Parameterized H<inf>∞</inf> controller design for adaptative trade-off by finite dimensional LMI optimization

Parameter Dependent H∞ Controller Design by Finite Dimensional Lmi Optimization: Application to Trade-Off Dependent Control

“…This point is a dramatic improvement with respect to previous approaches, e.g. (Dinh et al, 2003): we improve this approach by deriving conditions of similar complexity. The proposed approach can be applied to several parameters but by introducing conservatism.…”

“…In this paper, we focus on the design of a parameter dependent H ∞ controller for a parameter dependent plant. This problem can be applied to numerous controller design problems: gain scheduling control (Stilwell and Rugh, 1999), saturated system control (Megretski, 1996), spatial system control (de Castro and Paganini, 2002), trade-off dependent control (Dinh et al, 2003), to cite a few. It can be naturally cast into optimization problems involving parameter dependent Linear Matrix Inequalities, that is, an infinite dimensional optimization problem whose solution cannot be efficiently computed.…”

“…For sake of shortness, it is not developed here. In these approaches, the choice of function sets for the decision variables of the infinite dimensional optimization problem is the crucial point, as pointed out in (Dinh et al, 2003). In this last paper, we investigated the choice of rational functions with fixed denominator, which encompasses all previous ones.…”

“…In Section 3, this solution is applied to the trade-off dependent control with the control of a DC motor as a numerical example. A trade-off dependent controller is a controller K(s, θ) such that a set of specification trade-offs parameterized by a scalar θ ∈ [0, 1] is satisfied for a given LTI plant (Dinh et al, 2003). A trade-off is, here, formulated as an optimization problem involving a weighted H ∞ norm.…”

Mixed matrix sign function/DFT inversion method for solving parameter-dependent Riccati equation

“…A parameter-dependent algebraic Riccati equation (PDRE) often arises in the design of controllers such as gain scheduling control (Apkarian et al, 1995), (Stilwell et al, 1999), saturated system control (Megretski, 1996), and trade-off dependent control (Dinh et al, 2003), (Dinh et al, 2005).…”