# A novel resource-efficient control-schedule co-design technique exploiting non-uniform sampling (Bachelorthesis)

*04.10.2017*

## Mathias Hofmann

04.10.2017, 14:00, room 4981

## Abstract:

Increasingly more software-based control applications are being deployed on automotive embedded systems. Examples include automatic cruise control, engine control, electronic brake control, among others. Design of embedded control systems mainly involves two aspects: controller design and embedded platform design. Controller design boils down to finding the control gains while the platform design requires calculating the schedules. Moreover, the design must also consider certain requirements. On one hand, it must meet certain minimum control performance. In this work, I consider linear quadratic (LQ) cost as the performance metric. On the other hand, automotive systems are highly cost-sensitive and one would like to use as less resource as possible. Thus resource-efficiency must be considered while designing embedded control systems.

Towards these design objectives, in this work, I propose a resource-efficient control-scheduling co-design technique for a given performance requirement. I take an example of FlexRay-based ECU network as the underlying embedded platform. Such a platform allows implementation of controllers using only a set of sampling periods. In this setting, I propose to consider controller implementation using non-uniform sampling (i.e., multi-rate controller) where the period between any two sampling instances must be selected from the feasible set. I will illustrate that for a given performance requirement, a periodic controller may need a lower sampling period than the average sampling period of the multi-rate controller to meet the requirement. Thus, I exploit non-uniform sampling to save communication and computation resource.

Towards controller implementation with non-uniform sampling, this thesis has the following contributions. (i) I have considered delayed control loops and derived the discrete-time LQ cost function for a given continuous-time cost function. (ii) I have adapted the conventional LQR control design technique for the uniform sampling case to the non-uniform sampling case. Here, I have exploited the principle of dynamic programming. (iii) I have also suggested how to calculate the sampling sequences heuristically. The results show that it is indeed possible to save resource by using non-uniform sampling compared to the uniform sampling case.

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