Nonlinear Model Predictive Control Technique Research Articles

Planar curved path following controller for a small fixed-wing unmanned aerial vehicle with constrained parameters optimized by nonlinear model predictive control

Path following presents a pivotal challenge within the realm of small fixed-wing unmanned aerial vehicles. Firstly, a Lyapunov-stable path guidance law was formulated to follow specific planar curved paths. To ensure differentiability of the guidance law, a modified, smooth saturation function was derived. Secondly, an analysis was conducted to ascertain the interrelationship between control parameters and input constraints, thereby identifying the relevant parameter domains. Thirdly, the nonlinear model predictive control technique was harnessed to optimize both guidance law parameters, enhancing the unmanned aerial vehicle’s capacity to achieve optimal performance in both straight-line and circular path following, hereafter referred to as PFC_NMPC. By leveraging Lyapunov stability arguments for switched systems, the stability of the corresponding nonlinear switched system was guaranteed. In this study, square and circular paths were generated to assess the path-following control of a simulated fixed-wing unmanned aerial vehicle. The performance of various guidance laws, including those with fixed parameters (PFC), those with parameters tuned using fuzzy logic (PFC_FL), PFC_NMPC, vector field, and pure pursuit with line-of-sight, was compared. Notably, the proposed PFC_NMPC method exhibited the ability to expedite the unmanned aerial vehicle’s convergence to the desired path while maximizing the effective flight path length.

Design of a tracking controller for autonomous articulated heavy vehicles using a nonlinear model predictive control technique

This article proposes a design of a tracking controller for autonomous articulated heavy vehicles (AAHVs) using a nonlinear model predictive control (NLMPC) technique. Despite economic and environmental benefits in freight transportation, articulated heavy vehicles (AHVs) exhibit poor directional performance due to their large sizes, multi-unit vehicle configurations, and high centers of gravity (CGs). AHVs represent a 7.5 times higher risk of traffic accidents than single-unit vehicles (e.g. rigid trucks, cars, etc.) in highway operations. Human driver errors cause about 94% of traffic collisions. However, little attention has been paid to autonomous driving control of AHVs. To increase the safety of AHVs, we design a novel NLMPC-based tracking controller for an AHV, that is, a tractor/semi-trailer combination, and this tracking controller is distinguished from others with the feature of controlling both the lateral and longitudinal motions for both the leading and trailing units. To design the tracking controller, a new prediction AHV model is developed, which represents both the lateral and longitudinal dynamics of the vehicle and captures its rearward amplification feature over high-speed evasive maneuvers. With the proposed tracking controller, the AAHV tracks the predefined reference path and follows a planned forward-speed scheme. Co-simulation demonstrates the effectiveness and robustness of the proposed NLMPC tracking controller.

Improved nonlinear model predictive control with inequality constraints using particle filtering for nonlinear and highly coupled dynamical systems

Abstract Motion planning and controller design are challenging tasks for highly coupled and nonlinear dynamical systems such as autonomous vehicles and robotic applications. Nonlinear model predictive control (NMPC) is an emerging technique in which sampling-based methods are used to synthesize the control and trajectories for complex systems. In this study, we have developed the sampling-based motion planning algorithm with NMPC through Bayesian estimation to solve the online nonlinear constrained optimization problem. In the literature, different filtration techniques have been applied to extract knowledge of states in the presence of noise. Due to the detrimental effects of linearization, the Kalman filter with NMPC only achieves modest effectiveness. Moving horizon estimation (MHE), on the other hand, frequently relies on simplifying assumptions and lacks an effective recursive construction. Additionally, it adds another optimization challenge to the regulation problem that has to be solved online. To address this problem, particle filtering is implemented for Bayesian filtering in nonlinear and highly coupled dynamical systems. It is a sequential Monte Carlo method that involves representing the posterior distribution of the state of the system using a set of weighted particles that are propagated through time using a recursive algorithm. For nonlinear and strongly coupled dynamical systems, the novel sampling-based NMPC technique is effective and simple to use. The efficiency of the suggested method has been assessed using simulated studies.

