Adaptive Nonlinear Model Predictive Control Research Articles

Trajectory tracking for autonomous vehicles on varying road surfaces by friction-adaptive nonlinear model predictive control

ABSTRACTWe propose an adaptive nonlinear model predictive control (NMPC) for vehicle tracking control. The controller learns in real time a tyre force model to adapt to a varying road surface that is only indirectly observed from the effects of the tyre forces determining the vehicle dynamics. Learning the entire tyre model from data would require driving in the unstable region of the vehicle dynamics with a prediction model that has not yet converged. Instead, our approach combines NMPC with a noise-adaptive particle filter for vehicle state and tyre stiffness estimation and a pre-determined library of tyre models. The stiffness estimator determines the linear component of the tyre model during normal vehicle driving, and the control strategy exploits a relation between the tyre stiffness and the nonlinear part of the tyre force to select the appropriate full tyre model from the library, which is then used in the NMPC prediction model. We validate the approach in simulation using real vehicle parameters, demonstrate the real-time feasibility in automotive-grade processors using a rapid prototyping unit, and report preliminary results of experimental validation on a snow-covered test track.

A novel adaptive three stages model predictive control based on fuzzy systems: Application in MIMO controlling of MED-TVC process

In the present study, a novel technique is suggested for the adaptive non-linear model predictive control based on the fuzzy approach in three stages. In the presented approach, in the first stage, the prediction and control horizons are obtained from a fuzzy system in each control step. Another fuzzy system is employed to determine the weight factors before the optimization stage of developing new controller. The proposed controller gives the parameters of the model predictive control (MPC) in each control step in order to improve the performance of nonlinear systems. The proposed control scheme is compared with the traditional MPC and Generic Model Control for controlling MED-TVC process. The performances of the three proposed controllers have been investigated in the absence and presence of disturbance in order to evaluate the stability and robustness of the proposed controllers. The results reveal that the novel adaptive controller based on fuzzy approach performs better than the two other controllers in set-point tracking and disturbance rejection with lower IAE criteria. In addition, the average computational time for the adaptive MPC exhibits a decline of 34% in comparison with the traditional MPC.

Adaptive Nonlinear Model Predictive Control of the Combustion Efficiency under the NOx Emissions and Load Constraints

A data-driven modeling method with feature selection capability is proposed for the combustion process of a station boiler under multi-working conditions to derive a nonlinear optimization model for the boiler combustion efficiency under various working conditions. In this approach, the principal component analysis method is employed to reconstruct new variables as the input of the predictive model, reduce the over-fitting of data and improve modeling accuracy. Then, a k-nearest neighbors algorithm is used to classify the samples to distinguish the data by the different operating conditions. Based on the classified data, a least square support vector machine optimized by the differential evolution algorithm is established. Based on the boiler key parameter model, the proposed model attempts to maximize the combustion efficiency under the boiler load constraints, the nitrogen oxide (NOx) emissions constraints and the boundary constraints. The experimental results based on the actual production data, as well as the comparative analysis demonstrate: (1) The predictive model can accurately predict the boiler key parameters and meet the demands of boiler combustion process control and optimization; (2) The model predictive control algorithm can effectively control the boiler combustion efficiency, the average errors of simulation are less than 5%. The proposed model predictive control method can improve the quality of production, reduce energy consumption, and lay the foundation for enterprises to achieve high efficiency and low emission.

An Integrated Frequent RTO and Adaptive Nonlinear MPC Scheme Based on Simultaneous Bayesian State and Parameter Estimation

Changes in process parameters and measured/unmeasured disturbances shift the optimal point at which the economic benefits are maximized. Combinations of real time optimization (RTO) techniques, which periodically determine the economically optimum operating point using steady state optimization, and model predictive control (MPC) have been widely employed in the process industry for operating process plants optimally in the face of drifting disturbances and/or parameters. Due to the long wait time between two successive RTO invocations and model inconsistency between the RTO and MPC layers, the conventional RTO schemes can end up operating the plant suboptimally if the process parameters/unmeasured disturbances change significantly during the wait time. Recently proposed frequent RTO approaches attempt to address this difficulty by increasing the frequency of RTO invocation. An online update of the steady state model employed by the RTO layer using dynamic operating data is a major concern in implementati...

