Linear Parameter-Varying Control - Complexity of Analysis, Synthesis and Implementation

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Systems encountered in practice can often only be accurately represented by nonlinear or time-varying sets of differential equations. The paradigm of linear parameter-varying control is an attractive framework for modelling and controlling such systems, due to the availability of controller synthesis tools that guarantee stability and performance in the whole operating range. Even though these tools have already enabled many successful applications, their use is limited to systems of low complexity. We address challenges imposed by different types of complexity: analysis, synthesis and implementation complexity, each posing obstacles to be overcome in different stages during controller design. This will be done in four work packages. The first deals with the assessment of complexity of problems encountered in analysis, synthesis and implementation when using different types of LPV representations. Methods for the reduction of the number of scheduling parameters will be proposed that are based either on a transformation into different equivalent forms or on an approximation. As synthesizing controllers based on approximated models will render stability and performance guarantees void, the second work package will develop a posteriori analysis tools for checking whether guarantees still hold when the controller is applied to the original plant. An important benefit of this will be that off-line analysis can be performed with reduced conservatism, after simple synthesis methods have been used to obtain controllers of low implementation complexity. Taking this approach further, the third work package will aim at turning these analysis results into synthesis methods, starting with initial controllers based on approximated models and iterating between analysis and synthesis based on an accurate plant model. More sophisticated approaches will include combined gradient-LMI algorithms for efficiently solving the underlying nonlinear optimization problem. Such synthesis techniques will also be used when stability and performance guarantees have been lost and need to be recovered by optimizing the controller parameters.For more general LPV representations, we propose to investigate analysis methods that have been developed for classical gain-scheduling techniques. In the fourth work package the developed methods will be validated experimentally on a number of challenging plants, which are available at the Hamburg University of Technology.