An optimization approach to extend control period for dynamics control of Autonomous Underwater Vehicles with X-form rudders

This paper addresses the challenge of dynamics control with a long control period for an Autonomous Underwater Vehicle (AUV) equipped with four independent stern control planes. The goal is to minimize frequent actuator operations. To tackle the difficulties posed by the extended control period, the paper proposes a hierarchy controller architecture comprising high-level dynamics control and low-level control allocation. The dynamics controller is developed using the Nonlinear Model Predictive Control (NMPC) technique. It aims to generate optimal virtual steering moments while considering the differences in the periods of model updating, state prediction, and control output. Additionally, a constrained optimization problem is formulated for control allocation, taking into account the characteristics of the control planes. To validate the proposed approach, a test AUV is designed for experimental validation. The hydrodynamic parameters required for state prediction are identified through Computational Fluid Dynamics (CFD) analysis and verified by comparing characteristic indexes from maneuvering trials. Comparison with the Linear Quadratic Regulator (LQR) in dynamics control highlights that the proposed control methods offer a stable and effective control framework, particularly when dealing with a long control period.

Performance Assessment of the BLDC Motor in EV Drives using Nonlinear Model Predictive Control

In this paper, the Nonlinear Model Predictive Control (NMPC) technique is proposed for the control of BrushLess Direct Current (BLDC) motors to address the problem of over-excitation, specifically in Electric Vehicle (EV) applications. This over-excitation increases the overall energy consumption of the machine and eventually reduces the vehicle’s driving range. The developed NMPC incorporates a nonlinear model of the BLDC motor with EV load and obtains the optimal current through the optimal voltage applied to the machine to regulate the motor torque. The proposed NMPC is compared with three conventional control techniques, the Field-Oriented Control (FOC), the Direct Torque Control (DTC), and the hybrid (the combination of DTC and FOC) control. It is observed from the simulation results that the proposed NMPC controller is more energy efficient while maintaining performance. This paper also discusses the selection of the motor based on the specified vehicle requirements. This has been done by matching the vehicle speed-torque characteristic curve with the motor’s one.

Nonlinear Model Predictive Control of Single-Link Flexible-Joint Robot Using Recurrent Neural Network and Differential Evolution Optimization

A recurrent neural network (RNN) and differential evolution optimization (DEO) based nonlinear model predictive control (NMPC) technique is proposed for position control of a single-link flexible-joint (FJ) robot. First, a simple three-layer recurrent neural network with rectified linear units as an activation function (ReLU-RNN) is employed for approximating the system dynamic model. Then, using the RNN predictive model and model predictive control (MPC) scheme, an RNN and DEO based NMPC controller is designed, and the DEO algorithm is used to solve the controller. Finally, comparing numerical simulation findings demonstrates the efficiency and performance of the proposed approach. The merit of this method is that not only is the control precision satisfied, but also the overshoots and the residual vibration are well suppressed.

Steam Turbine Rotor Stress Control through Nonlinear Model Predictive Control

The current flexibility of the energy market requires operating steam turbines that have challenging operation requirements such as variable steam conditions and higher number of startups. This article proposes an advanced control system based on the Nonlinear Model Predictive Control (NMPC) technique, which allows to speed up the start-up of steam turbines and increase the energy produced while maintaining rotor stress as a constraint variable. A soft sensor for the online calculation of rotor stress is presented together with the steam turbine control logic. Then, we present how the computational cost of the controller was contained by reducing the order of the formulation of the optimization problem, adjusting the scheduling of the optimizer routine, and tuning the parameters of the controller itself. The performance of the control system has been compared with respect to the PI Controller architecture fed by the soft sensor results and with standard pre-calculated curves. The control architecture was evaluated in a simulation exploiting actual data from a Concentrated Solar Power Plant. The NMPC technique shows an increase in performance, with respect to the custom PI control application, and encouraging results.

Deep Reinforcement Learning for End-to-End Local Motion Planning of Autonomous Aerial Robots in Unknown Outdoor Environments: Real-Time Flight Experiments

Autonomous navigation and collision avoidance missions represent a significant challenge for robotics systems as they generally operate in dynamic environments that require a high level of autonomy and flexible decision-making capabilities. This challenge becomes more applicable in micro aerial vehicles (MAVs) due to their limited size and computational power. This paper presents a novel approach for enabling a micro aerial vehicle system equipped with a laser range finder to autonomously navigate among obstacles and achieve a user-specified goal location in a GPS-denied environment, without the need for mapping or path planning. The proposed system uses an actor–critic-based reinforcement learning technique to train the aerial robot in a Gazebo simulator to perform a point-goal navigation task by directly mapping the noisy MAV’s state and laser scan measurements to continuous motion control. The obtained policy can perform collision-free flight in the real world while being trained entirely on a 3D simulator. Intensive simulations and real-time experiments were conducted and compared with a nonlinear model predictive control technique to show the generalization capabilities to new unseen environments, and robustness against localization noise. The obtained results demonstrate our system’s effectiveness in flying safely and reaching the desired points by planning smooth forward linear velocity and heading rates.

