Differentiable predictive control: Deep learning alternative to explicit model predictive control for unknown nonlinear systems

Drgoňa, Ján; Kiš, Karol; Tuor, Aaron; Vrabie, Draguna; Klaučo, Martin

doi:10.1016/j.jprocont.2022.06.001

Cited by 27 publications

(8 citation statements)

References 54 publications

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“…ε−a (ν∆t + hx w + α max {a, b}). The final condition that must hold is (6), which can be checked using the following relations for y ∈ ∂C(t), x ∈ B η∆t (y): |h(x, t) − h(y, t)|= L x h x − y ≤ L x h η∆t and h(y, t) = 0 such that |h(x, t)|≤ L x h η∆t =: h, where L x h is the Lipschitz constant of h(x, t) on Ā × R. We also note that here X ⊆ R nx such that D = C ∪ Ā ⊂ X , and so the conditions of Theorem 2 hold. For α = 0.5, a = 0.03, and b = 0.00001, h is a SD-ZCBFII.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The control policy is a neural network trained offline via stochastic gradient descent with gradients obtained from automatic differentiation of the MPC problem cost functions and constraints. DPC has been implemented in several applications with high performance and low computational resources [5], [6]. There exist probabilistic guarantees of safety for DPC [3], but there are no deterministic, robustness guarantees that DPC will always satisfy the constraints and stabilize the system.…”

Section: Introductionmentioning

confidence: 99%

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Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach

Cortez¹,

Drgoňa²,

Tuor³

et al. 2022

Preprint

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We develop a novel form of differentiable predictive control (DPC) with safety and robustness guarantees based on control barrier functions. DPC is an unsupervised learning-based method for obtaining approximate solutions to explicit model predictive control (MPC) problems. In DPC, the predictive control policy parametrized by a neural network is optimized offline via direct policy gradients obtained by automatic differentiation of the MPC problem. The proposed approach exploits a new form of sampled-data barrier function to enforce offline and online safety requirements in DPC settings while only interrupting the neural network-based controller near the boundary of the safe set. The effectiveness of the proposed approach is demonstrated in simulation.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach

Cortez¹,

Drgoňa²,

Tuor³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The active control method exploited here [13] is an ALBC method, originally developed for dynamic control. The same approach can be applied in steady-state conditions, specifically for active wake steering.…”

Section: Hybrid Model-and Learning-based Control Methodsmentioning

confidence: 99%

“…Note that a key challenge with purely learningbased methods is that they can require a long time to train; therefore, hybrid model-and learning-based solutions, such as the solutions proposed in [13], showed to train faster than RL. To this end, hybrid methods have also shown interesting features for realworld problems, such as building control, but have not been tested on wind farm control.…”

Section: Introductionmentioning

confidence: 99%

Data–Driven Wake Steering Control for a Simulated Wind Farm Model

Simani¹,

Farsoni²,

Castaldi³

2023

Int. J. Robot. Autom. Technol.

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Upstream wind turbines yaw to divert their wakes away from downstream turbines, increasing the power produced. Nevertheless, the majority of wake steering techniques rely on offline lookup tables that translate a set of parameters, including wind speed and direction, to yaw angles for each turbine in a farm. These charts assume that every turbine is working well, however they may not be very accurate if one or more turbines are not producing their rated power due to low wind speed, malfunctions, scheduled maintenance, or emergency maintenance. This study provides an intelligent wake steering technique that, when calculating yaw angles, responds to the actual operating conditions of the turbine. A neural network is trained live to determine yaw angles from operating conditions, including turbine status, using a hybrid model and a learning-based method, i.e. an active control. The proposed control solution does not need to solve optimization problems for each combination of the turbines’ non-optimal working conditions in a farm; instead, the integration of learning strategy in the control design enables the creation of an active control scheme, in contrast to purely model-based approaches that use lookup tables provided by the wind turbine manufacturer or generated offline. The suggested methodology does not necessitate a substantial amount of training samples, unlike purely learning-based approaches like model-free reinforcement learning. In actuality, by taking use of the model during back propagation, the suggested approach learns more from each sample. Based on the flow redirection and induction in the steady state code, results are reported for both normal (nominal) wake steering with all turbines operating as well as defective conditions. It is a free tool for optimizing wind farms that The National Renewable Energy Laboratory (USA) offers. These yaw angles are contrasted and checked with those discovered through the resolution of an optimization issue. Active wake steering is made possible by the suggested solution, which employs a hybrid model and learning-based methodology, through sample efficient training and quick online evaluation. Finally, a hardware-in-the-loop test-bed is taken into consideration for assessing and confirming the performance of the suggested solutions in a more practical setting.

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“…In the literature the performance of MPC has been enhanced in many different ways taking advantage of machine learning techniques, by learning or improving the prediction model [26], or by obtaining explicit MPC laws to reduce the computation time [11,27]. Other works propose learning techniques to adapt the parameters of the MPC optimisation problem to improve its performance: in [15,25] bayesian optimisation is used to optimise an LQR controller (hence without enforcing constraints on states and inputs); In [5] the best linear model that approximates the nonlinear dynamics of a robotic system is chosen using bayesian optimisation in order to maximise the controller performance.…”

Section: Introductionmentioning

confidence: 99%

Learning-based MPC using Differentiable Optimisation Layers for Microgrid Energy Management

Casagrande,

Boem

2023

2023 European Control Conference (ECC)

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In this paper we present a learning-based Model Predictive Control (MPC) algorithm based on differentiable optimisation layers. Recent works show that it is possible to include an optimisation problem as a network layer in a Neural Network (NN) architecture. Here the MPC optimisation problem is integrated on the last layer of a NN which is used to estimate the uncertain parameters of the objective function. The NN is then trained online, end-to-end (E2E), based on previous control actions performance. We show that directly targeting the optimality of the control actions leads to improved control results with respect to the standard method of estimating the uncertain parameters and then perform the optimisation. The effectiveness of the proposed method is illustrated on a microgrid energy management problem where the future profile of the electricity price is not known.

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Differentiable predictive control: Deep learning alternative to explicit model predictive control for unknown nonlinear systems

Cited by 27 publications

References 54 publications

Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach

Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach

Data–Driven Wake Steering Control for a Simulated Wind Farm Model

Learning-based MPC using Differentiable Optimisation Layers for Microgrid Energy Management

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