A block based ALADIN scheme for highly parallelizable direct Optimal Control

Kouzoupis, Dimitris; Quirynen, Rien; Houska, Boris; Diehl, Moritz

doi:10.1109/acc.2016.7525066

Cited by 24 publications

(20 citation statements)

References 12 publications

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“…(a) Preparation Phase The preparation phase uses a predicted statex k|k−1 as a starting point obtained from the last nominal input trajectory in its shifted version to linearise and prepare a QP. The standard RTI Scheme only performs the aforementioned tasks and solves the QP in the feedback phase, however, in this work a small modification is used where the QP is iterated during preparation assuming δx k = 0 to find the vector of Lagrange Multipliers λ which is then used to compute the solution as given in equations (15) or (16).…”

Section: Computation Separationmentioning

confidence: 99%

“…(b) Feedback Phase Once the state measurement becomes available, the feedback phase quickly delivers an approximate solution by calculating the predicted state deviation δx k = x k −x k|k−1 and computing the "feedback phase" parts of equations (15) or (16), depending on which type of solution is being used. This allows the optimisation to have robustness against noise, disturbances and uncertainty.…”

Section: Computation Separationmentioning

confidence: 99%

“…After the optimisation is solved, definitions (17) and 18can be used to recover the solution in the original variables. This results in solutions (15) and (16) presented in the section 2.4 to change to:…”

Section: Blocked Solutionsmentioning

confidence: 99%

“…Finally, a common method for achieving faster computation times is by reducing the numbers of degrees of freedom; this can be done using input-parameterised solutions such as Move Blocking and Laguerre Polynomials [15] where an input-structure is embedded into the decision variables. Authors from [16] proposed methods for solving the blocked optimisation using highly parallelizable algorithms, which allow for even faster computation times. However, most works in this area, including [3,[16][17][18] have used blocking for NMPC with no regard to the recursive feasibility problem it presents.…”

Section: Introductionmentioning

confidence: 99%

“…Authors from [16] proposed methods for solving the blocked optimisation using highly parallelizable algorithms, which allow for even faster computation times. However, most works in this area, including [3,[16][17][18] have used blocking for NMPC with no regard to the recursive feasibility problem it presents.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Shifting strategy for efficient block‐based non‐linear model predictive control using real‐time iterations

Villarreal

Rossiter

2020

IET Control Theory & Applications

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Nonlinear Model Predictive Control (NMPC) requires the use of efficient solutions and strategies for its implementation in fast/real-time systems. A popular approach for this is the Real Time Iteration (RTI) Scheme which uses a shifting strategy, namely the Initial Value Embedding (IVE), that shifts the solution from one sampling time to the next. However, this strategy together with other efficient strategies such as Move Blocking, present a recursive feasibility problem. This paper proposes a novel modified shifting strategy which preserve both recursive feasibility and stability properties, as well as achieves a significant reduction in the computational burden associated with the optimisation. The proposed approach is validated through a simulation of an inverted pendulum where it clearly outperforms other standard solutions in terms of performance and recursive feasibility properties. Additionally, the approach was tested on two computing platforms: a laptop with an i7 processor and a Beaglebone Blue Linux-based computer for robotic systems, where computational gains compared to existing approaches are shown to be as high as 100 times faster.

show abstract

Section: Computation Separationmentioning

confidence: 99%

Section: Computation Separationmentioning

confidence: 99%

Section: Blocked Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Shifting strategy for efficient block‐based non‐linear model predictive control using real‐time iterations

Villarreal

Rossiter

2020

IET Control Theory & Applications

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Data‐driven coordination of subproblems in enterprise‐wide optimization under organizational considerations

Berg¹,

Petsagkourakis²,

Shah³

et al. 2023

AIChE Journal

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While decomposition techniques in mathematical programming are usually designed for numerical efficiency, coordination problems within enterprise-wide optimization are often limited by organizational rather than numerical considerations. We propose a "data-driven" coordination framework which manages to recover the same optimum as the equivalent centralized formulation while allowing coordinating agents to retain autonomy, privacy, and flexibility over their own objectives, constraints, and variables. This approach updates the coordinated, or shared, variables based on derivative-free optimization (DFO) using only coordinated variables to agent-level optimal subproblem evaluation "data." We compare the performance of our framework using different DFO solvers (CUATRO, Py-BOBYQA, DIRECT-L, GPyOpt) against conventional distributed optimization (ADMM) on three case studies: collaborative learning, facility location, and multiobjective blending. We show that in low-dimensional and nonconvex subproblems, the exploration-exploitation trade-offs of DFO solvers can be leveraged to converge faster and to a better solution than in distributed optimization.

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A Performance Analysis of Parallel Differential Dynamic Programming on a GPU

Plancher

Kuindersma

2020

Springer Proceedings in Advanced Robotics

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A block based ALADIN scheme for highly parallelizable direct Optimal Control

Cited by 24 publications

References 12 publications

Shifting strategy for efficient block‐based non‐linear model predictive control using real‐time iterations

Shifting strategy for efficient block‐based non‐linear model predictive control using real‐time iterations

Data‐driven coordination of subproblems in enterprise‐wide optimization under organizational considerations

A Performance Analysis of Parallel Differential Dynamic Programming on a GPU

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