Nonlinear Model Predictive Control Scheme Research Articles

A NEW HYBRID OPTIMIZATION METHOD USED IN PREDICTIVE CONTROL OF A NONLINEAR FRACTIONAL MODEL BASED ON FRACTIONAL HAMMERSTEIN STRUCTURE

Fractional Hammerstein models represent various nonlinear processes, such as thermal and mechanical. Their major drawback is the non-convex optimization problem in a nonlinear model predictive control scheme due to its static nonlinearity. Indeed, an efficient optimization algorithm is needed. This work proposes a hybrid optimization algorithm combining the Nelder Mead optimization method and the Honey Badger one to synthesize a predictive control algorithm based on fractional Hammerstein models. As illustrated through simulation results, the proposed method offers clear improvements in convergence and tracking performances.

Adaptive sliding mode control with nonlinear MPC-based obstacle avoidance using LiDAR for an autonomous surface vehicle under disturbances

This manuscript proposes a path-following and collision avoidance guidance and control system for an autonomous surface vehicle operating in cluttered environments under perturbations. A nonlinear model predictive control strategy handles the state and control constraints for obtaining a guidance law. The approach considers the vessel sideslip angle to provide the desired heading angle, satisfying path-following and obstacle avoidance. Additionally, to solve the nonlinear optimization problem for obtaining the guidance law in real-time, the acados software package is used. Furthermore, in order to guarantee that the vehicle tracks the guidance in presence of model uncertainties and external disturbances, a robust adaptive sliding mode low-level controller is adopted. This controller is finite time convergent, and dynamically adapts its control gain to use only the necessary control inputs. Furthermore, a low-memory and computationally-light obstacle detection strategy employing a LiDAR sensor is presented and proven to run in real-time. Simulation and experimental tests conducted using a customized prototype validate the advantages of the proposed strategy and demonstrate the effectiveness of the path following while evading multiple obstacles in the presence of external disturbances and model discrepancies.

MPC-Based Dynamic Velocity Adaptation in Nonlinear Vehicle Systems: A Real-World Case Study

Technological advancements have positively impacted the automotive industry, leading to the development of autonomous cars, which aim to minimize human intervention during driving, and thus reduce the likelihood of human error and accidents. These cars are distinguished by their advanced driving systems and environmental benefits due to their integration of cutting-edge autonomous technology and electric powertrains. This combination of safety, efficiency, and sustainability positions autonomous vehicles as a transformational solution for modern transportation challenges. Optimizing vehicle speed is essential in the development of these vehicles, particularly in minimizing energy consumption. Thus, in this paper, a method to generate the maximum velocity profile of a vehicle on a real road, extracted using online mapping platforms while ensuring compliance with maximum legal speed limits, is proposed. A nonlinear model, closely aligned with real-world conditions, captures and describes vehicle dynamics. Further, a nonlinear model predictive control strategy is proposed for optimizing the vehicle’s performance and safety in dynamic driving conditions, yielding satisfactory results that demonstrate the effectiveness of the method.

Control of pH neutralization process using NMPC based on discrete time NARX-Laguerre model

In this paper, we propose a NMPC scheme based on NARX-Laguerre model in its discrete-time structure in order to control the pH neutralization process. This model is the result of the development of discrete-time NARX model parameters on five independent Laguerre bases introducing the benefit of an essentially diminished number of parameters compared to the classical NARX model. The decrease in parametric complexity actually depends on choosing the ideal poles that characterize the Laguerre bases. In this paper, we develop an analytical technique to optimize the NARX-Laguerre poles. The parameters of the NARX-Laguerre model are reached using a recursive technique. The proposed model is utilized to integrate a nonlinear model predictive control, where we create a j-step ahead predictor on the prediction horizon [k+1,k+Np] and formulate the optimization problem using a performance criterion taking into consideration the restrictions imposed on the input and output of the process. The proposed nonlinear model predictive control strategy is validated on pH neutralization process.