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.

Model Predictive Control and Parameter Estimation applied to Gene Expression in Yeast

Abstract In this paper an adaptive Nonlinear Model Predictive Control (NMPC) scheme is proposed to control the gene expression of yeast using the application of osmostic shocks. The proposed control method handles the presence of delays, input constraints, as well as unknown model parameters during the controlled scenario. A controller was designed that optimized the integer-valued control sequence so that the output trajectory of the system follows a target reference signal. To tackle the unavoidable parameter uncertainties, a dedicated parameter estimation scheme is proposed that is then coupled to the NMPC design. Simulations are presented to assess the efficiency of the proposed framework in addressing the underlying control problem.

Adaptive nonlinear predictive control and estimation of microaerobic processes

Compared to other sectors, industrial biotechnology only employs a limited number of automatic control strategies. The applied control strategies are mainly recipe-based and often do not take directly the high variability and flexibility of biological systems into account. While this provides sharply defined conditions and quality by design guarantees, process are operated significantly below the optimum, with inefficient product yields and limited reproducibility. The information that is available online, the data from previous batches and the additional biological knowledge are not considered, usually because the integration of this information requires the use of control strategies with an adaptive character, which increases the the design complexity and the implementation cost.We present an approach which allows to optimize biotechnological production process and the corresponding growth model at the same time with reasonable computational cost. Employing a basal model with unknown parameters, the combination of moving horizon estimation and adaptive nonlinear model predictive control enables the identification of parameters for the whole growth range of the respective organism online. The adapted model is then used for prediction and control of the process, leading to an optimized process performance within one experiment. Such an adaptive strategy accelerates the design, characterization and optimization of new production processes. It furthermore reduces time and cost intensive traditional process development.

Adaptive nonlinear model predictive control design of a flexible-link manipulator with uncertain parameters

This paper presents a novel adaptive nonlinear model predictive control design for trajectory tracking of flexible-link manipulators consisting of feedback linearization, linear model predictive control, and unscented Kalman filtering. Reducing the nonlinear system to a linear system by feedback linearization simplifies the optimization problem of the model predictive controller significantly, which, however, is no longer linear in the presence of parameter uncertainties and can potentially lead to an undesired dynamical behaviour. An unscented Kalman filter is used to approximate the dynamics of the prediction model by an online parameter estimation, which leads to an adaptation of the optimization problem in each time step and thus to a better prediction and an improved input action. Finally, a detailed fuzzy-arithmetic analysis is performed in order to quantify the effect of the uncertainties on the control structure and to derive robustness assessments. The control structure is applied to a serial manipulator with two flexible links containing uncertain model parameters and acting in three-dimensional space.

Offset-free adaptive nonlinear model predictive control with disturbance observer for DC-DC buck converters

The aim of this paper is to design a nonlinear model predictive control for DC-DC buck converters to track constant reference signals with zero steady-state error. The online trained neural network (NN) model is employed as the predictor and the steady-state error, which is called the offset, is studied in the presence of the changes in system parameters and the external disturbances. The stability of the closed-loop system is investigated using the Lyapunov direct theory. The proposed method can provide offset-free behavior in the presence of constant disturbances. For rejecting nonconstant disturbances, a nonlinear disturbance observer based on the NN inverse model is proposed. Due to wide applications of the DC-DC converter in power electronics, control of its output voltage is considered in this paper. The effectiveness of the proposed control method is demonstrated by experimental results.

