Approximation of Time Optimal Control for Unknown Nonlinear Systems by Learning

The development and evolution in the field of actuators has led to very powerful and smart drives. Modern actuators combine mechanics with electronic and informatics, and offer new functionalities that call for the implementation of innovative, fast and complex control strategies. Take for example a compressor valve. Originally this component was driven passively by the compression process with the disadvantage that opening and closing were directly connected to the position of the piston. To increase the functionality, passive valves have been replaced by active hydraulically and/or electrically driven valves, which allow varying the opening and closing time point, and thus increasing the efficiency of compressor load control actions. However, the actuation system becomes more complex and, in some cases, the dynamic behaviour of the new system is slower than the original one.In the case of known systems the time optimal control can be formulated using standard methods like the Hamilton Jacobi Bellman principle or the Pontryagin Maximum Principle. Unfortunately, in rare cases the problem is convex, and this fact prevents the use of standard gradient-based methods to find the optimal solution.In the case of industrial actuators, an additional challenge comes from the fact that the system is frequently not modeled to a sufficient detail to allow a numerical computation of the optimal input directly from the system model. Against this background, this work, which was started in the framework of an industrial project, presents a method to obtain an approximation of the time optimal control by iterative learning.