Fast Gaussian Process based Model Predictive Control with Uncertainty Propagation

Nghiem, Truong X.; Nguyen, Trong-Doan; Le, Viet-Anh

doi:10.1109/allerton.2019.8919857

Cited by 3 publications

(13 citation statements)

References 10 publications

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“…To efficiently solve the optimization problem (22), we follow the concept of linear parameter-varying (LPV) predictive control of non-linear systems [23,24]. First, the dynamic equations of the prediction model are rewritten in an LPV form by selecting certain state-and input-dependent terms as scheduling variables.…”

Section: Efficient Solution By Lpv Iterationsmentioning

confidence: 99%

“…First, the dynamic equations of the prediction model are rewritten in an LPV form by selecting certain state-and input-dependent terms as scheduling variables. By considering a given scheduling trajectory, the approximative prediction model and the GP-MPC problem (22) reduces to a simple linear time-varying predictive control problem that can be rapidly solved by quadratic programming (QP). After solving the QP, the resulting input sequence is then applied to simulate the approximative non-linear predictive model and based on the resulting state response, the scheduling is updated and the previous steps are repeated.…”

Section: Efficient Solution By Lpv Iterationsmentioning

confidence: 99%

“…The majority of the GP-MPC implementations rely on the assumption that at every prediction time step, the state distribution can be well approximated by a normal distribution [9][10][11][12][13]. A few kernel functions even make it possible to compute the first two moments of the predicted output distribution analytically if the GP input is normally distributed [11][12][13][14]. This technique is often referred to as exact moment (EM) matching.…”

Section: Introductionmentioning

confidence: 99%

“…These approaches are based on a linearization of the optimization problem around a reference solution, and require the differentiation of the dynamic prediction model. Similar methods are available for non-linear systems with stochastic error processes [19,20] or GP-based stochastic autoregressive models based on predictive control [21,22]. However, the method of gradients may become computationally too intensive, when the moments of the GP-based state-prediction are computed with EM matching.…”

Section: Introductionmentioning

confidence: 99%

“…However, the method of gradients may become computationally too intensive, when the moments of the GP-based state-prediction are computed with EM matching. Hence, often only the Taylor approximation is used at the expanse of increased approximation error [12,22].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Efficient implementation of Gaussian process–based predictive control by quadratic programming

Polcz

Péni

Tóth

2023

IET Control Theory & Appl

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The paper addresses the problem of accelerating predictive control of non‐linear system models augmented with Gaussian processes (GP‐MPC). Due to the non‐linear and stochastic prediction model, predictive control of GP‐based models requires to solve a stochastic optimization problem. Different model simplification methods have to be applied to reformulate this problem to a deterministic, non‐linear optimization task that can be handled by a numerical solver. As these problems are still complex, especially with exact moment calculations, real‐time implementation of GP‐MPC is extremely challenging. The existing solutions accelerate the computations at the solver level by linearizing the non‐linear optimization problem and applying sequential convexification. In contrast, this paper proposes a novel GP‐MPC solution approach that without linearization formulates a series of surrogate quadratic programs (QP‐s) to iteratively obtain the solution of the original non‐linear optimization problem. The first step is embedding the non‐linear mean‐variance dynamics of the GP‐MPC prediction model in a linear parameter‐varying (LPV) structure and rewriting the constraints in parameter‐varying form. By fixing the scheduling trajectory at a known variation (based on previously computed or initial state‐input trajectories), optimization of the input sequence for the remaining varying linear model reduces to a linearly constrained quadratic program. After solving the QP, the non‐linear prediction model is simulated for the new control input sequence and new scheduling trajectories are updated. The procedure is iterated until the convergence of the scheduling, that is, the solution of the QP converges to the solution of the original non‐linear optimization problem. By designing a reference tracking controller for a 4DOF robot arm, we illustrate that the convergence is remarkably fast and the approach is computationally advantageous compared to current solutions. The proposed method enables the application of GP‐MPC algorithms even with exact moment matching on fast dynamical systems and requires only a QP solver.

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Section: Efficient Solution By Lpv Iterationsmentioning

confidence: 99%

Section: Efficient Solution By Lpv Iterationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient implementation of Gaussian process–based predictive control by quadratic programming

Polcz

Péni

Tóth

2023

IET Control Theory & Appl

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Learning‐based model predictive control for improved mobile robot path following using Gaussian processes and feedback linearization

Wang

Fader

Marshall

2023

Journal of Field Robotics

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This paper proposes a high‐performance path following algorithm that combines Gaussian processes (GP) based learning and feedback linearization (FBL) with model predictive control (MPC) for ground mobile robots operating in off‐road terrains, referred to as GP‐FBLMPC. The algorithm uses a nominal kinematic model and learns unmodeled dynamics as GP models by using observation data collected during field experiments. Extensive outdoor experiments using a Clearpath Husky A200 mobile robot show that the proposed GP‐FBLMPC algorithm's performance is comparable to existing GP learning‐based nonlinear MPC (GP‐NMPC) methods with respect to the path following errors. The advantage of GP‐FBLMPC is that it is generalizable in reducing path following errors for different paths that are not included in the GP models training process, while GP‐NMPC methods only work well on exactly the same path on which GP models are trained. GP‐FBLMPC is also computationally more efficient than the GP‐NMPC because it does not conduct iterative optimization and requires fewer GP models to make predictions over the MPC prediction horizon loop at every time step. Field tests show the effectiveness and generalization of reducing path following errors of the GP‐FBLMPC algorithm. It requires little training data to perform GP modeling before it can be used to reduce path‐following errors for new, more complex paths on the same terrain (see video at https://youtu.be/tC09jJQ0OXM).

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Gaussian Process Based Distributed Model Predictive Control for Multi-agent Systems using Sequential Convex Programming and ADMM

Nghiem

2020

2020 IEEE Conference on Control Technology and Applications (CCTA)

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Fast Gaussian Process based Model Predictive Control with Uncertainty Propagation

Cited by 3 publications

References 10 publications

Efficient implementation of Gaussian process–based predictive control by quadratic programming

Efficient implementation of Gaussian process–based predictive control by quadratic programming

Learning‐based model predictive control for improved mobile robot path following using Gaussian processes and feedback linearization

Gaussian Process Based Distributed Model Predictive Control for Multi-agent Systems using Sequential Convex Programming and ADMM

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