Control Parameters Tuning Method of Nonlinear Model Predictive Controller Based on Quantitatively Analyzing

[abstFig src='/00280005/11.jpg' width='300' text='ANMPC controller' ] The parameter-tuning method we discuss is for an Adaptive Nonlinear Model Predictive Controller (ANMPC). The MPC is optimization-based controller and decides control input to realize system output that tracks a reference trajectory through “optimal computation.” The reference trajectory is ideal trajectory of system output to converge on a desired value, i.e. controlled system performance depends on the reference trajectory. As a MPC controller which applies to the nonlinear systems, our group has already proposed an adaptive nonlinear MPC (ANMPC) for a tracking control problem of nonlinear two-link planar manipulators. This ANMPC uses a new reference trajectory having control parameters that must be tuned based on the desired controlled system’s responses and properties. To reduce troublesome parameter tuning, we propose new parameter-tuning method for ANMPC by a quantitative analysis of the relationship between a system’s behavior and ANMPC parameters. Numerically simulating the two-link nonlinear manipulator’s tracking control under various conditions demonstrates that proposed tuning method tunes the ANMPC effectively.

Nonlinear model predictive control applied to the separation of praziquantel in simulated moving bed chromatography

An adaptive nonlinear model predictive control of a simulated moving bed unit for the enantioseparation of praziquantel is presented. A first principle model was applied at the proposed purity control scheme. The main concern about this kind of model in a control framework is in regard to the computational effort to solve it; however, a fast enough solution was achieved. In order to evaluate the controller's performance, several cases were simulated, including external pumps and switching valve malfunctions. The problem of plant-model mismatch was also investigated, and for that reason a parameter estimation step was introduced in the control strategy. In every studied scenario, the controller was able to maintain the purity levels at their set points, which were set to 99% and 98.6% for extract and raffinate, respectively. Additionally, fast responses and smooth actuation were achieved.

A graph search and neural network approach to adaptive nonlinear model predictive control

Systems with a priori unknown and time-varying dynamic behavior pose a significant challenge in the field of Nonlinear Model Predictive Control (NMPC). When both the identification of the nonlinear system and the optimization of control inputs are done robustly and efficiently, NMPC may be applied to control such systems. This paper considers stable systems and presents a novel method for adaptive NMPC, called Adaptive Sampling Based Model Predictive Control (Adaptive SBMPC), that combines a radial basis function neural network identification algorithm with a nonlinear optimization method based on graph search. Unlike other NMPC methods, it does not rely on linearizing the system or gradient based optimization. Instead, it discretizes the input space to the model via pseudo-random sampling and feeds the sampled inputs through the nonlinear model, producing a searchable graph. For this discretization, an optimal path is found using Lifelong Planning A⁎, an efficient graph search method. Adaptive SBMPC is used in simulation to identify and control a simple plant with clearly visualized nonlinear behavior. In these simulations, both fixed and time-varying dynamic systems are considered. Results are compared with an adaptive version of Neural GPC, an existing NMPC algorithm based on Newton–Raphson optimization and a back propagation neural network model. When the cost function exhibits many local minima, Adaptive SBMPC is successful in finding a low-cost solution that appears close globally optimal while Neural GPC converges to a solution that is only locally optimal. This paper presents the method, soundness and completeness theory, and two simulated NMPC examples. The first is a transparent single-input single-output example, and the second considers a more complex power plant combustion process with two inputs and three outputs.

Non-linear model predictive control schemes with application on a 2 link vertical robot manipulator

The industrial requirements for controllers able to perform tasks in the presence of plant nonlinearities are growing. In addition, an increase in industrial computation power is allowing the implementation of more complex control algorithms in the fast processing industry. In this investigation three different nonlinear model predictive control algorithms are tested and evaluated in simulation and experimentally. The methodologies are adaptive nonlinear model predictive control (nMPC), PID based nMPC (PIDnMPC), and a novel simplified nMPC (SnMPC). These are tested in simulation with an inverted pendulum, a Van der Pol oscillator, and a planar 2-link vertical robotic arm. The controllers are tested experimentally using a fabricated planar 2-link vertical robotic arm apparatus. A comparison of the different algorithms is made with special attention to trajectory tracking, computational complexity and transient response dynamics.

