High-performance small-scale solvers for linear Model Predictive Control

Frison, Gianluca; Sørensen, Henrik Rokkjær; Dammann, Bernd; Jørgensen, John Bagterp

doi:10.1109/ecc.2014.6862490

Cited by 69 publications

(54 citation statements)

References 7 publications

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“…In the optimization of solvers for small scale problems, it is beneficial to merge linear algebra routines when possible, as shown in the Riccati recursion for unconstrained MPC problems in [9]. The main advantage is the reduction in the number of calls to linear algebra kernels.…”

Section: Merging Of Linear Algebra Routinesmentioning

confidence: 99%

“…The key operation in the algorithm presented in [9] is the computation of Q + A T · P · A, where Q is a positive semidefinite matrix. If all matrices A, P and Q have size n, then the most efficient way to compute this operation is…”

Section: Algorithmmentioning

confidence: 99%

“…To solve the nonlinear MPC (NMPC) and nonlinear MHE (NMHE) formulations we use the ACADO Code Generation Tool (CGT) [13] that implements the real-time iteration (RTI) scheme [4; 15]. The QP underlying the NMHE solver is solved using the implementation presented in Section 4, while the QP underlying the NMPC solver is handled with an efficient implementation from [9].…”

Section: Nonlinear Mhe and Mpc In Closed Loop: Real-time Numerical Simentioning

confidence: 99%

“…In particular, one of the key ingredients to obtain solvers giving high-performance for small matrices is the merging of linear algebra routines [8]. In the case of the MHE problem, the efficient Riccati recursion implementation proposed in [9] can not be employed, since the covariance of the state estimates (needed in the computation of the state estimates in the forwardbackward substitutions) is never computed explicitly, but instead only implicitly in a Cholesky factorization. Therefore, in this paper we consider a different recursion for MHE, corresponding to the information Kalman filter.…”

Section: Introductionmentioning

confidence: 99%

“…The real-world test problem in Section 5.2 falls into this class of problems. Furthermore, the developed solver can be easily embedded as a routine into an IPM to solve inequality-constrained MHE problems, similarly to [9] for the MPC problem case. In an IPM, a solver for the equality-constrained MHE problem is used to compute the Newton direction, that is the most computationally expensive part of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

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High-Performance Small-Scale Solvers for Moving Horizon Estimation

et al. 2015

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Abstract:In this paper we present a moving horizon estimation (MHE) formulation suitable to easily describe the quadratic programs (QPs) arising in constrained and nonlinear MHE. We propose algorithms for factorization and solution of the underlying Karush-Kuhn-Tucker (KKT) system, as well as the efficient implementation techniques focusing on small-scale problems. The proposed MHE solver is implemented using custom linear algebra routines and is compared against implementations using BLAS libraries. Additionally, the MHE solver is interfaced to a code generation tool for nonlinear model predictive control (NMPC) and nonlinear MHE (NMHE). On an example problem with 33 states, 6 inputs and 15 estimation intervals execution times below 500 microseconds are reported for the QP underlying the NMHE.

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Section: Merging Of Linear Algebra Routinesmentioning

confidence: 99%

Section: Algorithmmentioning

confidence: 99%

Section: Nonlinear Mhe and Mpc In Closed Loop: Real-time Numerical Simentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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High-Performance Small-Scale Solvers for Moving Horizon Estimation

et al. 2015

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Experimental validation of a semi‐distributed sequential quadratic programming method for optimal coordination of automated vehicles at intersections

Hult

Zanon

Frison

et al. 2020

Optim Control Appl Methods

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SummaryIn this article, we study the optimal coordination of automated vehicles at intersections. The problem can be stated as an optimal control problem (OCP), which can be decomposed as a bi‐level scheme composed by one nonlinear program (NLP) which schedules the access to the intersection and one OCP per vehicle which computes the appropriate vehicle commands. We discuss a practical implementation of the bi‐level controller where the NLP is solved with a tailored semi‐distributed sequential quadratic programming (SQP) algorithm that enables distribution of most computation to the vehicles. Results from an extensive experimental campaign are presented, where the bi‐level controller and the semi‐distributed SQP are implemented on a test setup consisting of three automated vehicles. In particular, we show that the vehicle‐level controller can enforce the scheduled intersection access beyond the accuracy admitted by the sensor system, and that the bi‐level controller can handle large perturbations and large communication delays, which makes the scheme applicable in practical scenarios. Finally, the use of wireless communication introduces delays in the outer control loop. To allow faster feedback, we introduce a real‐time iteration (RTI) like variation of the bi‐level controller. Experimental and simulated results indicate that the RTI‐like variation offers comparable performance using less computation and communication.

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PRESAS: Block‐structured preconditioning of iterative solvers within a primal active‐set method for fast model predictive control

Quirynen

Cairano

2020

Optim Control Appl Methods

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Summary Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This article proposes a primal active‐set strategy, called PRESAS, for the efficient solution of such block‐sparse QPs, based on a preconditioned iterative solver to compute the search direction in each iteration. Rank‐one factorization updates of the preconditioner result in a per‐iteration computational complexity of 𝒪(Nm2), where m denotes the number of state and control variables and N the number of control intervals. Three different block‐structured preconditioning techniques are presented and their numerical properties are studied further. In addition, an augmented Lagrangian based implementation is proposed to avoid a costly initialization procedure to find a primal feasible starting point. Based on a standalone C code implementation, we illustrate the computational performance of PRESAS against current state of the art QP solvers for multiple linear and nonlinear MPC case studies. We also show that the solver is real‐time feasible on a dSPACE MicroAutoBox‐II rapid prototyping unit for vehicle control applications, and numerical reliability is illustrated based on experimental results from a testbench of small‐scale autonomous vehicles.

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High-performance small-scale solvers for linear Model Predictive Control

Cited by 69 publications

References 7 publications

High-Performance Small-Scale Solvers for Moving Horizon Estimation

High-Performance Small-Scale Solvers for Moving Horizon Estimation

Experimental validation of a semi‐distributed sequential quadratic programming method for optimal coordination of automated vehicles at intersections

PRESAS: Block‐structured preconditioning of iterative solvers within a primal active‐set method for fast model predictive control

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