Sammendrag
In many practical applications switching devices are used to implemen t the control policies. Mathematically speaking this means that we ar e confron with the problem of controlling a hybrid system whose input s live on a finite set. Typically the controller is designed in conti nuous--time, and assuming a sufficiently fast sampling rate, the con tinuous control signal is approximated with a time--average of admiss ible points in the input space (via, e.g., a pulse--width--modulation strategy). Another approach to handle this problem is variable struc ture control where we try to generate sliding regimes in certain sub spaces of the state space via fast switching. We are interested in th is paper in situations when the fast switching assumption is not tena ble, and consequently we have to control directly the switching time of the actuator device. The solution we propose here consists of the following steps: First, we characterize in input space the subspaces where we regulate each output to constant values. This characterizat ion, which is very simple for affine systems of relative degree {1,1, ...., 1), allows us to decide whether a particular input (instantane ously) increases or decreases the outputs. Second, based on this clas sification, we choose the input points where all outputs are simultan eously regulated; in case of conflict an output priority policy is ap plied. This scheme will work if we are able to prove that, in steady --state, the output regulation subspaces induce a partition of the in put space that contains at least one point of the input set that driv es all outputs in the "right direction". And furthermore, that during the transient, the partition always allows us to regulate the prefer ed output.
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