Efficient direct multiple shooting for nonlinear model predictive control on long horizons

Kirches, Christian; Wirsching, Leonard; Bock, Hans Georg; Schlöder, Johannes P.

doi:10.1016/j.jprocont.2012.01.008

Cited by 65 publications

(31 citation statements)

References 26 publications

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“…[14] As shown in Table 4, our Algorithm 2 shows a higher performance in terms of CPU time as compared to all presented algorithms, still obtaining the the same objective function value as reported by other authors.…”

Section: Comparative Analysissupporting

confidence: 70%

Modified Multiple Shooting Combined with Collocation Method in JModelica.org with Symbolic Calculations

Lazutkin

Geletu

Hopfgarten

et al. 2014

Linköping Electronic Conference Proceedings

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Section: Comparative Analysissupporting

confidence: 70%

Modified Multiple Shooting Combined with Collocation Method in JModelica.org with Symbolic Calculations

Lazutkin

Geletu

Hopfgarten

et al. 2014

Linköping Electronic Conference Proceedings

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“…This is done by solving a sequence of Newton-system-like equations that correspond to unconstrained finite-time optimal control (uftoc) problems (Rao et al, 1998;Barclay et al, 1998;Betts, 2001;Vandenberghe et al, 2002;Kirches et al, 2012). Hence, many commonly used second-order methods for solving cftoc problems rely on highly efficient algorithms for computing the solutions to uftoc problems.…”

Section: Background and Motivationmentioning

confidence: 99%

Structure-Exploiting Numerical Algorithms for Optimal Control

Nielsen¹

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Cover illustration: An illustration of the structure of the Karush-Kuhn-Tucker matrix for the unconstrained finite-time optimal control problems considered in this thesis. Thank you Jonas Linder for helping me with the design.Linköping studies in science and technology. Dissertations.No. 1848 Tillägnas hela min underbara familj Structure-Exploiting Numerical Algorithms for Optimal Control AbstractNumerical algorithms for efficiently solving optimal control problems are important for commonly used advanced control strategies, such as model predictive control (mpc), but can also be useful for advanced estimation techniques, such as moving horizon estimation (mhe). In mpc, the control input is computed by solving a constrained finite-time optimal control (cftoc) problem on-line, and in mhe the estimated states are obtained by solving an optimization problem that often can be formulated as a cftoc problem. Common types of optimization methods for solving cftoc problems are interior-point (ip) methods, sequential quadratic programming (sqp) methods and active-set (as) methods. In these types of methods, the main computational effort is often the computation of the second-order search directions. This boils down to solving a sequence of systems of equations that correspond to unconstrained finite-time optimal control (uftoc) problems. Hence, high-performing second-order methods for cftoc problems rely on efficient numerical algorithms for solving uftoc problems. Developing such algorithms is one of the main focuses in this thesis. When the solution to a cftoc problem is computed using an as type method, the aforementioned system of equations is only changed by a low-rank modification between two as iterations. In this thesis, it is shown how to exploit these structured modifications while still exploiting structure in the uftoc problem using the Riccati recursion. Furthermore, direct (non-iterative) parallel algorithms for computing the search directions in ip, sqp and as methods are proposed in the thesis. These algorithms exploit, and retain, the sparse structure of the uftoc problem such that no dense system of equations needs to be solved serially as in many other algorithms. The proposed algorithms can be applied recursively to obtain logarithmic computational complexity growth in the prediction horizon length. For the case with linear mpc problems, an alternative approach to solving the cftoc problem on-line is to use multiparametric quadratic programming (mp-qp), where the corresponding cftoc problem can be solved explicitly off-line. This is referred to as explicit mpc. One of the main limitations with mp-qp is the amount of memory that is required to store the parametric solution. In this thesis, an algorithm for decreasing the required amount of memory is proposed. The aim is to make mp-qp and explicit mpc more useful in practical applications, such as embedded systems with limited memory resources. The proposed algorithm exploits the structure from the qp problem in the parametric solution in order to reduc...

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“…Real-time iteration (RTI) scheme is an approximation technique for optimal feedback control [17]. The most obvious benefit of RTI scheme is that it performs only one Newton-type iteration per NMPC sample [18].…”

Section: Introductionmentioning

confidence: 99%

Modeling and Control of Crane Overload Protection During Marine Lifting Operation Based on Model Predictive Control

Ren

Skjetne

Gao

2017

Volume 9: Offshore Geotechnics; Torgeir Moan Honoring Symposium

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This paper deals with a nonlinear model predictive control (NMPC) scheme for a winch servo motor to overcome the sudden peak tension in the lifting wire caused by a lumped-mass payload at the beginning of a lifting off or a lowering operation. The crane-wire-payload system is modeled in 3 degrees of freedom with the Newton-Euler approach. Direct multiple shooting and real-time iteration (RTI) scheme are employed to provide feedback control input to the winch servo. Simulations are implemented with MATLAB and CaSADi toolkit. By well tuning the weighting matrices, the NMPC controller can reduce the snatch loads in the lifting wire and the winch loads simultaneously. A comparative study with a PID controller is conducted to verify its performance.

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Efficient direct multiple shooting for nonlinear model predictive control on long horizons

Cited by 65 publications

References 26 publications

Modified Multiple Shooting Combined with Collocation Method in JModelica.org with Symbolic Calculations

Modified Multiple Shooting Combined with Collocation Method in JModelica.org with Symbolic Calculations

Structure-Exploiting Numerical Algorithms for Optimal Control

Modeling and Control of Crane Overload Protection During Marine Lifting Operation Based on Model Predictive Control

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