Computation of an optimal communication schedule in a nonlinear networked control system using sum-of-squares

In this paper, we consider the design of a control optimal communication schedule in nonlinear networked control with nonlinear affine plant systems. We focus here on periodic communication schedules in control systems with time-triggered control communication and assume the existence of predesigned controllers which need to be optimally integrated via the control communication system. For this, we formulate a quadratic cost function for the nonlinear affine plant. The system and the cost are first discretized using an exact mixed discretization approach which allows to lift the problem from the continuous-discrete domain into a purely discrete-time representation. Periodicity due to the fixed communication schedule is dealt with the discrete lifting technique. To allow for the computation of the cost, nonlinearities are approximated in terms of a Taylor series which allows the use of the sum-of-squares framework. Once a cost function of the networked control system for a given fixed communication schedule is defined, it is then possible to compare and choose those sequences that minimize this cost for optimal controller integration.