Nonlinear Model Predictive Control Problem Research Articles

Nonlinear model predictive control for trajectory-planning and tracking based on tilting technology to achieve vehicle obstacle avoidance

ABSTRACT High-speed autonomous vehicles can effectively improve the performance of obstacle-avoidance trajectory-planning and tracking control through integration with existing electronic control systems. However, relatively little research has been conducted in this field. This paper proposes a novel methodology of obstacle-avoidance trajectory-planning and tracking control based on active front-wheel steering integrated with tilting technology that can tilt the vehicle body toward the inside of the curve via active suspension when turning. The controller is designed using hierarchical control, in which the upper layer uses the point-mass vehicle model to design the trajectory-planning algorithm based on model predictive control. The lower layer uses the nonlinear vehicle model to design obstacle-avoidance tracking nonlinear model predictive control based on active steering integrated with tilt control. Then, the constrained nonlinear model predictive control problem is transformed into a constrained nonlinear programming problem, which is solved by sequential quadratic programming. Finally, simulations were performed using the CarSim/Simulink co-simulation platform. Two other hierarchical obstacle-avoidance tracking nonlinear model predictive controllers were designed as comparison objects. The simulation results show that the planning trajectory of the proposed integrated controller is closest to the obstacle. This controller effectively improves the vehicle obstacle-avoidance trajectory-tracking performance, handling stability, and maneuverability.

Asynchronous ADMM for nonlinear continuous‐time systems

AbstractThis paper presents synchronous as well as asynchronous formulations of the alternating direction method of multipliers (ADMM) for solving continuous‐time nonlinear distributed model predictive control (DMPC) problems. It is shown that the optimal control problems of certain system classes can be transformed to fit the consensus‐based ADMM variant problem formulation. The arising subproblems are solved locally on the agent level while the consensus step is solved centrally by a coordinator. Furthermore, the convergence of the synchronous and asynchronous ADMM algorithms to their respective first‐order optimality conditions is presented in a continuous‐time setting. The algorithm is applied to different example systems for which the convergence behavior and influence of the individual algorithmic parameters are investigated. The computation time of the agents remains unaffected by the system size and thus demonstrates the applicability to high‐scaled systems. Moreover, results show that the asynchronous algorithm performs better in terms of execution time when compared to its synchronous counterpart.

Multivariable robust tube-based nonlinear model predictive control of mammalian cell cultures

In this paper, the application of a robust nonlinear model predictive control (NMPC) framework to mammalian cell cultures is proposed, dealing with possible large kinetic parameter uncertainties. Industrial constraints formulated in view of good manufacturing practice and quality-by-design approach are also considered, namely the assurance that all state trajectories are contained within a corridor defined by lower and upper safety bounds. The latter are assimilated to the well-known tube-based paradigm which is used to formulate the corresponding robust NMPC problem. Both classical and tube-based NMPC performances are assessed in numerical simulations where specific key-species are regulated while dealing with an uncertain plant model. The capability of the tube-based method to reduce the impact of the parameter variations on the state trajectories and the violation of the constraints is highlighted, suggesting the transfer of the method on a real pharmaceutical process.

Notice of Violation of IEEE Publication Principles: Sequential Convex Programming for Collaboration of Connected and Automated Vehicles

Notice of Violation of IEEE Publication Principles<BR><BR>"Sequential Convex Programming for Collaboration of Connected and Automated Vehicles," <BR>by Xiaoxue Zhang, Jun Ma, Zilong Cheng, Frank L. Lewis, and Tong Heng Lee, <BR>in IEEE Transactions on Intelligent Vehicles, Early Access <BR><BR>After careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE’s Publication Principles. <BR><BR>This paper contains significant portions of original text from the paper cited below. The original text was copied without attribution (including appropriate references to the original author(s) and/or paper title) and without permission. <BR><BR>"Networked Model Predictive Control for Vehicle Collision Avoidance" <BR> by Bassam Alrifaee, <BR>in RWTH Aachen University, Dissertation, 04 May 2017 <BR>BR>"Sequential convex programming MPC for dynamic vehicle collision avoidance" <BR>by Bassam Alrifaee, Janis Maczijewski, Dirk Abel, <BR>in the Proceedings of the IEEE Conference on Control Technology and Applications, 2017, pp. 2202-2207 <BR><BR> <br/> This paper investigates the collaboration of multiple connected and automated vehicles (CAVs) in different scenarios. In general, the collaboration of CAVs can be formulated as a nonlinear and nonconvex MPC problem. Most of the existing approaches available for utilization to solve such an optimization problem suffer from the drawback of considerable computational burden, which hinders the practical implementation in real time. This paper proposes the use of SCP, which is a powerful approach to solving the nonlinear and nonconvex MPC problem in real time. To appropriately deploy the methodology, as a first stage, SCP requires linearization and discretization when addressing the nonlinear dynamics of the system model adequately. Based on the linearization and discretization, the original MPC problem can be transformed into a QCQP problem. Besides, SCP also involves convexification to handle the associated nonconvex constraints. Thus, the nonconvex QCQP can be reduced to a quadratic programming (QP) problem that can be solved rather quickly. Therefore, the computational efficiency is suitably improved despite the existence of nonlinear and nonconvex characteristics, whereby the implementation is realized in real time. Furthermore, simulation results in three different scenarios of autonomous driving are presented to validate the effectiveness and efficiency of our proposed approach.

