Observer-based tracking controller design for networked predictive control systems with uncertain Markov delays

This paper is concerned with a tracking controller design problem for discrete-time networked predictive control systems. The control law used here is a combined state-feedback control and integral control. Since not all the states are available in practice, a local Luenberger is utilized to estimate the state vector. The measured output and the estimated state vector are packed together and transmitted to the tracking controller via a communication channel with a limited capacity. Meanwhile, the control signal is also transmitted through a communication network. Networked-induced delays on both links are considered for the signal transmission and modeled by Markov chains. Moreover, it is assumed that the elements in the Markov transition matrices are subject to uncertainties. In order to fully compensate for the network-induced delay, the controller generates a sequence of control signals which are dependent on each possible delay on the feedforward channel. With the augmenting technique twice and the proposed control law, we obtain delay-free stochastic closed-loop systems and the controlled output is chosen as the tracking error. Sufficient conditions are provided for the energy-to-peak performance of the closed-loop systems. The feedback gains of the controller can be derived by solving a minimization problem. An example is illustrated to demonstrate the effectiveness of the proposed design method.