Application of Interior-Point Methods to Model Predictive Control

Rao, Chu-Feng; Wright, Stephen J.; Rawlings, James B.

doi:10.1023/a:1021711402723

Cited by 471 publications

(404 citation statements)

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“…Nevertheless, the technique has also been adopted in many other fields such as automotive, medical and aerospace applications along with faster onboard computers and better quadratic programming (QP) solvers, e.g. (Rao, et al, 1998). The prosperous progress of the algorithm was aroused after a systematic analysis of the stability issues achieved by Mayne (2000).…”

Section: Model Predictive Control (Mpc) 23mentioning

confidence: 99%

1-Bit processing based model predictive control for fractionated satellite missions

Bai

2014

Acta Astronautica

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In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller.As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work.Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components.Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission.The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers. V VI

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Section: Model Predictive Control (Mpc) 23mentioning

confidence: 99%

1-Bit processing based model predictive control for fractionated satellite missions

Bai

2014

Acta Astronautica

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“…The future states can be kept as decision variables and the system dynamics can be incorporated into the problem by enforcing equality constraints (Rao, Wright, and Rawlings, 1998;Wright, 1993Wright, , 1996. In this case, for any arbitrary K, if we let θ := [x T v T ] T where…”

Section: Non-condensed Approachmentioning

confidence: 99%

“…The resulting banded matrix has a half-band of size 2n + m. Such a linear system can be solved using a banded LDL T factorization in N (2n+m) 3 +4N (2n+m) 2 +N (2n+m) flops (Boyd and Vandenberghe, 2004, App. C), or through a block factorization method based on a sequence of Cholesky factorizations in O(N (n + m) 3 ) operations (Rao, Wright, and Rawlings, 1998). The memory requirements can be approximated by the cost of storing matrices H, G, F and A k , which are all sparse.…”

Section: Non-condensed Approachmentioning

confidence: 99%

“…In this case, the complexity of solving the QP scales cubically in the horizon length when using an interior-point method. For MPC problems that require long horizon lengths, the noncondensed formulation, which keeps the states as decision variables and considers the system dynamics implicitly by enforcing equality constraints (Rao, Wright, and Rawlings, 1998;Wright, 1993Wright, , 1996, can result in significant speed-ups. With this approach the problem becomes larger but its structure can be exploited to find a solution in time linear in the horizon length.…”

Section: Introductionmentioning

confidence: 99%

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A sparse and condensed QP formulation for predictive control of LTI systems

2012

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The computational burden that model predictive control (MPC) imposes depends to a large extent on the way the optimal control problem is formulated as an optimization problem. We present a formulation where the input is expressed as an affine function of the state such that the closed-loop dynamics matrix becomes nilpotent. Using this approach and removing the equality constraints leads to a compact and sparse optimization problem to be solved at each sampling instant. The problem can be solved with a cost per interior-point iteration that is linear with respect to the horizon length, when this is bigger than the controllability index of the plant. The computational complexity of existing condensed approaches grow cubically with the horizon length, whereas existing non-condensed and sparse approaches also grow linearly, but with a greater proportionality constant than with the method presented here.

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“…They, respectively, work in the spaces of dimension n U −n c , n c , n U and n U + n c where n U is the number of optimisation variables and n c the number of constraints. In the literature of model predictive control, the primal methods have dominated the numerical solutions (see for example, ) until recent years specially tailored interior-point methods applicable to MPC have appeared (see, for example (Rao, Wright, and Rawlings, 1998)). These algorithms solve the constrained control problem by utilising the special structure of the control system.…”

Section: Practical Solution Of the Qpmentioning

confidence: 99%