Active set prediction for nonlinear model predictive control on a shrinking horizon based on the principle of optimality

SummaryWe provide insights into the structure of the set of active constraints arising for optimal solutions to nonlinear model predictive control problems along a shrinking horizon. The principle of optimality combined with a particular order of the constraints allows the prediction of the future active sets without solving the corresponding optimization problem. By describing the development of optimal active sets along a shrinking horizon, we state an important relationship for transferring ideas such as dynamic programming approaches from the linear to the nonlinear case. We further use the information about active and inactive constraints to rearrange and remove constraints of the original nonlinear program as described in previous work and thus simplify the problem. Numerical experiments show for the problem class treated here that the inherent robustness coming with the regional characteristic of the active sets with respect to the state space makes this approach useful also if uncertainties are present.

Scenario-based model predictive control with probabilistic human predictions for human–robot coexistence

This paper proposes a real-time motion planning scheme for safe human–robot workspace sharing relying on scenario-based nonlinear model predictive control (NMPC), a well-known approach for solving stochastic NMPC problems. A scenario tree is generated via higher-order Markov chains to provide probabilistic predictions of the human motion. Scenario-based NMPC is then used to generate point-to-point motions of the robot manipulator based on the above-mentioned human motion predictions, accounting for safety constraints via speed and separation monitoring (SSM). This means that the robot speed is always modulated to be able to stop before a possible collision with the human occurs. After proving theoretical properties on recursive feasibility and closed-loop stability of the proposed motion planning strategy, this is tested experimentally on a Kinova Gen3 robot interacting with a human operator, showing superior performance with respect to an NMPC scheme not relying on human predictions and to a fixed-path SSM strategy.

Efficient nonlinear model predictive motion controller for autonomous vehicles from standstill to extreme conditions based on split integration method

Autonomous driving motion control based on nonlinear model predictive control (NMPC) faces integration stability issues when driving at low speeds. However, this issue has not received sufficient attention or been adequately addressed. Ensuring integration stability requires the adoption of an implicit method, which incurs a high computational burden, making this phenomenon crucial to the performance of NMPC. In this paper, a split integration method is proposed to utilize the gradient-based augmented Lagrangian approach (GRAMPC) to solve the integration stability problem and significantly improve the efficiency of NMPC. The proposed split integration method integrates the explicit second-order Runge–Kutta (RK) method and the second-order L-stable Rosenbrock (ROS2) method. To enhance integration stability for the stiff part of the state equation, the ROS2 method is used. For the non-stiff part of the system, the RK method is used to improve its efficiency. This approach results in an efficient nonlinear NMPC system that can be adapted to full range speeds. Simulations and real-world experiments demonstrate that the low-speed integration stability problem of NMPC is entirely resolved without compromising its efficiency.

Lattice piecewise affine approximation of explicit nonlinear model predictive control with application to trajectory tracking of mobile robot

AbstractTo promote the widespread use of mobile robots in diverse fields, the performance of trajectory tracking must be ensured. To address the constraints and nonlinear features associated with mobile robot systems, nonlinear model predictive control (MPC) is applied to realize trajectory tracking of mobile robots. Specifically, to alleviate the online computational complexity of nonlinear MPC, this paper devises a lattice piecewise affine (PWA) approximation method that can approximate both the nonlinear system and control law of explicit nonlinear MPC. The kinematic model of the mobile robot is successively linearized along the trajectory to obtain a linear time‐varying description of the system, which is then expressed using a lattice PWA model. Subsequently, the nonlinear MPC problem can be transformed into a series of linear MPC problems. Furthermore, to reduce the complexity of online calculation of multiple linear MPC problems, the optimal solution of the linear MPCs is approximated by using the lattice PWA models. That is, for different sampling states, the optimal control inputs are obtained offline, and lattice PWA approximations are constructed for the state control pairs. Simulations are performed to evaluate the performance of the method in comparison with the state‐of‐the‐art methods, and the results show that the method has a higher online computing speed and can decrease the offline computing time without significantly increasing the tracking error.

