Conventional Nonlinear Model Predictive Control Research Articles

Deep learning for deorbiting control of an electrodynamic tether system

This paper studies the nonlinear dynamics and deorbiting control of an electrodynamic tether (EDT) system in elliptical orbits. The orbital dynamics of the system under Lorentz forces is modelled using a set of modified equinoctial elements, whereas the attitude dynamics of the system is modelled based on the dumbbell assumption. A deep learning scheme of nonlinear model predictive control (NMPC) schemes is proposed for deorbiting control of the EDT system. To facilitate controller design, a time-scale separation method is utilized to simplify the attitude dynamics of the EDT system. A deep learning-based NMPC control law is developed with two stages. In the first stage, a large amount of data is generated using a conventional NMPC law to construct a dataset for training a deep neural network (DNN). In the second stage, the trained DNN is used to realize the real-time mapping from the system state to the system control, and thereby the feedback control of the system deorbit is achieved with extremely low computational cost. Finally, the efficacy and performance of the proposed deep learning-based NMPC control law are demonstrated via numerical case studies.

Novel enhancement of energy management in fuel cell hybrid electric vehicle by an advanced dynamic model predictive control

In this paper, an Advanced Dynamic Model Predictive Control (AMPC) based on a Nonlinear Model Predictive Control (NMPC) framework with a multi-objective cost function driven by dynamic weights is proposed to improve the energy performance of fuel cell hybrid electric vehicles whilst prolonging their component lifetime. By the use of dynamic weights, the cost function is effectively formulated as the combination of fuel consumption, rate of change of fuel cell power, battery power, the fuel cell efficiency, state of charge of the battery, and their temperatures. In order to enhance the adaptability of the AMPC, a Fuzzy Cognitive Map (FCM) is then newly designed to regulate online the dynamic weights to adjust the importance of each cost component according to the conditions prevailing during driving. A comparative study between the proposed AMPC, a constant weight based NMPC and a conventional NMPC having cost function with fewer objectives has been carried out by means of simulation using a FCHEV model from the simulation tool ADVISOR to illustrate the efficacy of the proposed AMPC.

Offset-free neural network-based nonlinear model predictive controller design using parameter adaptation

The performance of conventional nonlinear model predictive control $$\left( {{\text{NMPC}}} \right)$$ system relies heavily on the accuracy of the prediction model. In cases of significant plant-model mismatch, non-desirable responses may be observed in the controlled outputs. This paper proposes a parameter adaptation technique for tackling this problem. In the proposed approach, the output disturbance is selected as the adaptation parameter while the adaptation law is modelled as a function of the tracking error using a first-order difference equation. The adaptation law is integrated into a $$\mathrm{NMPC}$$ algorithm to achieve offset-free tracking. The effectiveness of the proposed scheme is demonstrated on two simulation case studies—a pH system and a continuously stirred tank reactor (CSTR); and an experimental cascaded two tank process. The simulation results obtained showed that the proposed scheme achieves zero offset in the face of significant plant-model mismatch arising from uncertainties in model parameters, unmeasured disturbances, and measurement noise and compared favourably with existing methods. The experimental results obtained during real-time implementation of the proposed control scheme corroborate this assertion and show its industrial applicability.

Reinforcement learning based optimal control of batch processes using Monte-Carlo deep deterministic policy gradient with phase segmentation

Batch process control represents a challenge given its dynamic operation over a large operating envelope. Nonlinear model predictive control (NMPC) is the current standard for optimal control of batch processes. The performance of conventional NMPC can be unsatisfactory in the presence of uncertainties. Reinforcement learning (RL) which can utilize simulation or real operation data is a viable alternative for such problems. To apply RL to batch process control effectively, however, choices such as the reward function design and value update method must be made carefully. This study proposes a phase segmentation approach for the reward function design and value/policy function representation. In addition, the deep deterministic policy gradient algorithm (DDPG) is modified with Monte-Carlo learning to ensure more stable and efficient learning behavior. A case study of a batch polymerization process producing polyols is used to demonstrate the improvement brought by the proposed approach and to highlight further issues.

