have developed many efficient hunting strategies. It is hypothesized that these types of predators only move along paths in a carefully selected manifold based on the prey’s motion in some of their hunting activities. Inspired by these studies, the predator-prey relationships are organized into a unified form and incorporated into the trajectory optimization formulation, which can reduce the computational cost in solving nonlinear constrained optimal trajectory planning problems. Specifically, three motion strategies are studied in this dissertation: motion camouflage, constant absolute target direction, and local pursuit. Necessary conditions based on the speed and obstacle avoidance constraints are derived. Strategies to tune initial guesses are proposed based on these necessary conditions to enhance the convergence rate and reduce the computational cost of the motion camouflage inspired strategy. The following simulations have been conducted to show the advantages of the proposed methods: a supersonic aircraft minimum-time-to-climb problem, a ground robot obstacle avoidance problem, and a micro air vehicle minimum time trajectory problem. The results show that the proposed methods can find the optimal solution with higher success rate and faster iv convergent speed as compared with some other popular methods. Among these three motion strategies, the method based on the local pursuit strategy has a relatively higher success rate when compared to the other two. In addition, the optimal trajectory planning method is embedded into a receding horizon framework with unknown parameters updated in each planning horizon using an Extended Kalman Filte