Cautious Bayesian MPC: Regret Analysis and Bounds on the Number of Unsafe Learning Episodes

This paper investigates the combination of model predictive control (MPC) concepts and posterior sampling techniques and proposes a simple constraint tightening technique to introduce cautiousness during explorative learning episodes. The provided theoretical analysis in terms of cumulative regret focuses on previously stated sufficient conditions of the resulting ‘Cautious Bayesian MPC’ algorithm and shows Lipschitz continuity of the future reward function in the case of linear MPC problems. In the case of nonlinear MPC problems, it is shown that commonly required assumptions for nonlinear MPC optimization techniques provide sufficient criteria for model-based RL using posterior sampling. Furthermore, it is shown that the proposed constraint tightening implies a bound on the expected number of unsafe learning episodes in the linear and nonlinear case using a soft-constrained MPC formulation. The efficiency of the method is illustrated using numerical examples.

Frenet-Cartesian model representations for automotive obstacle avoidance within nonlinear MPC

In recent years, nonlinear model predictive control has been extensively used for solving automotive motion control and planning tasks. In order to formulate the nonlinear model predictive control problem, different coordinate systems can be used with different advantages. We propose and compare formulations for the nonlinear MPC related optimization problem, involving a Cartesian and a Frenet coordinate frame in a single nonlinear program. We specify costs and collision avoidance constraints in the more advantageous coordinate frame, derive appropriate formulations and compare different obstacle constraints. With this approach, we exploit the simpler formulation of opponent vehicle constraints in the Cartesian coordinate frame, as well as road-aligned costs and constraints related to the Frenet coordinate frame. Comparisons to other approaches in a simulation framework highlight the advantages of the proposed methods.

A constrained cooperative guidance algorithm based on gray wolf optimization against highly maneuvering target

This paper investigates the problem of cooperative guidance of two pursuers against an evader equipped with higher maneuverability. The goal is that the distance between the Evader and at least one of the pursuers becomes less than a predetermined threshold at the end of flight time. To achieve this goal, firstly, the roles of pursuers are divided into two units, which include (1) pursuing the Evader and (2) Observing the Evader’s escape space. Secondly, a new cooperative guidance algorithm based on the separation of roles of the pursuers is proposed and formulated into a constrained nonlinear model predictive control problem. An objective function with time-variant weighting factors is presented to evaluate the constrained guidance commands. The proposed guidance algorithm uses a gray wolf-based optimization algorithm to calculate the guidance commands.

Hybrid model predictive control for premixed natural gas engine as distributed generator

The access to electricity is increasing worldwide with a considerable growing rate per year. Unfortunately, traditional large fossil power technologies based on coal and oil lead to a major concern in environmental pollution, so the distributed power generation utilizing natural gas engine is taken into consideration. In this paper, a hybrid model predictive control (HMPC) strategy is proposed for natural gas engines in distributed power generation. The original fourth-order double-input double-output (DIDO) nonlinear engine model is transformed into two simpler models, one is a first-order model for air–fuel ratio (AFR) control, and a linear model predictive control (LMPC) strategy is designed. The other is a second-order nonlinear model for speed control, and the AFR is used as one of its two inputs to design nonlinear model predictive control (NMPC) strategy. The advantage of this is that each model is simpler than the original fourth-order model, and prediction horizon can be lengthened to achieve better control performance. For the optimization problem of NMPC, a switching mechanism strategy is proposed. It can effectively reduce the number of SQP iterations in both transient and steady-state conditions. Both simulations and experiments verify the feasibility of the HMPC and the effectiveness of the switching mechanism.

