H_∞ tracking of linear continuous-time systems with stochastic uncertainties and preview

The problem of finite-horizon H_∞ tracking for linear continuous time-invariant systems with stochastic parameter uncertainties is investigated for both, the state-feedback and the output-feedback control problems. We consider three tracking patterns depending on the nature of the reference signal i.e. whether it is perfectly known in advance, measured on line or previewed in a fixed time-interval ahead. The stochastic uncertainties appear in both the dynamic and measurement matrices of the system. In the state-feedback case, for each of the above three cases a game theory approach is applied where, given a specific reference signal, the controller plays against nature which chooses the initial condition and the energy-bounded disturbance. The problems are solved using the expected value of the standard performance index over the stochastic parameters, where, in the state-feedback case, necessary and sufficient conditions are found for the existence of a saddle-point equilibrium. The corresponding infinite-horizon time-invariant tracking problem is also solved for the latter case, where a dissipativity approach is considered. The output-feedback control problem is solved as a max-min problem for the three tracking patterns, where necessary and sufficient condition are obtained for the solution. The theory developed is demonstrated by a simple example where we compare our solution with an alternative solution which models the tracking signal as a disturbance.