Parallel Explicit Tube Model Predictive Control

Wang, Kai; Jiang, Yuning; Oravec, Juraj; Villanueva, Mario E.; Houska, Boris

doi:10.1109/cdc40024.2019.9029177

Cited by 9 publications

(12 citation statements)

References 31 publications

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“…Then, we propose to use the parameterized RNMPC scheme (12) to deliver the value function needed in the proposed second-order LSTDQ-learning algorithm. Then, the actionvalue function in (15) results from solving the same RNMPC scheme with its first input constrained to the delivered action a.…”

Section: B Robust Mpc Formulationmentioning

confidence: 99%

“…The gradient and Hessian of the function Q θ needed in (19) require one to compute the sensitivities of the optimal value of NLP (15). Let us define the Lagrange function L θ associated to the RNMPC problem (15) as follows:…”

Section: B Sensitivity Analysismentioning

confidence: 99%

“…Variable µ is the Lagrange multiplier vector associated to the inequality constraints of the RNMPC scheme. Let us label the primal variables for the RNMPC scheme as p = {X, U}, where X, U are the state and control input trajectories predicted by (15). Then, the primal-dual variables read as z = {p, λ, µ}.…”

Section: B Sensitivity Analysismentioning

confidence: 99%

“…Model-plant mismatch and disturbances can be treated via Robust NMPC (RNMPC) techniques. For linear MPC models and polytopic disturbance models and constraints, tube-based MPC techniques provides computationally effective techniques [15], [16]. Treating nonlinear MPC models or generic disturbances and constraints is more challenging [17].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Approximate Robust NMPC using Reinforcement Learning

Esfahani¹,

Kordabad²,

Gros³

2021

Preprint

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We present a Reinforcement Learning-based Robust Nonlinear Model Predictive Control (RL-RNMPC) framework for controlling nonlinear systems in the presence of disturbances and uncertainties. An approximate Robust Nonlinear Model Predictive Control (RNMPC) of low computational complexity is used in which the state trajectory uncertainty is modelled via ellipsoids. Reinforcement Learning is then used in order to handle the ellipsoidal approximation and improve the closed-loop performance of the scheme by adjusting the MPC parameters generating the ellipsoids. The approach is tested on a simulated Wheeled Mobile Robot (WMR) tracking a desired trajectory while avoiding static obstacles.

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Section: B Robust Mpc Formulationmentioning

confidence: 99%

Section: B Sensitivity Analysismentioning

confidence: 99%

Section: B Sensitivity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximate Robust NMPC using Reinforcement Learning

Esfahani¹,

Kordabad²,

Gros³

2021

Preprint

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“…The first input is applied to the real system, and the problem is solved at each time instant based on the latest state of the system. The advantage of MPC is its ability to explicitly support state and input constraints, while producing a nearly optimal policy [12]. However, model uncertainties can severely impact the performance of the MPC policy.…”

Section: Introductionmentioning

confidence: 99%

Reinforcement Learning based on Scenario-tree MPC for ASVs

Kordabad

Esfahani

Lekkas

et al. 2021

2021 American Control Conference (ACC)

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In this paper, we present the use of Reinforcement Learning (RL) based on Robust Model Predictive Control (RMPC) for the control of an Autonomous Surface Vehicle (ASV). The RL-MPC strategy is utilized for obstacle avoidance and target (set-point) tracking. A scenario-tree robust MPC is used to handle potential failures of the ship thrusters. Besides, the wind and ocean current are considered as unknown stochastic disturbances in the real system, which are handled via constraints tightening. The tightening and other cost parameters are adjusted by RL, using a Q-learning technique. An economic cost is considered, minimizing the time and energy required to achieve the ship missions. The method is illustrated in simulation on a nonlinear 3-DOF model of a scaled version of the Cybership II.

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Explicit model predictive control through robust optimization

2023

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A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete‐time uncertain linear systems is presented. We consider uncertain processes, affected by box‐bounded multiplicative uncertainty as well as bounded additive uncertainty with linear state and inputs constraints. The proposed method includes (i) the calculation of a terminal set constraint and (ii) the robust reformulation of state constraints in the prediction horizon. These features allow the derivation of the desired policy by solving a single multiparametric quadratic programming problem that guarantees feasible operation in the presence of uncertainty. Additionally, we employ variable and constraint elimination approaches to enhance the computational performance of the strategy. We demonstrate the steps and benefits of these developments with a numerical example and a chemical engineering case study.

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Parallel Explicit Tube Model Predictive Control

Cited by 9 publications

References 31 publications

Approximate Robust NMPC using Reinforcement Learning

Approximate Robust NMPC using Reinforcement Learning

Reinforcement Learning based on Scenario-tree MPC for ASVs

Explicit model predictive control through robust optimization

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