Nonlinear Model Predictive Trajectory Tracking Control of Underactuated Marine Vehicles: Theory and Experiment

The article studies the trajectory tracking control problem of underactuated marine vehicles via the nonlinear model predictive control (NMPC) strategy, where practical control and state constraints present. It is a well-known challenging issue that the conventional NMPC is not applicable for underactuated marine vehicles, due to the fact that there does not exist a local static continuous state-feedback controller to stabilize the underactuated dynamics. To resolve this issue, this article proposes to construct an auxiliary time-varying tracking controller to aid terminal constraint design in the NMPC framework, where the time-varying tracking controller borrows the ideas from Lyapunov's direct method and backstepping approach. Based on this, a novel NMPC algorithm is designed to ensure trajectory tracking control of underactuated marine vehicles. Furthermore, a systematic parameter design approach is developed. Under the designed parameters, we show that the tracking error system is input-to-state stable (ISS). Finally, the effectiveness of the designed algorithm is verified by thorough simulation and hardware experiments.

An analytical approach to optimal control of nonlinear systems with input constraints

In this paper, a novel optimal control method with the analytical solution strategy is developed for a wide class of nonlinear systems with input constraints. First, an equivalent constrained optimisation problem is formulated by performing a quadratic performance index including the control inputs and the predicted tracking errors. Then, the problem is analytically solved by using the Kerush-Kuhn-Tucker (KKT) theorem to find the optimal control law. For comparison, a computational technique based on calling the genetic algorithm (GA) is also provided to online solving the developed optimisation problem. The proposed control method with two solutions is applied on a mathematical example and a chemical reactor which is a multi-input multi-output (MIMO) system. The results show that the proposed KKT-based predictive controller is effective from different aspects. Importantly, it is very fast, easy to solve and suitable for online implementation compared with the conventional nonlinear model predictive control (NMPC) method.

An analytical approach to optimal control of nonlinear systems with input constraints

In this paper, a novel optimal control method with the analytical solution strategy is developed for a wide class of nonlinear systems with input constraints. First, an equivalent constrained optimisation problem is formulated by performing a quadratic performance index including the control inputs and the predicted tracking errors. Then, the problem is analytically solved by using the Kerush-Kuhn-Tucker (KKT) theorem to find the optimal control law. For comparison, a computational technique based on calling the genetic algorithm (GA) is also provided to online solving the developed optimisation problem. The proposed control method with two solutions is applied on a mathematical example and a chemical reactor which is a multi-input multi-output (MIMO) system. The results show that the proposed KKT-based predictive controller is effective from different aspects. Importantly, it is very fast, easy to solve and suitable for online implementation compared with the conventional nonlinear model predictive control (NMPC) method.

Event triggered nonlinear model predictive control for a wastewater treatment plant

This paper presents an event triggered nonlinear model predictive control (NMPC) to improve the performance of a wastewater treatment plant (WWTP). The goal of this paper is to design a simplified event triggered NMPC(ETNMPC) suitable for practical implementation. Unlike the conventional NMPC where an optimisation problem is solved at each sampling instant, in the proposed event based formulation of NMPC, the optimisation problem is re-evaluated only when a certain triggering condition is satisfied. A triggering condition is designed based on deviation of error or one step ahead prediction of error from a predefined threshold value. If one of these goes beyond the predefined threshold limit or the time gap from the triggering of last event crosses the maximum allowable time limit, a new event is triggered. The controller is designed to improve the overall performance of a WWTP by regulating two significant variables, i.e. nitrate and dissolved oxygen concentrations at some specified set-points. A conventional NMPC is also designed. The performances of the proposed controller is compared with a conventional NMPC and PI controller. Both NMPC and ETNMPC are able to improve Effluent Quality and Overall Cost Index of the WWTP when compared with PI controller, but a significant reduction in computation and communication(almost 50%) is achieved in the case of ETNMPC when compared with the conventional NMPC.