Model predictive impedance control with Gaussian processes for human and environment interaction

Robotic tasks which involve uncertainty – due to variation in goal, environment configuration, or confidence in task model – may require human input to instruct or adapt the robot. In tasks with physical contact, several existing methods for adapting robot trajectory or impedance according to individual uncertainties have been proposed, e.g., realizing intention detection or uncertainty-aware learning from demonstration. However, isolated methods cannot address the wide range of uncertainties jointly present in many tasks.To improve generality, this paper proposes a model predictive control (MPC) framework which plans both trajectory and impedance online, can consider discrete and continuous uncertainties, includes safety constraints, and can be efficiently applied to a new task. This framework can consider uncertainty from: contact constraint variation, uncertainty in human goals, or task disturbances. An uncertainty-aware task model is learned from a few (≤3) demonstrations using Gaussian Processes. This task model is used in a nonlinear MPC problem to optimize robot trajectory and impedance according to belief in discrete human goals, human kinematics, safety constraints, contact stability, and frequency-domain disturbance rejection. This MPC formulation is introduced, analyzed with respect to convexity, and validated in co-manipulation with multiple goals, a collaborative polishing task, and a collaborative assembly task.

Neighboring extremal nonlinear model predictive control of a rigid body on SO(3)

AbstractThe issue of implementing nonlinear model predictive control (NMPC) on mechanical systems evolving on special orthogonal group (SO(3)) is taken into consideration in the first place. Necessary conditions of optimality are extracted based on Lie group variational integrators, leading to a two-point boundary value problem (TPBVP) which is solved using sensitivity derivatives and indirect shooting methods. Fast Newton-like methods referred to as fast solvers which are commonly used to solve the TPBVP are established based on the repetition of a nonlinear process. The numerical schemes employed to alleviate the computation burden consist of eliminating some constraint-related but non-essential terms in the trend of sensitivity derivatives calculation and for solving the TPBVP equations. As another claim, assuming that a first attempt to resolve the NMPC problem is accessible, the problem subjected to some changes in its initial conditions (due to some re-planning schemes) can be resolved cost-effectively based on it. Instead of solving the whole optimization process from the scratch, the optimal control inputs and states of the system are updated based on the neighboring extremal (NE) method. For this purpose, two approaches are considered: applying NE method on the first solution that leads to a neighboring optimal solution, or assisting this latter by updating the NMPC-related optimization using exact TPBVP equations at some predefined intermediate steps. It is shown through an example that the first method is not accurate enough due to error accumulations. In contrast, the second method preserves the accuracy while reducing the computation time significantly.

Real-time nonlinear model predictive control for optimizing the ammonia coverage ratio of an SCR system based on TC-QPSO

SCR systems with complex chemical reaction dynamics are important components of emission aftertreatment systems. Their contradictory emission requirements of higher NOx conversion efficiency and lower NH3 slip can be simultaneously achieved by optimizing the ammonia coverage ratio, which can be accomplished with a nonlinear model predictive control (NMPC) framework. However, how to find a reasonable NMPC approach for optimizing the ammonia coverage ratio and utilize an appropriate method to solve it remain a formidable challenge. In this paper, a two-layer hierarchical control framework for an SCR system is developed to decouple the optimization and tracking control of the ammonia coverage ratio. In the upper layer, an NMPC controller with a long prediction horizon is designed to account for the emission objectives and constraints and generate optimal trajectories for the ammonia coverage ratio. In the lower layer, a robust observing and tracking controller with a short horizon is employed which takes the planned trajectories as the tracking target. Moreover, an improved thermonuclear-initiation and cross-boundary quantum-behaved particle swarm optimization (TC-QPSO) method for optimizing the ammonia coverage ratio based on its dynamic characteristics is proposed to solve the NMPC problem. The simulation results show that the proposed TC-QPSO emission optimization effects of NOx and NH3 are closest to those of the SQP method (the benchmark controller) with a slight computation time penalty. The experimental results under the three transient cycles show that the average NOx conversion efficiency of the proposed two-layer hierarchical control framework with the TC-QPSO algorithm can reach more than 98% with an average NH3 slip of less than 11 ppm, which is able to satisfy emission requirements, and that compared to the traditional QPSO algorithm, the average NH3 slip of the proposed TC-QPSO algorithm is improved by 45.6% with an average NOx conversion efficiency penalty of 1.09% and its emission optimization effects have better robustness for uncertainties in transient cycles.