Nonlinear Model Predictive Control with Evolutionary Data-Driven Prediction Model and Particle Swarm Optimization Optimizer for an Overhead Crane

This paper presents a new approach to the nonlinear model predictive control (NMPC) of an underactuated overhead crane system developed using a data-driven prediction model obtained utilizing the regularized genetic programming-based symbolic regression method. Grammar-guided genetic programming combined with regularized least squares was applied to identify a nonlinear autoregressive model with an exogenous input (NARX) prediction model of the crane dynamics from input–output data. The resulting prediction model was implemented in the NMPC scheme, using a particle swarm optimization (PSO) algorithm as a solver to find an optimal sequence of the control actions satisfying multi-objective performance requirements and input constraints. The feasibility and performance of the controller were experimentally verified using a laboratory crane actuated by AC motors and compared with a discrete-time feedback controller developed using the pole placement technique. A series of experiments proved the effectiveness of the controller in terms of robustness against operating condition variation and external disturbances.

Reinforcement learning based MPC with neural dynamical models

This paper presents an end-to-end learning approach to developing a Nonlinear Model Predictive Control (NMPC) policy, which does not require an explicit first-principles model and assumes that the system dynamics are either unknown or partially known. The paper proposes the use of available measurements to identify a nominal Recurrent Neural Network (RNN) model to capture the nonlinear dynamics, which includes constraints on the state variables and inputs. To address the issue of suboptimal control policies resulting from simply fitting the model to the data, this paper uses Reinforcement learning (RL) to tune the NMPC scheme and generate an optimal policy for the real system. The approach’s novelty lies in the use of RL to overcome the limitations of the nominal RNN model and generate a more accurate control policy. The paper discusses the implementation aspects of initial state estimation for RNN models and integration of neural models in MPC. The presented method is demonstrated on a classic benchmark control problem: cascaded two tank system (CTS).

Health-conscious optimal control of Li-ion cell using simplified full homogenized macro-scale model

This article presents the optimal charging of a Li-ion cell based on a simplified full homogenized macro-scale (FHM) model. A solid electrolyte interface (SEI) layer model is included in the simplified FHM model to quantify cell degradation. With these models, a multi-objective optimal control problem subject to constraints from safety concerns is formulated to achieve health-conscious optimal charging. This constrained optimal control problem is converted to a nonlinear programming problem (NLP). A nonlinear model predictive control (NMPC) strategy is adopted by solving the NLP at each sampling time using the pseudo-spectral optimization method. The effect of the input current upper bound on the cell film resistance Rfilm and state of health (SoH) reveals that Rfilm and SoH are more sensitive to input current upper bound at lower values of input current upper bound. Simulation results show that the simplified model and pseudo-spectral method are crucial for reducing the computational load of the model. The proposed algorithm is more efficient in reducing health degradation than the conventional constant current constant voltage (CCCV) charging algorithm since it can explicitly handle the film resistance and capacity as health parameters. Multiple cycle charging simulations revealed that the health-conscious algorithm decreases health degradation and increases battery life.

Learning Lyapunov terminal costs from data for complexity reduction in nonlinear model predictive control

AbstractA classic way to design a nonlinear model predictive control (NMPC) scheme with guaranteed stability is to incorporate a terminal cost and a terminal constraint into the problem formulation. While a long prediction horizon is often desirable to obtain a large domain of attraction and good closed‐loop performance, the related computational burden can hinder its real‐time deployment. In this article, we propose an NMPC scheme with prediction horizon and no terminal constraint to drastically decrease the numerical complexity without significantly impacting closed‐loop stability and performance. This is attained by constructing a suitable terminal cost from data that estimates the cost‐to‐go of a given NMPC scheme with long prediction horizon. We demonstrate the advantages of the proposed control scheme in two benchmark control problems.

