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# Investigation on Robust Codesign Methods for Networked Control Systems

Sanad Al-Areqi

### Cite this publication as

Sanad Al-Areqi, Investigation on Robust Codesign Methods for Networked Control Systems (2015), Logos Verlag, Berlin, ISBN: 9783832594350

### Beschreibung

The problem of jointly designing a robust controller and an intelligent scheduler for networked control systems (NCSs) is addressed in this thesis. NCSs composing of multiple plants that share a single channel communication network with uncertain time-varying transmission times are modeled as switched polytopic systems with additive norm-bounded uncertainty. Switching is deployed to represent scheduling, the polytopic uncertainty to overapproximatively describe the uncertain time-varying transmission times.

Based on the resulting NCS model and a state feedback control law, the control and scheduling codesign problem is then introduced and formulated as a robust (minimax) optimization problem with the objective of minimizing the worst-case value of an associated infinite time-horizon quadratic cost function. Five robust codesign strategies are investigated for tackling the introduced optimization problem, namely:

Periodic control and scheduling (PCS), Receding-horizon control and scheduling (RHCS), Implementation-aware control and scheduling (IACS), Event-based control and scheduling (EBCS), Prediction-based control and scheduling (PBCS).

All these codesign strategies are determined from LMI optimization problems based on the Lyapunov theory. The properties of each are evaluated and compared in terms of computational complexity and control performance based on simulation and experimental study, showing their effectiveness in improving the performance while utilizing the limited communication resources very efficiently.

Based on the resulting NCS model and a state feedback control law, the control and scheduling codesign problem is then introduced and formulated as a robust (minimax) optimization problem with the objective of minimizing the worst-case value of an associated infinite time-horizon quadratic cost function. Five robust codesign strategies are investigated for tackling the introduced optimization problem, namely:

Periodic control and scheduling (PCS), Receding-horizon control and scheduling (RHCS), Implementation-aware control and scheduling (IACS), Event-based control and scheduling (EBCS), Prediction-based control and scheduling (PBCS).

All these codesign strategies are determined from LMI optimization problems based on the Lyapunov theory. The properties of each are evaluated and compared in terms of computational complexity and control performance based on simulation and experimental study, showing their effectiveness in improving the performance while utilizing the limited communication resources very efficiently.

### Inhaltsverzeichnis

- BEGINN
- 1 Introduction
- 1.1 Networked Control Systems
- 1.2 Motivating Examples
- 1.3 Network-Induced Imperfections
- 1.4 MAC Protocols for NCSs
- 1.5 Modeling and Analysis of NCSs
- 1.6 Control and Scheduling Codesign
- 1.7 Objectives and Contributions
- 1.8 Outline and Publications
- 2 Modeling
- 2.1 NCS Architecture
- 2.2 NCS Model
- 2.3 Polytopic Formulation
- 2.4 Cost Function
- 3 Codesign Problem
- 3.1 Problem Formulation
- 3.2 Problem Properties
- 4 Periodic Control and Scheduling (PCS)
- 4.1 Problem Formulation
- 4.2 Upper Bound Derivation
- 4.3 Periodic Control
- 4.4 Solution based on Exhaustive Search
- 4.5 Solution based on Relaxation
- 4.6 Solution based on Optimal Pointer Placement
- 4.7 Illustrative Example
- 5 Receding-Horizon Control and Scheduling (RHCS)
- 5.1 Problem Formulation
- 5.2 Dynamic Programming Solution
- 5.3 Relaxed Dynamic Programming Solution
- 5.4 Illustrative Example
- 6 Implementation-Aware Control and Scheduling (IACS)
- 6.1 Problem Formulation
- 6.2 Solution based on Lyapunov-Metzler
- 6.3 Illustrative Example
- 7 Event-Based Control and Scheduling (EBCS)
- 7.1 NCS Model Extension
- 7.2 Problem Formulation
- 7.3 Solution based on the S-Procedure
- 7.4 Illustrative Example
- 8 Prediction-Based Control and Scheduling (PBCS)
- 8.1 NCS Model Extension
- 8.2 Problem Formulation
- 8.3 Solution based on the S-Procedure
- 8.4 Illustrative Example
- 9 Evaluation and Implementation
- 9.1 Evaluation
- 9.2 Implementation
- 10 Conclusions and Future Work
- 10.1 Conclusions
- 10.2 Future Work
- A Appendix