Constrained Continuous-time Proportional Integral Derivative Control Based on Convex Algorithms

Abstract

AbstractIt is noted that the tracking problem for the output PDF can be considered as an infinite dimensional tracking problem for a function. Up to now, most of the proposed PDF tracking control laws were obtained through the numeral optimization techniques (see [157, 158, 160, 163, 164]). As a result, the control structures were complicated and the rigorous stability analysis was difficult to provide. Since the controlled output is the shape of the conditional output PDF, the B-spline NN approximation has been effectively used for the modeling of output PDFs so that the problem can be reduced to a tracking problem for the weight systems [58, 61, 63, 64, 88, 160, 161, 163, 164, 166, 167, 173, 181–184, 188, 196]. It is noted that for the square root B-spline expansion model, a constraint on the weight vector should be satisfied, which leads to some additional obstacles in the tracking controller design. Generally speaking, three tasks should be achieved in the PDF tracking problem.KeywordsTracking ProblemExogenous DisturbanceTracking Control ProblemNonlinear Matrix InequalityTracking Controller DesignThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.