Towards a Nonlinear Model Predictive Control using the Extended Modal Series Method

Devia, Carlos Andrés; Roa, Maria Camila; Colorado, Julián; Patino, and Diego

doi:10.23919/ecc.2018.8550444

Cited by 3 publications

(2 citation statements)

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“…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].…”

Section: Introductionmentioning

confidence: 99%

“…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].…”

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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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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Pagone¹,

Boggio²,

Novara³

et al. 2022

Preprint

View full text Add to dashboard Cite

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Continuous-time nonlinear model predictive control based on Pontryagin Minimum Principle and penalty functions

Pagone,

Boggio,

Novara

et al. 2024

International Journal of Control

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

Pagone¹,

Boggio²,

Novara³

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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We propose a Nonlinear Model Predictive Control approach to spacecraft rendezvous in non-Keplerian Lunar orbits. The approach is based on the Pontryagin Minimum Principle and allows the accomplishment of minimum-propellant maneuvers. The relative motion between the chaser and the target is described by the nonlinear and unstable dynamics of the circular restricted three body-problem. In the proposed formulation, we design a minimum-propellant controller, which leads to a bang-bang behavior of the control signal. Under suitable assumptions, simplified dynamics is employed as prediction model, in order to reduce the complexity of the controller algorithm but, at the same time, without penalizing the controller tracking performance. The proposed approach's effectiveness is validated by a simulation example.

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Towards a Nonlinear Model Predictive Control using the Extended Modal Series Method

Cited by 3 publications

References 8 publications

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

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

Continuous-time nonlinear model predictive control based on Pontryagin Minimum Principle and penalty functions

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

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