A New Adaptive Explicit Nonlinear Model Predictive Control Design for a Nonlinear MIMO System: An Application to Twin Rotor MIMO System

This paper proposed an adaptive explicit nonlinear model predictive control (AENMPC) technique using multiple estimation models with a convex combination framework [18] for a class of nonlinear MIMO systems. Here, the explicit solution for the control signal is obtained from an optimal performance index which can be formulated without online optimization. In this work, a closed-form control law is developed by approximating the tracking error in the receding horizon by its Taylor series expansion. The control performance of any model-based control technologies explicitly depends on the quality of the unknown system parameters hence an adaptive parameter estimator is used to estimate the system parameter online [16,17]. To ensure the boundedness of the estimated parameter within a predefined compact region, a projection based adaptive law is used [43]. Using an aerodynamic laboratory set-up, known as the twin-rotor multi-input multi-output system (TRMS), the effectiveness of the proposed control algorithm has been verified. The complete state information of the system to the proposed adaptive controller is given from an extended Kalman filter based state observer. The performance of the proposed adaptive control algorithm has been verified successfully in simulations as well as real-time experimental setup of the TRMS model and compared with an existing control approach.

NMPC Through qLPV Embedding: A Tutorial Review of Different Approaches

Abstract Nonlinear Model Predictive Control (NMPC) formulations through quasi-Linear Parameter Varying (qLPV) embeddings have been brought to focus in recent literature. The qLPV realisation of the nonlinear dynamics yields linear predictions at each sampling instant. Thereby, these strategies generate online programs with reduced numerical burden, much faster to solve than the Nonlinear Programs generated with regular NMPC. The general lines of these methods: (i) The qLPV embedding is formulated with state-dependent scheduling parameters; (ii) Recursive extrapolation procedures are used to estimate the values of these parameters along the prediction horizon; (iii) These estimates are used to compute linear predictions, which are incorporated by the constrained optimisation procedure. This paper details the overall concept of these novel NMPC techniques and reviews two different (efficient) implementation options. Realistic academic examples are provided to illustrate their performances.

Horizontal Nonlinear Path Following Guidance Law for a Small UAV With Parameter Optimized by NMPC

In this study, the problem of guiding a small fixed-wing unmanned aerial vehicle (UAV) toward a predefined horizontal path is studied. A stable nonlinear guidance law, which is a function of the inertial positions and velocities of the UAV and the predefined path, is designed using Lyapunov stability arguments. The concept of the nonlinear model predictive control (NMPC) technique was applied to optimize a key parameter of the guidance law to improve the performance of the controller (PFC_NMPC), where the stability of the relative nonlinear system is maintained. The proposed method was verified in the MATLAB/Simulink environment to realize following the straight-line, square and circular paths. The path- following performance of the proposed method is compared with those of the guidance laws with parameter fixed (PFC) or tuned by fuzzy logic (PFC_FL). With the predictive ability, the proposed method can make the UAV fly more on the desired square and circular paths than the other two methods, PFC and PFC_FL. The error overshoot by using PFC_NMPC is much smaller than those by using the PFC and PFC_FL methods in the presence of wind at 8m/s.

A parametrized nonlinear predictive control strategy for relaxing COVID-19 social distancing measures in Brazil

The SARS-CoV-2 virus was first registered in Brazil by the end of February 2020. Since then, the country counts over 150000 deaths due to COVID-19 and faces a profound social and economic crisis; there is also an ongoing health catastrophe, with the majority of hospital beds in many Brazilian cities currently occupied with COVID-19 patients. Thus, a Nonlinear Model Predictive Control (NMPC) scheme used to plan appropriate social distancing measures (and relaxations) in order to mitigate the effects of this pandemic is formulated in this paper. The strategy is designed upon an adapted data-driven Susceptible–Infected–Recovered–Deceased (SIRD) model, which includes time-varying auto-regressive immunological parameters. A novel identification procedure is proposed, composed of analytical regressions, Least-Squares optimization and auto-regressive model fits. The adapted SIRD model is validated with real data and able to adequately represent the contagion curves over large forecast horizons. The NMPC strategy is designed to generate piecewise constant quarantine guidelines, which can be reassessed (relaxed/strengthened) each week. Simulation results show that the proposed NMPC technique is able to mitigate the number of infections and progressively loosen social distancing measures. With respect to a “no-control” condition, the number of deaths could be reduced in up to 30% if the proposed NMPC coordinated health policy measures are enacted.