Fast economic nonlinear model predictive control strategy of Organic Rankine Cycle for waste heat recovery: Simulation-based studies

Effective control for Organic Rankine Cycle (ORC) systems is required to ensure safety of each component and attain satisfactory performance in spite of the waste heat sources varying in a broad range. To maximally recover the waste heat and to handle the multivariate constraints during the ORC transient operation, in this paper an economic nonlinear model predictive controller (EMPC) using the net power output as an objective is designed. To fast obtain a solution of EMPC in practical applications, the computation of the gradient of the EMPC objective is simplified and the quasi-sequential method is employed for the online dynamic optimization of EMPC. Unlike the conventional nonlinear model predictive control (MPC) scheme, the results in a case study show that the proposed EMPC can quickly improve the net power output of the ORC system during the operation while still satisfying the load tracking requirements.

Model-Predictive Control Strategy for an Array of Wave-Energy Converters

To facilitate the commercialization of wave energy in an array or farm environment, effective control strategies for improving energy extraction efficiency of the system are important. In this paper, we develop and apply model-predictive control (MPC) to a heaving point-absorber array, where the optimization problem is cast into a convex quadratic programming (QP) formulation, which can be efficiently solved by a standard QP solver. We introduced a term for penalizing large slew rates in the cost function to ensure the convexity of this function. Constraints on both range of the states and the input capacity can be accommodated. The convex formulation reduces the computational hurdles imposed on conventional nonlinear MPC. For illustration of the control principles, a point-absorber approximation is adopted to simplify the representation of the hydrodynamic coefficients among the array by exploiting the small devices to wavelength assumption. The energy-capturing capabilities of a two-cylinder array in regular and irregular waves are investigated. The performance of the MPC for this two-WEC array is compared to that for a single WEC, and the behavior of the individual devices in head or beam wave configuration is explained. Also shown is the reactive power required by the power takeoff system to achieve the performance.

Learning-Based Predictive Control for Discrete-Time Nonlinear Systems With Stochastic Disturbances.

In this paper, a learning-based predictive control (LPC) scheme is proposed for adaptive optimal control of discrete-time nonlinear systems under stochastic disturbances. The proposed LPC scheme is different from conventional model predictive control (MPC), which uses open-loop optimization or simplified closed-loop optimal control techniques in each horizon. In LPC, the control task in each horizon is formulated as a closed-loop nonlinear optimal control problem and a finite-horizon iterative reinforcement learning (RL) algorithm is developed to obtain the closed-loop optimal/suboptimal solutions. Therefore, in LPC, RL and adaptive dynamic programming (ADP) are used as a new class of closed-loop learning-based optimization techniques for nonlinear predictive control with stochastic disturbances. Moreover, LPC also decomposes the infinite-horizon optimal control problem in previous RL and ADP methods into a series of finite horizon problems, so that the computational costs are reduced and the learning efficiency can be improved. Convergence of the finite-horizon iterative RL algorithm in each prediction horizon and the Lyapunov stability of the closed-loop control system are proved. Moreover, by using successive policy updates between adjoint time horizons, LPC also has lower computational costs than conventional MPC which has independent optimization procedures between two different prediction horizons. Simulation results illustrate that compared with conventional nonlinear MPC as well as ADP, the proposed LPC scheme can obtain a better performance both in terms of policy optimality and computational efficiency.

Constrained control Lyapunov function-based control of nonlinear systems

In this paper, we present an algorithm to address the problem of guaranteed stabilization of nonlinear systems from the largest set of initial conditions from where stabilization is possible, the so-called null controllable region (NCR), while also handling state constraints and partial unboundedness of the NCR. The controller uses the geometry of the NCR to inform a constrained control Lyapunov function which in turn provides feasibility and stability guarantees. The NCR is produced from a novel iterative growth algorithm that exploits a certain invariance property. The new controller implementation is illustrated using a chemical reactor system and compared to a conventional nonlinear model predictive control (MPC) implementation.