Real-time implementation of nonlinear model predictive control for high angle of attack Maneuvers in fighter aircrafts using deep learning

ABSTRACT Nonlinear model predictive control (NMPC) provides a nice framework for accounting for multivariable nonlinear dynamics subject to constraints; however, the cost of implementing NMPC is high due to the need to solve a large-scale nonlinear program to optimality in real-time. This research is focussed on the design of real-time solution to NMPC (low computations) for fast dynamic systems. In this work, a comprehensive and innovative solution based on a deep learning-based approximate NMPC scheme has been proposed to overcome these computational challenges. The main idea is to learn a deep neural network followed by the symbolic simplification of the NMPC law, whose evaluation cost and memory footprint can be optimized offline. Since not all the states of the system are measured, we also combine the deep learning based NMPC approach with an unscented Kalman filter (UKF) as well as show how this scheme can be easily modified to be offset-free (i.e. remove steady-state error due to persistent disturbances and modelling error). The proposed approach is implemented on a highly fast dynamic system (i.e. F-16 fighter aircraft to perform a high angle of attack maneuver) to check the controller efficiency. Fighter aircraft need to be able to make fast and complex maneuvers (that exploit strongly nonlinear dynamics) to be able to maintain air superiority. However, such aggressive maneuvers require strong coordination between the actions to avoid destabilizing the system. A quantitative analysis from comparison with the standard MPC approach shows the practical utility of the proposed approach.

Application of a stabilizing model predictive controller to path following for a car‐like agricultural robot

AbstractThis work addresses the problem of path following for a car‐like agricultural robot by means of a finite control set model predictive control (FCS‐MPC) strategy that considers the control actions in a set composed of a limited amount of elements. Recent results on a stabilizing MPC formulation that replaces the classical control invariant set by a pair of inner‐outer sets are extended to preserve stability properties with different control and prediction horizons and are then used for the aforementioned application. Being particularly simple, the presented approach can explicitly deal with nonlinearities and constraints at the expense of resolution in the vehicle steering system, which in practice does not affect the controller performance as will be shown. In addition to describing the control method, simulations and a comparison with another nonlinear MPC strategy are presented to illustrate the advantages of the proposed scheme.

Robust learning control for autonomous vehicle with network delays and disturbances

This paper deals with a robust learning nonlinear model predictive control (RL-NMPC) scheme under time-varying delays and disturbances. It is well known that the in-vehicle network has considerable advantages over the traditional point-to-point communication. However, on the other hand, these technologies would also induce the probability of time-varying delays, which would be a hazard in the active safety of over-actuated autonomous vehicles (AVs). To enjoy the advantages and deal with in-vehicle network delays and external disturbances, a robust learning nonlinear model predictive control (RL-NMPC) scheme is proposed. First, the machine learning (Support Vector Machine called SVM) method is adopted to train delayed measurement signals and disturbances. Then, according to the predictions of the SVM and corrupted sensory signals, the Unscented Kalman filter (UKF) is applied to acquire accurate predictions of the vehicle motion states. Furthermore, the NMPC scheme is used to generate real-time control signals by solving an open-loop optimization problem. The main purpose of the addressed problem is to design a robust learning controller to ensure that the AVs can track the desirable path and run smoothly suffering network delays and disturbances. Finally, simulations with a full-vehicle model are carried out to show the effectiveness of our proposed control scheme.

An edge architecture for enabling autonomous aerial navigation with embedded collision avoidance through remote nonlinear model predictive control

In this article, we present an edge-based architecture for enhancing the autonomous capabilities of resource-constrained aerial robots by enabling a remote nonlinear model predictive control scheme, which can be computationally heavy to run on the aerial robots' onboard processors. The nonlinear model predictive control is used to control the trajectory of an unmanned aerial vehicle while detecting, and preventing potential collisions. The proposed edge architecture enables trajectory recalculation for resource-constrained unmanned aerial vehicles in relatively real-time, which will allow them to have fully autonomous behaviors. The architecture is implemented with a remote Kubernetes cluster on the edge side, and it is evaluated on an unmanned aerial vehicle as our controllable robot, while the robotic operating system is used for managing the source codes, and overall communication. With the utilization of edge computing and the architecture presented in this work, we can overcome computational limitations, that resource-constrained robots have, and provide or improve features that are essential for autonomous missions. At the same time, we can minimize the relative travel time delays for time-critical missions over the edge, in comparison to the cloud. We investigate the validity of this hypothesis by evaluating the system's behavior through a series of experiments by utilizing either the unmanned aerial vehicle or the edge resources for the collision avoidance mission.