Estimation and adaptive nonlinear model predictive control of selective catalytic reduction systems in automotive applications

The demands of high NOx conversion efficiency and low tailpipe ammonia slip for urea-based selective catalytic reduction (SCR) systems have been substantially increased in the past decade, as NOx emission legislations for Diesel engines are becoming more stringent than ever before. Since catalyst aging has a significant impact on SCR performance, robust and adaptive SCR control has been preferred for degraded SCR systems to realize emission control objectives. The purpose of this paper is twofold. Firstly, a robust ammonia coverage ratio observer was designed for estimating the ammonia coverage ratio reference for catalysts with different aging levels. An ammonia storage capacity observer was developed for estimating the actual ammonia storage capacity which can be reduced due to catalyst aging. An adaptive ammonia coverage ratio reference design was then developed to estimate the desired ammonia coverage ratio ranges at each instantaneous engine operating point for both single-cell and two-cell SCR systems at different aging levels based on a singular perturbation method. Secondly, to ensure the estimated ammonia coverage ratio falls in the desired ranges for most of engine operating conditions, robust nonlinear model predictive control (NMPC) algorithms were designed for both single-cell and two-cell SCR systems. Experimental data over US06 cycle were collected from a Diesel engine and aftertreatment system platform for controller verification. Simulation results under US06 test cycle demonstrate that the proposed NMPC algorithms were capable of consistently achieving high NOx conversion efficiency (>95.6%) and constrained tailpipe ammonia slip (<10ppm on average and <12ppm on the peak) for both fresh catalyst and aged catalyst with 30% loss of ammonia storage capacity.

Nonlinear Parameters and State Estimation for Adaptive Nonlinear Model Predictive Control Design

This paper deals with an adaptive nonlinear model predictive control (NMPC) based estimator in cases of mismatch modeling, presence of perturbations and/or parameter variations. Thus, we propose an adaptive nonlinear predictive controller based on the second-order divided difference filter (DDF) for multivariable systems. The controller uses a nonlinear state-space model for parameters and state estimation and for the control law synthesis. Two nonlinear optimization layers are included in the proposed algorithm. The first optimization problem is based on the output error (OE) model with a tuning factor, and it is dedicated to minimize the error between the model and the system at each sample time by estimating unknown parameters when assuming that all system states are available. The second optimization layer is used by the centralized nonlinear predictive controller to generate the control law which minimizes the error between future setpoints and future outputs along the prediction horizon. The proposed algorithm leads to a good tracking performance with an offset-free output and an effectiveness in perturbation attenuation. Practical results on a real setup show the reliability of the proposed approach.

Robust and Adaptive Nonlinear Model Predictive Controller for Unsteady and Highly Nonlinear Unmanned Aircraft

The nonlinear and unsteady nature of aircraft aerodynamics in the presence of adverse conditions and external disturbances, together with a limited range of flight variables makes the use of the linear control theory inadequate in such conditions. To address these constraints and significantly enhance aircraft control capabilities, this brief presents an adaptive framework for a robust nonlinear model predictive control (NMPC). Control algorithms are tested on a 1100-pound unmanned aerial system, with nonlinear, coupled, and unstable open-loop dynamics, subjected to environmental disturbances and measurement noise. Given the usual frequency content exclusion between disturbance and noise, this solution addresses the lack of robustness in model predictive control by the inclusion of frequency-dependent weighting matrices and a nonlinear version of the mixed sensitivity approach. Furthermore, real-time aerodynamic parameter estimation and predictive model updating is carried out by online adaptive artificial neural networks. Through assessment and validity of control algorithms, it is demonstrated that two originally competing control concepts, robustness and performance, are integrally attained in real time. This is usually unreachable in the classical NMPC framework for complex systems.

Model predictive control of blood sugar in patients with type‐1 diabetes

SummaryIn this article, two adaptive model predictive controllers (AMPC) are applied to regulate the blood glucose in type 1 diabetic patients. The first controller is constructed based on a linear model, while the second one is designed by using a nonlinear Hammerstein model. The adaptive version of these control schemes is considered to make them more robust against model mismatches and external disturbances. The least squares method with forgetting factor is used to update the model parameters. For simulation study, two well‐known mathematical models namely, Puckett and Hovorka which describe the dynamical behavior of patient's body have been selected. The performances and robustness of the proposed controllers are tested for regulating the blood glucose of diabetic patients in presences of model mismatches and measurement noises. Simulation results indicate that the non‐linear model predictive controller (NMPC) outperforms the linear one. To improve the performance of the NMPC in rejecting the meal disturbances, two different feedforward control strategies have been considered. Simulation results indicate that the combined adaptive NMPC with feedforward controller has a better performance over the other considered control schemes. Copyright © 2015 John Wiley &amp; Sons, Ltd.

