Nonlinear Model Predictive Control Scheme Research Articles

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.

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.

Stability and Performance Analysis of NMPC: Detectable Stage Costs and General Terminal Costs

We provide a stability and performance analysis for nonlinear model predictive control (NMPC) schemes subject to input constraints. Given an exponential stabilizability and detectability condition w.r.t. the employed state cost, we provide a sufficiently long prediction horizon to ensure asymptotic stability and a desired performance bound w.r.t. the infinite-horizon optimal controller. Compared to existing results, the provided analysis is applicable to positive semi-definite (detectable) cost functions, provides tight bounds using a linear programming analysis, and allows for a seamless integration of general positive-definite terminal cost functions in the analysis. The practical applicability of the derived theoretical results are demonstrated with numerical examples.

Optimal operation of a large-scale packed bed chemical-looping combustion process using nonlinear model predictive control

In this work, a nonlinear model predictive control (NMPC) scheme is presented for chemical-looping combustion (CLC) in a large-scale packed bed reactor. For NMPC, the plant is represented by a multiscale model comprised of mass and energy balances for both the reactor and particles, with states dependent on their location within both the spatial and temporal domains. A kinetic scheme was chosen from existing literature such that it can accurately predict the process behaviour obtained from multiple sets of literature data, attained using reactors of different sizes operating under different inlet flowrates and temperatures. The multiscale model was used to simulate the plant behaviour, while a pseudo-homogeneous model was used as the internal NMPC model to reduce computational costs for implementation of feedback control. For the pseudo-homogeneous model, it was verified that the gradients within the particles could be assumed to be negligible, and the number of states is decreased by about 87% by focusing on the reactor behaviour. The resulting NMPC scheme is implemented for packed bed CLC and was performed for both the oxidation and reduction stages of CLC. For NMPC of the oxidation stage, manipulating both the inlet air and inert gas fluxes allowed the outlet gas temperature to track a given setpoint. In this case, the oxidation stage generated energy for three times as long as the case when a constant inlet air flux is used. When NMPC was implemented for the reduction stage, improved CO2 selectivity could be achieved by manipulating the inlet fuel flowrate. This improved the CO2 and H2O purity of the outlet stream by over 20% and thus improved the carbon capture effectiveness of the process.

NMPC-PID control of secondary regulated active heave compensation system for offshore crane

In this paper, an offshore crane driven by a secondary controlled unit (SCU) which offers advantages in terms of high dynamic behavior and energy efficiency is investigated. To counteract the negative impact of the support vessel's heave motion on the station-keeping and trajectory tracking performance of heavy payload, an adaptive robust control scheme for the secondary regulated active heave compensation (AHC) system is proposed based on the combination of a nonlinear model predictive control (NMPC) strategy, a conventional proportional-integral-derivative (PID) control scheme and a vessel heave motion prediction algorithm. The motivation of utilizing the PID-based control structure is given by the excellent resistance against irregular external disturbances and robust capability to eliminate the uncertainties, with real-time tuning gains provided by the NMPC synthesized with the autoregressive integrated moving average (ARIMA) model to ensure optimal evolution that satisfies state and input constraints while accounting for model nonlinearities. Comparative simulation studies in the practical Simulink-based mechanical-electrical-hydraulic research system demonstrate the superior tracking and heave compensation performance, strong robustness, constraint satisfaction, and energy efficiency of the proposal.

Energy Management Strategy of Hybrid Ships Using Nonlinear Model Predictive Control via a Chaotic Grey Wolf Optimization Algorithm

Reducing energy consumption and carbon emissions from ships is a major concern. The development of hybrid technologies offers a new direction for the rational distribution of energy. Therefore, this paper establishes a torque model for internal combustion engines and motors based on first principles and fitting the data collected from the test platform; in turn, it develops a model for fuel consumption and carbon emissions. Furthermore, the effect of irregular waves using an extended Kalman filter is estimated as well as feedback to the controller as a disturbance variable. Then, a parallel hybrid ship energy management strategy based on a new real-time nonlinear model of predictive control is designed to achieve energy conservation and emission decrease. A hybrid algorithm of chaotic optimization combined with grey wolf optimization is utilized to solve the nonlinear optimization problem in the nonlinear model predictive control strategy and a local refined search is performed using sequential quadratic programming. Through the comparison of fuel consumption, carbon emissions, real-time performance, and the engine load path, the superiority of the nonlinear model predictive control energy management strategy based on the chaotic grey wolf optimization algorithm is verified.

Nonlinear model predictive control of large-scale urban road networks via average speed control

Controlling traffic in large-scale urban road networks is a challenging problem. Aggregated dynamical models, based on the macroscopic fundamental diagram (MFD) of urban traffic, enable model-based control design. As an alternative to perimeter control actuation commonly used in MFD-based control, in this paper, we propose actuation over regional space-mean speeds, which we name average speed control. The method involves manipulation of regional speeds via instrumentation similar to variable speed limits in freeways, or using vehicle-to-infrastructure communication. We develop nonlinear model predictive control schemes considering actuation over average speed and perimeter control. Their performances are compared using simulations on congested scenarios, the results of which suggest potential of the method as an alternative or complementary actuation to perimeter control.