Real-time Learning-based Nonlinear Model Predictive Control of a virtual motorcycle employing grey-box modeling through Gaussian processes

Virtual prototyping tools simulations are nowadays largely adopted methods in the automotive industry. However, to achieve effective simulative tests for two-wheeled vehicles, a virtual rider, i.e. a controller for virtual motorcycles, is typically needed due to the inherent instability of the system. Different control strategies have been employed to deal with this control task, and promising results have been obtained using Nonlinear Model Predictive Control (NMPC). Yet, performance of NMPC highly relies on the plant characterization, that can be highly complex to obtain analytically for 2-wheel vehicles. To improve it, learning dynamics approaches can be used within a Learning-based Nonlinear Model Predictive Control (LbNMPC) framework, exploiting the combination of data-driven techniques and NMPC strategy. In this manuscript, we present a tailored real-time capable LbNMPC for a virtual motorcycle that relies on a continuous grey-box model based on Gaussian Processes (GPs), method that has proven to be effective for 4-wheel vehicle applications. To cope with the real-time requirement, a feature selection procedure and sparse GP approximations have been adopted. A comparison with a physics-based model NMPC implementation taken from the literature has been carried out, analyzing the impact of different sparse GP representations. Remarkable improvements in both model accuracy and tracking performance have been obtained, and the generalization properties of the grey-box model have been assessed.

Nonlinear Terminal-Free MPC on Multitype Bend Tracking With Discontinuous Reference Paths for Autonomous Vehicles

In this paper, multitype bend tracking with discontinuous reference paths is researched by a nonlinear terminal-free model predictive control (MPC) with an artificial reference path for an autonomous vehicle. The MPC strategy without terminal penalty and terminal state constraints is proposed to deal with the discontinuous reference paths, which improves solvability on an optimization problem effectively. The artificial reference path is designed to realize replanning and smoothing for multitype bend paths. Both recursive feasibility and stability are discussed for the autonomous vehicle by a lower bound of prediction horizon and a controlled forward invariance set. Effectiveness of the nonlinear terminal-free MPC strategy is shown by experimental results on multitype bend path for the autonomous vehicle.

MPC for the Indoor Climate Control and Energy Optimization of a Building-Integrated Rooftop Greenhouse Systems

In this work, we design a nonlinear model predictive control (NMPC) strategy to optimize energy management in integrated rooftop greenhouses and buildings, aimed at minimizing operational expenses and reducing climate irregularities. This integrated system is tailored to maintain ideal conditions for both plant growth and building occupancy, utilizing the building’s excess heat and air to lower energy consumption and CO2 emissions. The NMPC framework employs dynamic nonlinear models for temperature, humidity, and CO2, enhanced with real-time weather data, to improve control accuracy beyond traditional MPC methods. It manages various systems—including fans, pad cooling, shading devices, heating, ventilation, air conditioning, CO2 injection, and lighting—to precisely control environmental conditions. A case study from a rooftop greenhouse in Brooklyn, New York, demonstrates the NMPC’s efficacy, showing an average energy savings of 15.2%. These results highlight the significant potential of NMPC to advance urban agricultural systems and building management practices.

Nonlinear MPC for Insulin Titratio2shn of Type 2 Diabetes

This paper explores the development and application of both linear and nonlinear model predictive control (MPC) strategies for insulin titration in type 2 diabetes (T2D) subjects. By utilizing daily blood glucose measurements, alongside information on insulin injections and meal intake from the previous day, we adjust the insulin sensitivity parameter of the internal model of the controller. This adjustment is based on the steady-state glucose error between the internal model and the plant model. The performance of these strategies was assessed using a high-fidelity T2D model, demonstrating their potential in enhancing the management of T2D.