Distributed Cooperative MPC for Autonomous Driving in Different Traffic Scenarios

A cooperative control approach for autonomous vehicles is developed in order to perform different complex traffic maneuvers, e.g., double lane-switching or intersection situations. The problem is formulated as a distributed optimal control problem for a system of multiple autonomous vehicles, and then solved using a nonlinear Model Predictive Control (MPC) technique, where the distributed approach is used to make the problem computationally feasible in real-time. To provide safety, a collision avoidance constraint is introduced, also in a distributed way. In the proposed method, each vehicle computes its own control inputs using estimated states of neighboring vehicles. In addition, a compatibility constraint is defined that takes collision avoidance into account but also ensures that each vehicle does not deviate significantly from what is expected by neighboring vehicles. The method allows us to construct a cost function for several different traffic scenarios. The asymptotic convergence of the system to the desired destination is proven, in the absence of uncertainty, and disturbances, for a sufficiently small MPC control horizon. Simulation results show that the distributed algorithm scales well with increasing number of vehicles.

The Bionics and its Application in Energy Management Strategy of Plug-in Hybrid Electric Vehicle Formation

A novel distributed cooperative formation control method inspired by the aggregate behaviors of fish groups is proposed for plug-in hybrid electric vehicle (PHEV) formation. Firstly, a hierarchical control architecture is established for formation keeping with fuel consumption (FC) optimization simultaneously. The top layer is to generate a leader with the optimal performance based on the nonlinear model predictive control (MPC) technique. A fish swarm optimization (FSO) algorithm is proposed to solve the nonlinear MPC problem by imitating the predation behaviors of the fish swarm. The middle layer is a decentralized intelligent cruise control (ICC) for follower vehicles to track their leader imitated the behaviors of fish swarm, and some design criteria are presented based on the Lyapunov stability theory. The under layer is to achieve a satisfying performance for the hybrid powertrain systems of followers. Finally, the bio-inspired method applied for PHEV formation is verified with a satisfying robustness, fuel economy, car-following and also real-time processing performances. According to the results, the PHEV formation using the proposed method represents a better car-following performance compared with the normal adaptive cruise control (ACC) method and a 21.26% improvement of FC compared with the rule-based energy management strategy (EMS). The computational burden is also reduced by the bio-inspired method.

A Computationally Efficient Path-Following Control Strategy of Autonomous Electric Vehicles With Yaw Motion Stabilization

This article proposes a computationally efficient path-following control strategy of autonomous electric vehicles (AEVs) with yaw motion stabilization. First, the nonlinear control-oriented model, including path-following model, single-track vehicle model, and magic formula tire model, is constructed. To handle the stability constraints with ease, the nonlinear model predictive control (NMPC) technique is applied for path-following issue. Here, NMPC control problem is reasonably established with the constraints of vehicle sideslip angle, yaw rate, steering angle, lateral position error, and Lyapunov stability. To mitigate the online calculation burden, the continuation/generalized minimal residual (C/GMRES) algorithm is adopted. The dead-zone penalty functions are employed for handling the inequality constraints and holding the smoothness of solution. Moreover, the varying predictive duration is utilized in this article to gain the good initial solution fast by numerical algorithm. Finally, the simulation validations are carried out, which yields that the proposed strategy can achieve desirable path following and vehicle stability efficacy, while greatly reducing the computational burden compared with the NMPC controllers by active set algorithm or interior point algorithm.

