Polytopic Approximation of Explicit Model Predictive Controllers

Jones, Colin N.; Morari, Manfred

doi:10.1109/tac.2010.2047437

Cited by 97 publications

(52 citation statements)

References 31 publications

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“…for all x ∈ R. Proof: Follows as consequence ofû(x) expressed as an interpolation by barycentric coordinates [10], [26]. Lemma 2 leads us to the following result.…”

Section: A Stability Guarantees Of Approximate Controllersmentioning

confidence: 85%

A Multiresolution Approximation Method for Fast Explicit Model Predictive Control

Summers

Jones

Lygeros

et al. 2011

IEEE Trans. Automat. Contr.

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Abstract-A model predictive control law is given by the solution to a parametric optimization problem that can be precomputed offline and provides an explicit map from state to control input. In this paper, an algorithm is introduced based on wavelet multiresolution analysis that returns a low complexity explicit model predictive control law built on a hierarchy of second order interpolets. The resulting interpolation is shown to be everywhere feasible and continuous. Further, tests to confirm stability and to compute a bound on the performance loss are introduced. Since the controller approximation is built on a grid hierarchy, convergence to a stabilizing control law is guaranteed and the evaluation of the control law in real-time systems is naturally fast and runs in a bounded logarithmic time. Two examples are provided; A two-dimensional example with an evaluation speed of 31 ns and a four-dimensional example with an evaluation speed of 119 ns.

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“…for all x ∈ R. Proof: Follows as consequence ofû(x) expressed as an interpolation by barycentric coordinates [10], [26]. Lemma 2 leads us to the following result.…”

Section: A Stability Guarantees Of Approximate Controllersmentioning

confidence: 85%

A Multiresolution Approximation Method for Fast Explicit Model Predictive Control

Summers

Jones

Lygeros

et al. 2011

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The -optimal‖ solution also includes the consideration of online computation time frame, memory size and performance. In ) and (Jones and Morari 2010), direct approximations for inner and/or outer polytopic convex sets are applied to pre-specify the number of pieces in an EMPC problem. Also, an input to state stability approach is developed in Genuit, et al (2012) so the approximation errors can be bounded to preserve the closed-loop stability of the approximation method.…”

Section: Approximate Methods Based Empcmentioning

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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“…We define the j-th iteration cost as the cost (12) of the j-th trajectory at time t = 0, Finally we define the, barycentric function (Jones and Morari (2010))…”

Section: Terminal Costmentioning

confidence: 99%

Learning Model Predictive Control for Iterative Tasks: A Computationally Efficient Approach for Linear System

Rosolia

Borrelli

2017

IFAC-PapersOnLine

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A Learning Model Predictive Controller (LMPC) for linear system is presented. The proposed controller builds on previous work on nonlinear LMPC and decreases its computational burden for linear system. The control scheme is reference-free and is able to improve its performance by learning from previous iterations. A convex safe set and a terminal cost function are used in order to guarantee recursive feasibility and non-increasing performance at each iteration. The paper presents the control design approach, and shows how to recursively construct the convex terminal set and the terminal cost from state and input trajectories of previous iterations. Simulation results show the effectiveness of the proposed control logic.

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Polytopic Approximation of Explicit Model Predictive Controllers

Cited by 97 publications

References 31 publications

A Multiresolution Approximation Method for Fast Explicit Model Predictive Control

A Multiresolution Approximation Method for Fast Explicit Model Predictive Control

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

Learning Model Predictive Control for Iterative Tasks: A Computationally Efficient Approach for Linear System

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