Recent Advances in Quadratic Programming Algorithms for Nonlinear Model Predictive Control

Kouzoupis, Dimitris; Frison, Gianluca; Zanelli, Andrea; Diehl, Moritz

doi:10.1007/s10013-018-0311-1

Cited by 71 publications

(44 citation statements)

References 69 publications

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“…where Z = {z ≤ z ≤ z} and λ ∈ R T nx is the vector of Lagrange multipliers associated with the equality constraints in (3). The dual problem of ( 3) is…”

Section: Algorithm a Augmented Lagrangian Methodsmentioning

confidence: 99%

“…Apart from small-scale linear timeinvariant (LTI) MPC problems whose explicit MPC control law can be obtained [2], deploying an MPC controller in an electronic control unit requires an embedded Quadratic Programming (QP) solver. In the past decades, the MPC community has made tremendous research efforts to develop embedded QP algorithms [3], based on interior-point methods [4], [5], active-set algorithms [6], [7], gradient projection methods [8], the alternating direction method of multiplier (ADMM) [9], [10], and other techniques [11]- [14].…”

Section: Introductionmentioning

confidence: 99%

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A Simple and Fast Coordinate-Descent Augmented-Lagrangian Solver for Model Predictive Control

Wu¹,

Bemporad²

2021

Preprint

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This paper proposes a novel Coordinate-Descent Augmented-Lagrangian (CDAL) solver for linear, possibly parameter-varying, model predictive control problems. At each iteration, an augmented Lagrangian (AL) subproblem is solved by coordinate descent (CD), whose computation cost depends linearly on the prediction horizon and quadratically on the state and input dimensions. CDAL is simple to implement and does not require constructing explicitly the matrices of the quadratic programming problem to solve. To favor convergence speed, CDAL employs a reverse cyclic rule for the CD method, the accelerated Nesterov's scheme for updating the dual variables, and a simple diagonal preconditioner. We show that CDAL competes with other state-of-the-art first-order methods, both in case of unstable linear time-invariant and prediction models linearized at runtime. All numerical results are obtained from a very compact, library-free, C implementation of the proposed CDAL solver.

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“…where Z = {z ≤ z ≤ z} and λ ∈ R T nx is the vector of Lagrange multipliers associated with the equality constraints in (3). The dual problem of ( 3) is…”

Section: Algorithm a Augmented Lagrangian Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Simple and Fast Coordinate-Descent Augmented-Lagrangian Solver for Model Predictive Control

Wu¹,

Bemporad²

2021

Preprint

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show abstract

“…We now return to control-affine dynamics (1). and recall when and how they can be transformed to a bilinear form through the Koopman canonical transform [18].…”

Section: B the Koopman Canonical Transformmentioning

confidence: 99%

“…The process of designing high performance controllers for agile robotic systems that satisfy state and actuation constraints is challenging for systems with important nonlinear dynamical effects. Model predictive control (MPC) can capture appropriate performance objectives and constraints, and it can be used with nonlinear dynamics models if carefully implemented [1]- [3]. However, obtaining a sufficiently accurate dynamical model is crucial to achieve good performance with nonlinear MPC (NMPC).…”

Section: Introductionmentioning

confidence: 99%

Quadrotor Trajectory Tracking with Learned Dynamics: Joint Koopman-based Learning of System Models and Function Dictionaries

Folkestad¹,

Wei²,

Burdick³

2021

Preprint

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Nonlinear dynamical effects are crucial to the operation of many agile robotic systems. Koopman-based model learning methods can capture these nonlinear dynamical system effects in higher dimensional lifted bilinear models that are amenable to optimal control. However, standard methods that lift the system state using a fixed function dictionary before model learning result in high dimensional models that are intractable for real time control. This paper presents a novel method that jointly learns a function dictionary and lifted bilinear model purely from data by incorporating the Koopman model in a neural network architecture. Nonlinear MPC design utilizing the learned model can be performed readily. We experimentally realized this method on a multirotor drone for agile trajectory tracking at low altitudes where the aerodynamic ground effect influences the system's behavior. Experimental results demonstrate that the learning-based controller achieves similar performance as a nonlinear MPC based on a nominal dynamics model in medium altitude. However, our learningbased system can reliably track trajectories in near-ground flight regimes while the nominal controller crashes due to unmodeled dynamical effects that are captured by our method.

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“…As we seek to deploy NMPC on dynamic robotic platforms, it is critical that these optimization problems are well conditioned and do not provide difficulty to numerical solvers. In particular, when B i in (14a) is positive semi-definite (p.s.d), the resulting QP is convex and can be efficiently solved [23,45].…”

Section: B Quadratic Approximation Strategymentioning

confidence: 99%

Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions

Grandia

Taylor

Singletary

et al. 2020

Robotics: Science and Systems XVI

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The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difficult cost function and parameter tuning required by NMPC. Therefore the unified controller improves the performance of each isolated controller and simplifies the overall design process.

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Recent Advances in Quadratic Programming Algorithms for Nonlinear Model Predictive Control

Cited by 71 publications

References 69 publications

A Simple and Fast Coordinate-Descent Augmented-Lagrangian Solver for Model Predictive Control

A Simple and Fast Coordinate-Descent Augmented-Lagrangian Solver for Model Predictive Control

Quadrotor Trajectory Tracking with Learned Dynamics: Joint Koopman-based Learning of System Models and Function Dictionaries

Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions

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