access icon free Standard solution to mixed control with regular Riccati equation

© The Institution of Engineering and Technology
Received 17/01/2020, Accepted 25/11/2020, Revised 25/11/2020, Published 07/01/2021

In this study, the authors are concerned with the long-standing mixed problem for discrete linear systems. The main contribution is to derive the standard solution of the mixed problem by a regular Riccati equation. Firstly, in -optimisation procedure, the optimal strategy is explicitly given where the -norm is maximised by w and -norm is minimised by u at the same time. It is noted that there exists an arbitrary item in the optimal strategy for the positive semi-definite weighting matrices. Secondly, the -optimisation problem is explicitly solved with respect to the arbitrary item. Finally, the standard solution of the mixed problem is explicitly given in terms of regular Riccati equations by combining the optimal strategy in optimisation procedure and the optimal solution of optimisation procedure. Examples are presented to show the effectiveness of the proposed approach.

Inspec keywords: linear systems; Riccati equations

Other keywords: discrete linear systems; regular Riccati equation; optimal strategy; positive semidefinite weighting matrices; standard solution; optimal solution; arbitrary item

Subjects: Linear algebra (numerical analysis); Optimal control; Optimisation techniques; Linear control systems

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