Sequential ℓ1 Quadratic Programming for Nonlinear Model Predictive Control

Boiroux, Dimitri; Jørgensen, John Bagterp

doi:10.1016/j.ifacol.2019.06.107

Cited by 8 publications

(8 citation statements)

References 16 publications

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“…Secondly, the absolute value function is not differentiable, which means that the classical gradient-based optimisation method cannot be used. In spite of the second of the mentioned computational difficulties, in the literature, is it possible to find applications of gradient-based nonlinear optimisation methods to solve the MPC-L

optimisation task ( 5 ) [ 23 , 24 , 28 ]. The objective of this work is to derive a much more computationally simple approach to the MPC-L

problem in which nonlinear optimisation is not used.…”

Section: Computationally Efficient Nonlinear Mpc Using the L Cost-functionmentioning

confidence: 99%

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Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

Ławryńczuk

Nebeluk

2021

Sensors

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Model Predictive Control (MPC) algorithms typically use the classical L2 cost function, which minimises squared differences of predicted control errors. Such an approach has good numerical properties, but the L1 norm that measures absolute values of the control errors gives better control quality. If a nonlinear model is used for prediction, the L1 norm leads to a difficult, nonlinear, possibly non-differentiable cost function. A computationally efficient alternative is discussed in this work. The solution used consists of two concepts: (a) a neural approximator is used in place of the non-differentiable absolute value function; (b) an advanced trajectory linearisation is performed on-line. As a result, an easy-to-solve quadratic optimisation task is obtained in place of the nonlinear one. Advantages of the presented solution are discussed for a simulated neutralisation benchmark. It is shown that the obtained trajectories are very similar, practically the same, as those possible in the reference scheme with nonlinear optimisation. Furthermore, the L1 norm even gives better performance than the classical L2 one in terms of the classical control performance indicator that measures squared control errors.

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optimisation task ( 5 ) [ 23 , 24 , 28 ]. The objective of this work is to derive a much more computationally simple approach to the MPC-L

problem in which nonlinear optimisation is not used.…”

Section: Computationally Efficient Nonlinear Mpc Using the L Cost-functionmentioning

confidence: 99%

“…Examples of nonlinear MPC-L

algorithms in which the Sequential Quadratic Programming algorithm is used are described in [ 23 , 24 ]. A trust-region sequential quadratic programming method is used in [ 28 ].…”

Section: Introductionmentioning

confidence: 99%

Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

Ławryńczuk

Nebeluk

2021

Sensors

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“…Remark 1: The optimization problem (3) is numerically hard to tackle, since u is a continuous-time signal and thus the number of decision variables is infinite. The direct solution of the OCP requires a finite parametrization of the input signal u (see, e.g., [24]). For example, as illustrated in Section V a piece-wise constant parametrization can be assumed, with changes of value at the nodes τ 1 , .…”

Section: Nmpc Frameworkmentioning

confidence: 99%

“…To sum up, the proposed NMPC framework shows the following advantages: i) conversely to the numerical methods where a discretization of state, input and constraints before optimization is required [24], the PMP-based solution does not need the input parametrization anymore, resulting in a better accuracy in tracking the reference; ii) the PMP-based NMPC seems to perform an more efficient trade-off between computational complexity and final reference tracking with respect to the direct methods, making him suitable for on-line applications.…”

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confidence: 99%

A barrier function approach to constrained Pontryagin-based Nonlinear Model Predictive Control