A Novel Superlinearly Convergent Trust Region-Sequential Quadratic Programming Approach for Optimal Gait of Bipedal Robots Via Nonlinear Model Predictive Control

A type of trust region-sequential quadratic programming (TRSQP) approach with superlinearly convergent property is first proposed, investigated, and implemented on bipedal robots based on nonlinear model predictive control (NMPC). NMPC is utilized to predict the system behavior and optimize the control move in a receding horizon way, which will result in recursive efficiency and stability. Considering that the classical line search rules are expensive or hard in particular applications, the attempted trust region search is leveraged to avoid the drawbacks of the classical line search rules. Moreover, the feasible descent direction is contained in the trust region via a novelly truncated technique which avoids to recompute the quadratic programming subproblem (QPS) for the main search direction. Owing to some suitable conditions, the globally/superlinearly convergent performance and well-defined properties are analyzed and verified for the TRSQP. The main result is illustrated on a simple bipedal robot which is called as compass-like bipedal robot (CLBR) through numerical simulations and is used to generate dynamic locomotion via TRSQP and NMPC. Furthermore, to demonstrate the feasibility and superiority of a complex bipedal robot which is called as a high-dimensional bipedal robot, numerical simulations are conducted on the model of a three-link bipedal robot (TLBR) and a five-link robot (RABBIT). Furthermore, simulation results show that the TRSQP approach is effectiveness and superiority through comparing with the classical approaches, which included discrete mechanics and optimal control (DMOC) and hybrid zero dynamic (HZD), and control Lyapunov function-quadratic programming (CLF-QP) for the optimal gait of bipedal robot. In addition, to verify the robustness, the TLBR model with parameter’s disturbance 1.5 times is investigated and analyzed via TRSQP with NMPC technique. Last,this study develops an interesting framework to exploiting control methods on bipedal robots through accurately and effectively solving nonlinear programming problems.

A Novel Discrete-time Nonlinear Model Predictive Control Based on State Space Model

This paper proposes a novel finite dimensional discrete-time Nonlinear Model Predictive Control. This technique is based on discrete-time state-space models, Taylor series expansion for prediction and performance index optimization. Furthermore, the technique extends the concept of the Lie derivative for the discrete time case using Euler backwards method. The performance validation for the discrete-time Nonlinear Model Predictive Control uses the simulation of a single-link flexible joint robot and the inverted pendulum. Comparison of the proposed finite dimensional discrete-time Nonlinear Model Predictive Control technique with Feedback Linearization Control is also discussed. Analytical and numerical results show excellent performances for both, the single-link flexible joint and inverted pendulum controllers using the proposed discrete-time Nonlinear Model Predictive Control technique.

Leveraging experience for robust, adaptive nonlinear MPC on computationally constrained systems with time-varying state uncertainty

This paper presents a robust-adaptive nonlinear model predictive control (MPC) technique that leverages past experiences to achieve tractability on computationally constrained systems. We propose a robust extension of the Experience-driven Predictive Control (EPC) algorithm via a Gaussian belief propagation strategy that computes an uncertainty set, bounding the evolution of the system state in the presence of time-varying state uncertainty. This uncertainty set is used to tighten the constraints in the predictive control formulation via a chance-constrained approach, thereby providing a probabilistic guarantee of constraint satisfaction. The parameterized form of the controllers produced by EPC coupled with online uncertainty estimates ensures that this robust constraint satisfaction property persists, even as the system switches controllers and experiences variations in the uncertainty model. We validate the online performance and robust constraint satisfaction of the proposed Robust EPC algorithm through a series of trials with a simulated ground robot and three experimental platforms: (1) a small quadrotor aerial robot executing aggressive maneuvers in wind with degraded state estimates, (2) a skid-steer ground robot equipped with a laser-based localization system, and (3) a hexarotor aerial robot equipped with a vision-based localization system.

Variable speed limit control scheme for vehicle in the vicinity of signalized intersection

In this paper, a variable speed limit control approach for improving the efficiency of signalized intersection is proposed from the cyber-physical view. In the proposed control scheme, vehicle-to-vehicle communication is being utilized fully such that the preceding vehicle’s optimal information is exploited for optimizing the motion of the current vehicle. To prepare the control scheme for dynamical optimization, nonlinear model predictive control technique is used to optimally control vehicle speed limit and a new traffic model is constructed by considering vehicle dynamics. Moreover, this paper evaluates the influence of communication distance on the traffic. The results show that extending communication distance in the vicinity of signalized intersection can improve vehicles’ average fuel economy.

Simulation of three-phase induction motor using nonlinear model predictive control technique

In this paper, nonlinear model predictive control (NMPC) has been used to control an induction motor (IM). The IM model that is used in the control is third or fifth order model that is based in th...