Constrained Discrete-time Proportional Integral Control Based on Convex Algorithms

Abstract

Following the recent developments on PDF shape control, new realizable generalized PI control structures are proposed for SDC problems in the discrete-time context. Here we use the square root B-spline expansion and nonlinear discrete-time weight system to identify the unknown dynamical relationship between the control input and the output PDF. As a result, the tracking control strategy is studied for the complex discrete-time weight models where there exist a time delay term, non-zero equilibrium, partial state constraint, exogenous disturbance and model uncertainty. Improved LMI algorithms are used to design a generalized discrete-time PI controller such that stabilization, tracking performance, robustness and state constraints can be guaranteed simultaneously. Furthermore, the L₁ performance index is used to formulate the disturbance attenuation, which generalizes the corresponding result for linear systems with zero equilibrium (see [133]). It is noted that the proposed result represents a significant extension of the previous results [61, 63, 64], and has also independent significance in robust discrete-time PI tracking control fields.