Robust adaptive control: The qLPV paradigm

The study of LPV systems is motivated by the gain scheduling control design methodology. The classical approach to gain-scheduling involves the design of several LTI controllers for a parameterized family of linearized models of a system and the interpolation of the controller gains. LPV control theory has been proven useful to simplify the interpolation and realization problems associated with conventional gain-scheduling since it allows us to treat gain-scheduled controllers as a single entity, with the gain-scheduling achieved entirely by the parameter dependent controller. Using scaled small-gain theorem, a systematic gain scheduling control design technique has been developed. When the parameter dependency in both plant and controller is linear fractional, the existence of such a gain-scheduled controller is fully characterized in terms of linear matrix inequalities (LMIs). The underlying synthesis problem is therefore a convex problem for which efficient optimization techniques are available. This control structure is applicable whenever the value of parameter is measured in real-time. The resulting controller is time-varying and smoothly scheduled by the measurements of parameter. In a parallel approach a single, possible parameter-dependent, Lyapunov function has been used in the analysis and control design for parameter-dependent plants in robust control framework. Known bounds on the rate of parameter variation can be also incorporated into the analysis conditions. The solution to the LPV control synthesis problem was formulated as a parameter-dependent LMI optimization problem. For a general parameter dependence a brutal force griding method can be used to divide the parameter space and to render the semiinfinite optimization problem to be finite one; an alternative and very appealing solution can be applied for affine parameterizations.