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Low-Rank Modifications of Riccati Factorizations for Model Predictive Control
- Source :
- IEEE Transactions on Automatic Control. 63:872-879
- Publication Year :
- 2018
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2018.
-
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 the CFTOC problem using an active-set ( AS ) method is often spent on computing the search directions, which in MPC 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 for AS type methods. The system of equations to be solved at each AS iteration is changed only by a low-rank modification of the previous one, and exploiting this structured change is important for the performance of AS -type solvers. In this paper, theory for how to exploit these low-rank changes by modifying the Riccati factorization between AS 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 for AS -type solvers used for linear, nonlinear, and hybrid MPC .
- Subjects :
- 0209 industrial biotechnology
Mathematical optimization
Speedup
Rank (linear algebra)
02 engineering and technology
Linear-quadratic regulator
Control Engineering
Linear-quadratic-Gaussian control
Optimal control
Computer Science Applications
Algebraic Riccati equation
Model predictive control
020901 industrial engineering & automation
Reglerteknik
Optimization and Control (math.OC)
Control and Systems Engineering
FOS: Mathematics
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
Indexes
Linear matrix inequalities
Optimization
Predictive control
Search problems
Sparse matrices
MPC
Riccati recursion
low-rank
optimization
Electrical and Electronic Engineering
Mathematics - Optimization and Control
Sparse matrix
Mathematics
Subjects
Details
- ISSN :
- 15582523 and 00189286
- Volume :
- 63
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Automatic Control
- Accession number :
- edsair.doi.dedup.....f16bc756d961e99c1c5ff210223fa143