1. Low-Rank Modifications of Riccati Factorizations for Model Predictive Control.
- Author
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Nielsen, Isak and Axehill, Daniel
- Subjects
PREDICTIVE control systems ,RICCATI equation ,LOW-rank matrices ,MATHEMATICAL optimization ,ALGORITHMS ,MATHEMATICAL models - Abstract
In model predictive control (
MPC ), the control input is computed by solving a constrained finite-time optimal control (CFTOC ) problem at each sample in the control loop. The main computational effort when solving theCFTOC problem using an active-set (AS ) method is often spent on computing the search directions, which inMPC corresponds to solving unconstrained finite-time optimal control (UFTOC ) problems. This is commonly performed using Riccati recursions or generic sparsity exploiting algorithms. In this paper, the focus is efficient search direction computations forAS type methods. The system of equations to be solved at eachAS iteration is changed only by a low-rank modification of the previous one, and exploiting this structured change is important for the performance ofAS -type solvers. In this paper, theory for how to exploit these low-rank changes by modifying the Riccati factorization betweenAS iterations in a structured way is presented. A numerical evaluation of the proposed algorithm shows that the computation time can be significantly reduced by modifying, instead of re-computing, the Riccati factorization. This speedup can be important forAS -type solvers used for linear, nonlinear, and hybridMPC . [ABSTRACT FROM PUBLISHER]- Published
- 2018
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