Pagone¹,

Boggio²,

Novara³

et al. 2022

Preprint

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A Pontryagin-based approach to solve a class of constrained Nonlinear Model Predictive Control problems is proposed which employs the method of barrier functions for dealing with the state constraints. Unlike the existing works in literature the proposed method is able to cope with nonlinear input and state constraints without any significant modification of the optimization algorithm. A stability analysis of the closed-loop system is carried out by using the L 2 -norm of the predicted state tracking error as a Lyapunov function. Theoretical results are tested and confirmed by numerical simulations on the Lotka-Volterra prey/predator system. I. INTRODUCTIONOver the last years, Model Predictive Control (MPC) has been accepted as a powerful control tool for a wide range of technological applications [1], [2], thanks to its capability to design control algorithms for multivariate systems under state, input, and output constraints. The resulting controller also provide optimality of a predefined performance index.The key point of the MPC design is the method for addressing optimal control problems (OCP) with receding horizon. To cope with nonlinear dynamics and constraints, as well as with non-convex performance indexes, Nonlinear MPC (NMPC) have been introduced (see, e.g. [3] and references therein). To find the global optimum in this situation is difficult, optimization algorithms are computationally intensive and, in general, the solution rarely admits an explicit closed-form representation [4], [5].In this paper, we propose a solution that is based on the Pontryagin's Minimum Principle (PMP)[6]: under some assumptions on the Hamiltonian function, we can obtain an explicit control law -as function of the state and the costate -even if the system dynamics and/or constraints are nonlinear. The price paid for this is the necessity to solve a Two-Points Boundary Value Problem (TPBVP) in order to find the state and co-state functions. The first applications of the PMP to receding horizon control date back to works by [7], [8] and [9] who have also established important higher degree optimality conditions based on the theory of Lie algebras.Although TPBVP problems usually cannot be solved analytically, a number of efficient numerical algorithms to solve OCP in real time have been proposed [10] such as, e.g., the stabilized continuation method [7] and its accelerated versions [11], the Newton-type algorithm [12] and the extended modal series method, approximating OCP with nonlinear constraints by standard LQR problems [13]. An efficient active set method of solving discrete-time PMP equations arising in MPC problems with input and terminal state constraints was developed in [14]. Continuous-time OCP can be accurately approximated by discrete-time ones as demonstrated by the recent work [15].Whereas initial and terminal state constraints can be accommodated by existing PMP-based MPC algorithms, direct application of PMP becomes problematic in the situation where the state vector is constrained at any time [3], [16]. In th...

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“…The Kernel functions (K) used in the SVR for this paper are linear (19), radial basis function (RBF) (18), and polynomial (20). For an overall evaluation, the quadratic programming (L1QP) [84], iterative single data algorithm optimization (ISDA) [85], and sequential minimal optimization (SMO) [86] optimizers were used. For the initial comparison of ensemble models, the linear Kernel function and the L1QP optimizer were adopted.…”

Section: Ensemble Learning Modelsmentioning

confidence: 99%

Fault Prediction Based on Leakage Current in Contaminated Insulators Using Enhanced Time Series Forecasting Models

Neto¹,

Stefenon²,

Meyer³

et al. 2022

Preprint

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To improve the monitoring of the electrical power grid it is necessary to evaluate the influence of contamination in relation to leakage current and its progression to a disruptive discharge. In this paper, insulators were tested in a saline chamber to simulate the increase of salt contamination on their surface, and to evaluate the supportability of these components. From the time series forecasting of the leakage current, it is possible to evaluate the development of the fault before a flashover occurs. Choosing which method to use is always a difficult task since some models may have higher computational effort. In this paper, for a complete evaluation, the long short-term memory (LSTM), group method of data handling (GMDH), adaptive neuro-fuzzy inference system (ANFIS), bootstrap aggregation (bagging), sequential learning (boosting), random subspace, and stacked generalization (stacking) ensemble learning models are analyzed. A review and comparison of these well-established methods for time series forecasting is performed. From the results of the best structure of the model, the hyperparameters are evaluated and the Wavelet transform is used to obtain an enhanced model.

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Sequential ℓ1 Quadratic Programming for Nonlinear Model Predictive Control

Cited by 8 publications

References 16 publications

Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

A barrier function approach to constrained Pontryagin-based Nonlinear Model Predictive Control

Fault Prediction Based on Leakage Current in Contaminated Insulators Using Enhanced Time Series Forecasting Models

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