Efficient Numerics for Nonlinear Model Predictive Control

Kirches, Christian; Wirsching, Leonard; Säger, Sebastian; Bock, Hans Georg

doi:10.1007/978-3-642-12598-0_30

Cited by 25 publications

(17 citation statements)

References 18 publications

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“…The measurement time points of the optimal experimental designs are placed at the beginning and at the end of the time interval [0,15] in which a first state and parameter estimation is performed. During the optimal control phase starting from t = 15 the non-robust and robust optimal experimental designs suggest measuring once, respectively twice, at the steep descent/ascent of the populations on the interval [15,20] where a larger information content is expected compared to the equidistant time points next to the trajectories' steady state. The heterogeneity in the improvement of the parameters' uncertainties results in the used objective function trace(F −1 (t f )) with which the averaged parameter uncertainty is minimized and not each uncertainty separately.…”

Section: Discussionmentioning

confidence: 99%

“…Note that the norms are evaluated pointwise, as Mayer term and the FIM in Problems (6) and (12) are evaluated at time t f . However, the analysis of Section 3.1 can not be applied in a straightforward way due to the derivative term in the objective function (20), as the weights may jump asp changes locally. Intuition and numerical results hint into the direction that also for the robust case discrete designs are optimal, probably with the same bounds on the number of support points.…”

Section: Robustificationmentioning

confidence: 99%

“…This speedup is mainly due to the faster algorithms and only partially due to the hardware speedup. Surveys on efficient numerical approaches to NMPC and MHE can be found in, e.g., [7,[18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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A Feedback Optimal Control Algorithm with Optimal Measurement Time Points

Jost

Säger

2017

Processes

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Nonlinear model predictive control has been established as a powerful methodology to provide feedback for dynamic processes over the last decades. In practice it is usually combined with parameter and state estimation techniques, which allows to cope with uncertainty on many levels. To reduce the uncertainty it has also been suggested to include optimal experimental design into the sequential process of estimation and control calculation. Most of the focus so far was on dual control approaches, i.e., on using the controls to simultaneously excite the system dynamics (learning) as well as minimizing a given objective (performing). We propose a new algorithm, which sequentially solves robust optimal control, optimal experimental design, state and parameter estimation problems. Thus, we decouple the control and the experimental design problems. This has the advantages that we can analyze the impact of measurement timing (sampling) independently, and is practically relevant for applications with either an ethical limitation on system excitation (e.g., chemotherapy treatment) or the need for fast feedback. The algorithm shows promising results with a 36% reduction of parameter uncertainties for the Lotka-Volterra fishing benchmark example.

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Section: Discussionmentioning

confidence: 99%

Section: Robustificationmentioning

confidence: 99%

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A Feedback Optimal Control Algorithm with Optimal Measurement Time Points

Jost

Säger

2017

Processes

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“…In as methods it is often crucial to be able to update the factorization of the kkt matrix instead of re-factorizing it, and for this reason the Riccati factorization has been considered more useful in ip methods than in as methods (Kirches et al, 2010). However, recently it was shown in Nielsen et al (2013) that it is also possible to update the Riccati factorization when it is used in an as method.…”

Section: Low-rank Modifications Of Riccati Factorizationsmentioning

confidence: 99%

On Structure Exploiting Numerical Algorithms for Model Predictive Control

Nielsen

2015

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One of the most common advanced control strategies used in industry today is Model Predictive Control (mpc), and some reasons for its success are that it can handle multivariable systems and constraints on states and control inputs in a structured way. At each time-step in the mpc control loop the control input is computed by solving a constrained finite-time optimal control (cftoc) problem on-line. There exist several optimization methods to solve the cftoc problem, where two common types are interior-point (ip) methods and active-set (as) methods. In both these types of methods, the main computational effort is known to be the computation of the search directions, which boils down to solving a sequence of Newton-system-like equations. These systems of equations correspond to unconstrained finite-time optimal control (uftoc) problems. Hence, high-performance ip and as methods for cftoc problems rely on efficient algorithms for solving the uftoc problems.The solution to a uftoc problem is computed by solving the corresponding Karush-Kuhn-Tucker (kkt) system, which is often done using generic sparsity exploiting algorithms or Riccati recursions. When an as method is used to compute the solution to the cftoc problem, the system of equations that is solved to obtain the solution to a uftoc problem is only changed by a low-rank modification of the system of equations in the previous iteration. This structured change is often exploited in as methods to improve performance in terms of computation time. Traditionally, this has not been possible to exploit when Riccati recursions are used to solve the uftoc problems, but in this thesis, an algorithm for performing low-rank modifications of the Riccati recursion is presented.In recent years, parallel hardware has become more commonly available, and the use of parallel algorithms for solving the cftoc problem and the underlying uftoc problem has increased. Some existing parallel algorithms for computing the solution to this type of problems obtain the solution iteratively, and these methods may require many iterations to converge. Some other parallel algorithms compute the solution directly (non-iteratively) by solving parts of the system of equations in parallel, followed by a serial solution of a dense system of equations without the sparse structure of the mpc problem. In this thesis, two parallel algorithms that compute the solution directly (non-iteratively) in parallel are presented. These algorithms can be used in both ip and as methods, and they exploit the sparse structure of the mpc problem such that no dense system of equations needs to be solved serially. Furthermore, one of the proposed parallel algorithms exploits the special structure of the mpc problem even in the parallel computations, which improves performance in terms of computation time even more. By using these algorithms, it is possible to obtain logarithmic complexity growth in the prediction horizon length.v Populärvetenskaplig sammanfattningModellprediktiv reglering (eng. Model Predictive...

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“…Note that Moving Horizon Estimation (MHE) techniques typically require the online solution of a similar OCP formulation. For this purpose, tailored online algorithms have been developed for real-time optimal control as discussed in (Diehl et al, 2009;Kirches et al, 2010;Ohtsuka, 2004). …”

Section: Introductionmentioning

confidence: 99%

Hardware Tailored Linear Algebra for Implicit Integrators in Embedded NMPC

et al. 2017

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Nonlinear Model Predictive Control (NMPC) requires the efficient treatment of the dynamic model in the form of a system of continuous-time differential equations. Newtontype optimization relies on a numerical simulation method in addition to the propagation of first or higher order derivatives. In the case of stiff or implicitly defined dynamics, implicit integration schemes are typically preferred. This paper proposes a tailored implementation of the necessary linear algebra routines (LU factorization and triangular solutions), in order to allow for a considerable computational speedup of such integrators. In particular, the opensource BLASFEO framework is presented as a library of efficient linear algebra routines for small to medium-scale embedded optimization applications. Its performance is illustrated on the nonlinear optimal control example of a chain of masses. The proposed library allows for considerable speedups and it is found to be overall competitive with both a code-generated solver and a high-performance BLAS implementation.

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Efficient Numerics for Nonlinear Model Predictive Control

Cited by 25 publications

References 18 publications

A Feedback Optimal Control Algorithm with Optimal Measurement Time Points

A Feedback Optimal Control Algorithm with Optimal Measurement Time Points

On Structure Exploiting Numerical Algorithms for Model Predictive Control

Hardware Tailored Linear Algebra for Implicit Integrators in Embedded NMPC

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