OBJECTIVES

1. Stochastic optimal design for unknown networked control system over unreliable communication network Faculty Advisor: Dr. Jagannathan Sarangapani, ECE Department Student: Hao Xu, ECE Department • Simulation Results • Consider the linear time-invariant batch reactor dynamics • After random delays and packet losses due to unreliable communication network, the original time-invariant system was discretized and represented as a time-varying system • (Note: since the random delays and packet losses are considered, the NCS model is not only time varying , but also a function of time k) • Performance evaluation of proposed optimal control with AO and AE • Stability: • Figure 5 Stability performance • As shown in Figure 5, if we use a PID without considering effects of unreliable communication network (i.e. delays and packet losses), the NCS will be unstable(Figure 5-(a)). However, when we implement proposed AO and AE optimal control, the NCS can still maintain stable(Figure 5-(b)). • Observability: • Figure 6 Observer performance • As shown in Figure 6-(a), proposed AO can force observed system stable to converge to actual system state quickly. In Figure 6-(b), the stability region for proposed AO is shown. Since system dynamics is unknown, the region of proposed method is tighter than region of AO with known system dynamics. • Adaptive Observer Design for NCS • In this work, TCP protocol is considered for NCS. Since TCP uses acknowledgements to indicate the acceptance of the packet, network information set can be defined as • Based on TCP protocol, adaptive observer design can be separated into two steps: 1) innovation step and 2) correction step. • Innovation step at time : • Predicted future system states: • where , and is independent and identically distributed white Gaussian noise (i.e. ) • Prediction error: • Correction step at time : • Update law for adaptive observer: • Convergence: when , and at the same time. • OBJECTIVES • Investigate the effects of unreliable communication network (e.g. TCP) on the stability of the NCS with unknown dynamics • Develop an adaptive observer (AO) to estimate networked control system (NCS) states; • Develop an adaptive estimator (AE)-based stochastic optimal control for unknown NCS under unreliable communication network by using observed system states. • BACKGROUND • Networked control can reduce the installation costs and increase productivity through the use of wireless communication technology • The challenging problems in control of networked-based system are unreliable communication network effects (e.g. network delay and packet losses). These effects do not only degrade the performance of NCS, but also can destabilize the system. • Approximate dynamic programming (ADP) techniques intent to solve optimal control problems of complex systems without the knowledge of system dynamics in a forward-in-time manner. • Figure 1 Networked control system * • The proposed approach for optimal controller design involves using a combination of adaptive observer (AO) and adaptive estimator (AE). The effects of unreliable communication work are incorporated in the dynamic model which will be used for observer and controller development. • * L. Marschall, “Five Decades of Automation”, Siemens Technical Report,2005. • AE-based Stochastic Optimal Control • When NCS system states are observed, AE-based stochastic optimal control can be derived based on observed states. • Set up stochastic Vale-function: • where • Using the adaptive estimator to represent Value-function: • where and is the Kronecker product quadratic polynomial basis vector • Define the update law to tune the adaptive estimator • Represent residual error: • where and • Update law for adaptive estimator: • where is a constant, and • Determine the AE stochastic optimal control input based on observed states • Convergence: when , and . • CONCLUSIONS • Effects of unreliable communication network such as random delays and packet losses degrade the performance of NCS and can cause instability unless they are explicitly accounted for. • Proposed stochastic optimal control based on AO and AE for linear NCS renders acceptable performance without requiring system dynamics and unreliable communication network. • Proposed optimal controller works forward in time and suitable for real-time control. • Networked Control System Model • Networked control system representation • and • Figure 2 depicts a block diagram representation: • Figure 2 Block diagram of networked control system • AE-based Stochastic Optimal Control (2) • Figure 3 present the flowchart for the AE-based stochastic optimal regulator of NCS • Figure 3 Stochastic optimal regulator flowchart • FUTURE WORK • Design a novel cross-layer communication network protocol to improve the effects of unreliable communication network. • Joint optimize the NCS from both control part and unreliable communication network part. • Extend the NCS work to developing theory for cyber physical systems