Advanced-step Nonlinear Model Predictive Control Based on Contraction Analysis

Recently, an approach of advanced-step nonlinear model predictive control (NMPC) based on nonlinear programming (NLP) sensitivity was developed for controlling large-scale complex plants. It can reduce the online computation time significantly while maintaining the same nominal stability of the conventional NMPC. However, the sensitivity based fast online update method cannot be applied to those cases where the NMPC problem contains a non-convex economic cost function or constraints. In this paper, based on contraction analysis, a novel online update mechanism, differential Lyapunov based MPC, which involves solving a quadratic programming problem with stability constraints is proposed to address this issue. A case study with non-convex state constraints is presented to demonstrate the concepts.

Dual Control and Information Gain in Controlling Uncertain Processes

In controlling uncertain processes, it is decisive to utilize information provided by measurements in order to estimate parameters and states. Nonlinear Model Predictive Control (NMPC) is a popular method to implement feedback control and deal with uncertainties. Conventional NMPC or nominal control, however, sometimes does not provide enough information for system estimation, leading to unsatisfactory performance. Dual control attempts to strike a balance between the two goals of enhancing system estimation and optimizing the nominal objective function. In this paper, we analyze the performance of these strategies through the interplay between the performance control task and the information gain task in connection with Optimal Experimental Design. Examples illustrate the conflict and agreement between the two tasks and explain why in some cases nominal control performs well. It is also observed that measurement noise provides excitation helping to improve the quality of estimates.

A field-programmable gate array implementation of a real-time nonlinear Runge–Kutta model predictive control

This paper presents the very first field-programmable gate array (FPGA) implementation of the Runge–Kutta model predictive control (RKMPC) mechanism to the real-time experimental electromagnetic levitation system, which is an unstable nonlinear continuous-time system with a very small time constant. In the control mechanism, the so called Runge–Kutta model of the nonlinear system is employed as an approximate discrete-time model of the system and used in the model predictive control loop for prediction and derivative calculation purposes. Experimental results have shown the effectiveness of the proposed implementation under different control conditions. Moreover, the RKMPC has been compared to a conventional nonlinear model predictive control (NMPC) method to show the advantages of the RKMPC over the NMPC.

Integration of multiple model based fault detection and nonlinear model predictive fault‐tolerant control

In this paper, we present a new fault‐tolerant control system for a class of nonlinear systems with input constraints. Because of many important factors that stabilize a nonlinear model predictive controller, it can be used as a powerful controller in the event of fault occurrence. So, the reconfigurable controller is designed based on the quasi‐infinite model predictive control (QIMPC) approach as a fault‐tolerant approach. On the other hand, a fault detection and diagnosis (FDD) system is designed based on the multiple model method. The bank of extended Kalman filters (EKFs) is used to detect the predefined actuator fault and estimate the unknown parameters of a fault. When a fault is detected, the proposed FDD information is used to correct the model of the faulty system recursively and reconfigure the controller. Delay on FDD decision may lead to performance degradation or even instability for some systems. The timely proposed FDD approach will preserve stability. Moreover, a framework is presented to ensure stability when a fault occurs. The effectiveness of this method is demonstrated, in comparison with conventional nonlinear model predictive control, by two practical examples. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

The advanced-step NMPC controller: Optimality, stability and robustness

Widespread application of dynamic optimization with fast optimization solvers leads to increased consideration of first-principles models for nonlinear model predictive control (NMPC). However, significant barriers to this optimization-based control strategy are feedback delays and consequent loss of performance and stability due to on-line computation. To overcome these barriers, recently proposed NMPC controllers based on nonlinear programming (NLP) sensitivity have reduced on-line computational costs and can lead to significantly improved performance. In this study, we extend this concept through a simple reformulation of the NMPC problem and propose the advanced-step NMPC controller. The main result of this extension is that the proposed controller enjoys the same nominal stability properties of the conventional NMPC controller without computational delay. In addition, we establish further robustness properties in a straightforward manner through input-to-state stability concepts. A case study example is presented to demonstrate the concepts.