DNN-Based ADNMPC of an Industrial Pickling Cold-Rolled Titanium Process via Field Enhancement Heat Exchange

The dynamic neural network based adaptive direct nonlinear model predictive control is designed to control an industrial microwave heating pickling cold-rolled titanium process. The identifier of the direct adaptive nonlinear model identification and the controller of the adaptive nonlinear model predictive control are designed based on series-parallel dynamic neural network training by RLS algorithm with variable incremental factor, gain, and forgetting factor. These identifier and controller are used to constitute intelligent controller for adjusting the temperature of microwave heating acid. The correctness of the controller structure, the convergence, and feasibility of the control algorithms is tested by system simulation. For a given point tracking, model mismatch simulation results show that the controller can be implemented on the system to track and overcome the mismatch system model. The control model can be achieved to track on pickling solution concentration and temperature of a given reference and overcome the disturbance.

Adaptive Optimizing Control of an Ideal Reactive Distillation Column

Control of reactive distillation (RD) systems is a challenging problem due to nonlinear dynamic and steady state behavior arising from complex interactions between reaction kinetics and vapor liquid equilibria. The focus of work reported in the literature on control of RD systems is on solving servo and regulatory control problems. However, when the unmeasured disturbances / system parameters drift from their nominal values, the operating performance of a RD system can potentially be improved if real time optimization (RTO) techniques are employed for deciding the optimum operating point on-line. In this work, an integrated RTO and adaptive nonlinear model predictive control (NMPC) approach has been proposed for operating an RD system in a economically optimal manner. At the core of the integrated scheme is a nonlinear Bayesian state and parameter estimator, which is used as a common link between the RTO and the NMPC components. Estimates of the drifting unmeasured disturbances / parameters generated by the state estimator are used to update the steady state model used for RTO and the dynamic model used for predictions. This facilitates relatively frequent application of RTO without having to wait for the system to reach steady state and makes the NMPC formulation adaptive. Efficacy of the proposed integrated optimizing control scheme is demonstrated by conducting simulation studies on an ideal RD column. The control problem under investigation is optimal inferential control of product concentrations in the face of drifting reactant flow disturbance. Analysis of the simulation results reveals that the proposed integrated approach is able to satisfactorily identify and track economically beneficial optimum operating point of the system.

Online artificial neural network model‐based nonlinear model predictive controller for the meridian UAS

SUMMARYA worldwide accident survey of manned and unmanned aircraft shows in‐flight loss of control remains a major contributor to aircraft accidents. Operation outside the normal fight envelope is usually subject to failure of components, inappropriate crew response, and environmental conditions. The aerodynamic model of aircraft associated with hazardous weather and abnormal conditions is inherently nonlinear and unsteady. A novel adaptive nonlinear model predictive controller is proposed and conceptually proven to ensure safe control of the Meridian unmanned aerial system in off‐nominal conditions. Nonlinear model predictive controllers are capable of handling input and output constraints that directly satisfy safety and performance requirements in off‐nominal conditions. The performance of a nonlinear model predictive controller relies heavily on the physics‐based model. Controller performance is improved by updating the physics‐based model by using real‐time nonlinear estimation of aerodynamic forces. Real‐time nonlinear estimation of aerodynamic forces is obtained utilizing artificial neural networks with time‐varying adaptive parameters. The adaptive nonlinear model predictive controller, coupled with real‐time parameter identification, is shown to exhibit robust characteristics and to successfully mitigate the impact of nonlinear and unsteady aerodynamics while preventing loss of control. Copyright © 2013 John Wiley &amp; Sons, Ltd.