Microalgae Production and Maintenance Optimization via Mixed-Integer Model Predictive Control

This paper studies the joint production and maintenance scheduling in microalgae manufacturing systems comprised of multiple machines, which are subject to coupled production demand agreements and operational maintenance constraints. Namely, there are some microalgae production demands to be met over a given horizon, and the maintenance of each microalgae manufacturing unit must be done before a given deadline. Moreover, the number of units whose maintenance can be done simultaneously over the same day is limited, and the units that undergo maintenance cannot contribute to microalgae production during their maintenance day. To solve the considered problem, we design a mixed-integer nonlinear model predictive controller, which is implemented in two optimization stages. The former regards a mixed-integer model predictive control problem, while the latter considers a nonlinear model predictive control problem. The proposed approach allows us to decouple the mixed-integer and nonlinear parts of the whole problem, and thus provides more flexibility on the optimization solvers that can be employed. In addition, the first stage also evaluates the attainability of the demand agreements, and provides a mechanism to minimally adjust such constraints so that their satisfaction can be guaranteed at the second stage. The overall model predictive control approach is based on experimental data collected at VAXA Technologies Ltd., and the effectiveness of the proposed method is validated through numerical simulations including multiple manufacturing units and uncertainties.

Model predictive controlled subsurface drainage and irrigation for peatland groundwater management

A dynamic simulation model for the water balance in a field with controlled subsurface drainage and irrigation is derived. The model is then applied to groundwater table height control, using the model predictive control (MPC) paradigm. The nonlinear constrained MPC problem is solved and results illustrated in simulations. The role of automation of controlled subsurface drainage in cultivated peatlands is discussed.

Integrated approach to AUV docking based on nonlinear offset-free model predictive control

This study proposes an integrated docking approach for autonomous underwater vehicle (AUV), which directly generate control force and torque from visual guidance features to drive precise AUV docking. Accurate docking control has been constructed as nonlinear offset-free model predictive control (OFNMPC) problem to effectively deal with external disturbances, model mismatch, and various other constraints. For the problem of state and disturbance estimation required by OFNMPC, observers have been presented based on the extended Kalman filter (EKF) and moving horizon estimation (MHE). A visual observation model is proposed so that the observer can directly use visual measurements. OFNMPC was integrated with EKF and MHE, and the proposed OFNMPC-EKF and OFNMPC-MHE docking approaches were applied to an actual AUV model. The simulation results show that the proposed approaches could drive the AUV to complete accurate docking along a reasonable trajectory based on visual measurements. The navigation, guidance, and control functions of docking were effectively integrated. It was observed that in the presence of external disturbances and measurement noise, OFNMPC-EKF has better robustness.

Design for Real-Time Nonlinear Model Predictive Control With Application to Collision Imminent Steering

Model predictive control (MPC) is a competitive option in modern control systems due to its ability to account for future response and incorporation of complex control objectives. As applications become more intricate, nonlinearities limit the utility of linear control strategies, thus requiring more sophisticated architectures, often at a significant computational cost. This article investigates the computational cost of solving nonlinear MPC problems and provides a framework for designing nonlinear MPC architectures compatible with real-time performance. To motivate the computational complexity associated with nonlinear MPC, the design of an automotive collision imminent steering system and the controller is considered. Various trajectory optimization strategies are examined and compared for this application, identifying multiple-shooting-based Runge–Kutta explicit integration as the most suitable. The control algorithm is then mapped into a graphics processor unit-based hardware system, where special considerations of the parallel hardware architecture are discussed. Compared to the single-shooting solution as the benchmark, multiple shootings on parallel hardware achieve three orders of magnitude improvement in wall time, supporting real-time implementation.

N-GKLS: An NMPC problem generator and a test platform for NMPC solvers

Nonlinear Model Predictive Control (NMPC) solves a series of optimization problems online during the entire operational time of the controlled plant, and the performance of NMPC depends on the superiority of the solver embedded in NMPC. Traditionally, gradient-based deterministic methods are used as NMPC solvers, but metaheuristics are now becoming more and more popular for its ability to find the global optimal solution. In order to verify the superiorities of different algorithms to be NMPC solvers, a novel NMPC problem generator named NMPC-based GKLS generator (N-GKLS) is proposed. With the help of Optimal-Replace Method (ORM), a reliable comparison of the closed-loop performances result from receding horizon strategy in NMPC is guaranteed. In addition, comparison techniques named accumulated operational characteristic and accumulated operational zone are proposed to directly compare different optimization algorithms for solving various NMPC problems generated by N-GKLS. An auxiliary comparison table is also proposed to report numerical comparative results. In this way, N-GKLS is not only an NMPC problem generator, but also a test platform for verifying the superiorities of different algorithms as NMPC solvers. Finally, simulation results based on 8 metaheuristics and 3 deterministic methods are used to illustrate the effectiveness of the proposed N-GKLS. A corresponding MATLAB APP demo is designed and is available online: https://github.com/JiahongXu123/N-GKLS.