NOILC: Natural Extensions
Following a discussion of the use of filtered signals, the chapter illustrates the wider interpretation of NOILC by considering its flexibility using multi-rate discrete time systems followed by an analysis of situations where variation of the initial conditions is possible and can be regarded as part of the input signal. Changes in the form of the reference signal that can be used in practice are then illustrated by a solution of the Intermediate Point Tracking Problem where outputs are required only to take specified values at a finite number of intermediate point in time. This approach is then merged with the material in the previous chapter to form a Multi-task NOILC Algorithm that allows reference signals to be defined on subintervals only with periods where tracking is not needed but where discrete, isolated values are specified at intermediate points. The great potential of the NOILC formulation is then used to create Predictive Optimization-based Algorithms using a receding horizon principle. These are shown to be monotonically convergent and to offer the potential for improved convergence rates.