Optimal control for networked control system via δ-operator formulation

This paper deals with an optimal control problem for networked control systems, which have network induced time delays in communication networks. A linear quadratic controller for the systems with random delays in delta domain is proposed by using a dynamic programming approach. The derived optimal controller in delta domain can be represented as linear delay-depended feedback of the states and the previous control signal. In the discrete time case, this is natural extension of the previous result in the limit as sampling time tend to zero. Finally, we compare three controllers in each domain to further illustrate the effectiveness of the proposed controller for a networked control system by utilizing delta discrete-time formulation.