Nonlinear Model Predictive Control for Enhanced Navigation of Autonomous Surface Vessels

This article proposes an approach for collision avoidance, path following, and anti-grounding of autonomous surface vessels under consideration of environmental forces based on Nonlinear Model Predictive Control (NMPC). Artificial Potential Fields (APFs) set the foundation for the cost function of the optimal control problem in terms of collision avoidance and anti-grounding. Depending on the risk of a collision given by the resulting force of the APFs, the controller optimizes regarding an adapted heading and travel speed by additionally following a desired path. For this purpose, nonlinear vessel dynamics are used for the NMPC. To extend the situational awareness concerning environmental disturbances impacted by wind, waves, and sea currents, a nonlinear disturbance observer is coupled to the entire NMPC scheme, allowing for the correction of an incorrect vessel motion due to external forces. In addition, the most essential rules according to the Convention on the International Regulations for Preventing Collisions at Sea (COLREGs) are considered. The results of the simulations show that the proposed framework can control an autonomous surface vessel under various challenging scenarios, including environmental disturbances, to avoid collisions and follow desired paths.

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.

Predictive control scheme by integrating event-triggered mechanism and disturbance observer under actuator failure and sensor fault

Liquid-level control in an interacting storage-tank system exhibits major challenges due to the effect of interaction and the presence of combustible/flammable liquid as it faces huge threats from the unmeasurable disturbances, irregular geometry and unmodelled dynamics of the process plant. A combination of tanks with multiple geometries may be preferred for storing liquids using common pumps for energy conservation. Continuous improvement of risk assessment, predicting hazardous scenarios and implementation of inherently-safer-control systems ensure process safety and, as a result, ease out the safe operation. From the process analysis, it was observed that the dynamics of the interacting tank are very sensitive to effective parameters like valve coefficient and pump gain. To overcome the loss of inventory or production, we investigate the synthesis of a non-linear model predictive control scheme with an outline of simultaneous state and parameter estimation strategies. This mechanism deals with a stochastic event-trigger cubature Kalman filter scheme to estimate process states while performing servo operations. To mitigate plant uncertainty, reduce the impact of large disturbances and nullify the effect of actuator failure/sensor fault, influential model parameters are estimated simultaneously with the model state(s). Predicted values of the model states/parameters/faults are used to derive an effective control effort. An inferential non-linear model predictive control paradigm is proposed, where the primary variable(s) is (are) measured with the help of measurable secondary state(s). To demonstrate the practical utility and effectiveness of the control framework for safe operation and loss prevention, a complex industrial process (quadrupled tank) is considered for control, where the system dynamics have been structured newly. Realistic simulations such as servo-regulatory compliance and elimination of measurement noise with a state-of-the-art simulator ensures the efficacy of the proposed scheme. The results are analysed further for a comparative study with traditional non-linear model predictive control law. To guarantee convergence of the estimator and stability of the closed-loop controller, the Lyapunov theorem is well blended.

Nonlinear MPC design for incrementally ISS systems with application to GRU networks

This brief addresses the design of a Nonlinear Model Predictive Control (NMPC) strategy for exponentially incremental Input-to-State Stable (ISS) systems. In particular, a novel formulation is devised, which does not necessitate the onerous computation of terminal ingredients, but rather relies on the explicit definition of a minimum prediction horizon ensuring closed-loop stability. The designed methodology is particularly suited for the control of systems learned by Recurrent Neural Networks (RNNs), which are known for their enhanced modeling capabilities and for which the incremental ISS properties can be studied thanks to simple algebraic conditions. The approach is applied to Gated Recurrent Unit (GRU) networks, providing also a method for the design of a tailored state observer with convergence guarantees. The resulting control architecture is tested on a benchmark system, demonstrating its good control performances and efficient applicability.