An improved ellipsoid optimization algorithm in subspace predictive control

Abstract

Purpose The purpose of this paper is to derive the output predictor for a stationary normal process with rational spectral density and linear stochastic discrete-time state-space model, respectively, as the output predictor is very important in model predictive control. The derivations are only dependent on matrix operations. Based on the output predictor, one quadratic programming problem is constructed to achieve the goal of subspace predictive control. Then an improved ellipsoid optimization algorithm is proposed to solve the optimal control input and the complexity analysis of this improved ellipsoid optimization algorithm is also given to complete the previous work. Finally, by the example of the helicopter, the efficiency of the proposed control strategy can be easily realized. Design/methodology/approach First, a stationary normal process with rational spectral density and one stochastic discrete-time state-space model is described. Second, the output predictors for these two forms are derived, respectively, and the derivation processes are dependent on the Diophantine equation and some basic matrix operations. Third, after inserting these two output predictors into the cost function of predictive control, the control input can be solved by using the improved ellipsoid optimization algorithm and the complexity analysis corresponding to this improved ellipsoid optimization algorithm is also provided. Findings Subspace predictive control can not only enable automatically tune the parameters in predictive control but also avoids many steps in classical linear Gaussian control. It means that subspace predictive control is independent of any prior knowledge of the controller. An improved ellipsoid optimization algorithm is used to solve the optimal control input and the complexity analysis of this algorithm is also given. Originality/value To the best knowledge of the authors, this is the first attempt at deriving the output predictors for stationary normal processes with rational spectral density and one stochastic discrete-time state-space model. Then, the derivation processes are dependent on the Diophantine equation and some basic matrix operations. The complexity analysis corresponding to this improved ellipsoid optimization algorithm is analyzed.