Research on energy management strategy of fuel-cell vehicles based on nonlinear model predictive control

Fuel cell hybrid electric vehicles (FCHEV) are one of the most promising new energy vehicles. The cost and lifetime of its powertrain have limited its commercial development. This paper proposed an energy management strategy based on nonlinear model predictive control (NMPC) technology to solve the economy and durability problem of FCHEVs. Based on Markov Monte Carlo(MCMC) method, a prediction model of multi-scale operating conditions is established, and dynamic programming(DP) is used to realize the optimal control in the predicted time domain. The “constant speed prediction” is innovatively adopted in the transition stage to improve the prediction accuracy and enable the model to be realized online. The ways to reduce calculating amount of NMPC are also discussed in this paper. This simplification leads to suboptimal fuel economy and durability of control system but can have obvious reduction in calculating time. The simulation results show that, compared with the thermostat strategy and the power following strategy, the degradation cost decrease of 11.1% and 23.9% and the total operation cost of NMPC decrease of 11.0% and 23.5% respectively. The NMPC strategy has better economy and durability than the rule-based energy management strategy, is close to the global optimal result obtained by dynamic programming and can meet the requirements of real-time control.

Path Following and Collision Avoidance of a Ribbon-Fin Propelled Underwater Biomimetic Vehicle-Manipulator System.

This paper addresses the problem of path following and dynamic obstacle avoidance for an underwater biomimetic vehicle-manipulator system (UBVMS). Firstly, the general kinematic and dynamic models of underwater vehicles are presented; then, a nonlinear model predictive control (NMPC) scheme is employed to track a reference path and collision avoidance simultaneously. Moreover, to minimize the tracking error and for a higher degree of robustness, improved extended state observers are used to estimate model uncertainties and disturbances to be fed into the NMPC prediction model. On top of this, the proposed method also considers the uncertainty of the state estimator, while combining a priori estimation of the Kalman filter to reasonably predict the position of dynamic obstacles during short periods. Finally, simulations and experimental results are carried out to assess the validity of the proposed method in case of disturbances and constraints.

High-Quality Positioning Strategy for Biaxial Contour Machining System With Nonlinear Model Predictive Control

The trajectory tracking ability is an important index to measure the computer numerical control (CNC) machining tools. In this paper, the nonlinear model predictive control strategy (NMPC) is proposed to improve the trajectory tracking ability of the biaxial contour machining system (BCMS). The position-, velocity-, and current-loop of the permanent magnet synchronous motors (PMSMs) of the BCMS are considered as the complete control object to construct a single-loop nonlinear model predictive controller. Meanwhile, the matching non-linear disturbance observer (NL-DOB) is designed to estimate the uncertainty disturbances caused by the parameters mismatch, external load changes and harmonic disturbances in real-time. And the estimated disturbance values are used as feed-forward compensations, which can improve the steady-state performance of the system. At last, the positioning performance comparison between the proposed strategy and the conventional ones are carried on the testbench. The experimental results indicate that the positioning errros can be reduced by up to 40% with the proposed algorithm.

IMPACTS OF QUANTIFYING SOCIAL DISTANCING MEASURES ON MPC PERFORMANCE FOR SIR-TYPE SYSTEMS

Currently, there has been a sharp increase in epidemic control research as a result of recent epidemic outbreaks. Several strategies aiming to minimize the Epidemic Final Size and/or to keep the Infected Peak Prevalence under a specific value were proposed. However, not many strategies focused on analyzing the impact of applying quantified measures instead of continuous control action. This analysis is a crucial aspect since policymakers design their non-pharmaceutical intervention based on a discrete scale of intensity, from mask-wearing to hard lockdown. In this work, we present a quantized-input non-linear Model Predictive Control strategy to manage non-pharmaceutical interventions during an epidemic outbreak. The impact of quantifying the social distancing measure is computed through several simulations based on a COVID-19 epidemic model and considering different quantization levels of the non-pharmaceutical intervention. Finally, the control performance in each quantization level is evaluated with the computation of four epidemic indices.

A non-linear model predictive control strategy to minimise mechanical degradation effects of lithium-ion battery

Mechanical stresses are not only developed inside the active material of the composite electrode, but also in the solid electrolyte interface layer (SEI) due to the graphite expansion. Due to diffusion induced stress (DIS) phenomena, stresses in the negative electrode are generated during charging and discharging cycles. This article presents the proposed optimal charging profile explicitly incorporating the effects of mechanical degradation. Non-linear model predictive control approach along with Gauss pseudo-spectral method is used to optimise charging trajectories. It is assumed that active material is not the weakest material but system is modelled based on SEI break and repair effect. The dynamics of battery is represented by a single particle model. The simulated results are compared with benchmark constant current constant voltage (CCCV) strategy. Furthermore, proposed methodology is compared with optimal CCCV using cycle life ageing experimental scenario. It is estimated that stress amplitude decreased by 7% and nominal capacity increased by 11% using the proposed optimal charging profile.

Deep Imitation Learning of Nonlinear Model Predictive Control Laws for a Safe Physical Human–Robot Interaction

This paper proposes motion planning algorithms for industrial manipulators in the presence of human operators based on deep neural networks (DNNs), aimed at imitating the behavior of a nonlinear model predictive control (NMPC) scheme. The proposed DNN solutions retain the safety features of NMPC in terms of speed and separation monitoring, defined according to the guidelines in the ISO/TS 15066 standard. At the same time, they improve the robot performance in terms of task completion time, and of a-posteriori evaluation of the NMPC cost function on experimental data. The reasons for this improvement are the reduced computational delay of running a DNN compared to solving the nonlinear programs associated to NMPC, and the ability to implicitly learn how to predict the human operator's motion from the training set.