Event-Triggered Cloud-based Nonlinear Model Predictive Control with Neighboring Extremal Adaptations

In this paper a hierarchical model predictive control framework for the energy management of a hybrid electric vehicle is extended by replacing the supervisory linear model predictive controller with a nonlinear model predictive controller. The nonlinear system dynamics of a parallel hybrid electric vehicle are incorporated into a nonlinear optimal control problem which is solved at each time instance. The discretization of the continuous time system dynamics is realized via direct multiple shooting. The low-level linear model predictive controller considers the actuator dynamics for optimal tracking of the driver's torque demand while the high-level controller considers the slow dynamics of the vehicle and the battery. The proposed strategy is validated in simulation with the worldwide harmonized light vehicles test cycle and compared to a hierarchical model predictive control framework with linearized system dynamics.

Trajectory tracking is a basic function required for autonomous helicopters, but it also poses challenges to control design due to the complexity of helicopter dynamics. This article introduces an explicit model predictive control (MPC) to solve this problem, which inherits the advantages of non-linear MPC but eliminates time-consuming online optimization. The explicit solution to the non-linear MPC problem is derived using Taylor expansion and exploiting the helicopter model. With the explicit MPC solution, the control signals can be calculated instantaneously to respond to the fast dynamics of helicopters and suppress disturbances immediately. On the other hand, the online optimization process can be removed from the MPC framework, which can accelerate the software development and simplify onboard hardware. Due to these advantages of the proposed method, the overall control framework has a low complexity and high reliability, and it is easy to deploy on small-scale helicopters. The proposed explicit non-linear MPC has been successfully validated in simulations and in actual flight tests using a Trex-250 small-scale helicopter.

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.

A magnetic levitation system (Maglev) is a sensitive, multi-parameter, nonlinear, and unstable system that is utilized to levitate a ferromagnetic object in free space. Due to its vast applications, various research studies in the field of control strategy have become extremely important and challenging. This work proposes the design of a nonlinear model predictive (NMPC) control scheme for the object position control against the nonlinearities and uncertainties of a Maglev system. A novel bio-inspired Artificial Protozoa Optimization (APO) algorithm is used to fine-tune the NMPC parameters, which include best weighting matrices ( ), shorter prediction horizons ( ), and shorter time steps ( ) to minimize the objective cost function. The effective performance of the NMPC is verified using simulation-based results in MATLAB. The CasADi toolbox is utilized to solve nonlinear optimization problems and handle the nonlinearity of the Maglev system model. Simulations are implemented for three trajectories tracking (step, sine, and square) with 20% and without Maglev parameters perturbations. To prove the superiority of the proposed controller, comparisons are made with the conventional Linear Quadratic Regulator (LQR) and proportional-integral-derivative (PID) controllers. Two performance indices are introduced, Integral of Squared Error (ISE) and Integral of Absolute Error (IAE), to examine the tracking performances of the NMPC, LQR, and PID controller. The NMPC controller has shown more efficient performance and accurate results than other controllers. The contributions of this work include a new optimization technique of APO, a new engineering application of the APO integrated with NMPC to control a Maglev system, consideration of inherent nonlinearities and system constraints, and robustness improvement under perturbation.

Designing non-linear model predictive control (NMPC) laws for controlling multiple autonomous surface vessels in arbitrary formations in environments containing obstacles are reported in this paper. Two leader-follower decentralized geometrical control schemes that are required for defining a unique two-dimensional formation are considered. A three-degree-of-freedom dynamic model of surface vessels has been used for the controller design. It is assumed that the surface vessels are under-actuated and obstacles are present in the vessels' work environment. The real-time optimization abilities of the NMPC method has been used to improve the response of the unactuated DOF of the vessels and to directly incorporate the local obstacle avoidance into the formation control eliminating the need for an external local obstacle avoidance algorithm. This leads to more effective obstacle avoidance decisions based on the dynamics of the vehicle. The effectiveness the developed control law, even in the presence of model uncertainty and external disturbances are demonstrated via computer simulations.

In this article, we present a quasi-infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi-infinite horizon terminal cost. As a result, we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. The practicality of this approach is demonstrated with a benchmark example.

A roadmap for in silico development and evaluation of industrial NMPC applications: A practical case study

SUMMARYA multistep nonlinear model predictive control (MPC) framework is developed to achieve steady‐state offset‐free control in the presence of plant–model mismatch. Our formulation explicitly accounts for the effect of plant–model mismatch by involving the output feedback error, which is expressed as the difference between the measured process output and the predicted model output at the previous sampling instance, in the multistep model recursive prediction. The proposed scheme is capable of improving the performance of nonlinear MPC, because the plant–model mismatch is effectively compensated through the recursive prediction propagation. We prove that this formulation is able to remove the steady‐state error to achieve offset‐free control. The proposed nonlinear MPC framework is applied to a highly nonlinear two‐input two‐output continuous stirred tank reactor, in comparison with other MPC implementations. The results obtained demonstrate that the proposed technique outperforms some existing popular MPC schemes and can realise offset‐free control even under significant plant–model mismatch and unmeasured disturbances. Copyright © 2012 John Wiley & Sons, Ltd.

Nonlinear model predictive controllers (NLMPC) using fundamental dynamic models and online nonlinear optimization have been in service in ExxonMobil Chemical since 1994. The NLMPC algorithm used in this work employs a state space formulation, a finite prediction horizon, a performance specification in terms of desired closed loop response characteristics for the outputs, and costs on incremental manipulated variable action. The controller can utilize fundamental or empirical models. The simulation and optimization problems are solved simultaneously using sequential quadratic programming (SQP). In the paper, we present results illustrating regulatory and grade transition (servo) control by NLMPC on several industrial polymerization processes. The paper outlines the NLMPC technology employed, describes the current status in industry for extending linear model predictive control to nonlinear processes or applying NLMPC directly, and identifies several needs for improvements to components of NLMPC.

Thermal processes with prolonged and variable delays pose considerable difficulties due to unpredictable system dynamics and external disturbances, often resulting in diminished control effectiveness. This work presents a hybrid control strategy that synthesizes deep reinforcement learning (DRL) strategies with nonlinear model predictive control (NMPC) to improve the robust control performance of a thermal process with a long time delay. In this approach, NMPC cost functions are formulated as learning functions to achieve control objectives in terms of thermal tracking and disturbance rejection, while an actor–critic (AC) reinforcement learning agent dynamically adjusts control actions through an adaptive policy based on the exploration and exploitation of real-time data about the thermal process. Unlike conventional NMPC approaches, the proposed framework removes the need for predefined terminal cost tuning and strict constraint formulations during the control execution at runtime, which are typically required to ensure robust stability. To assess performance, a comparative study was conducted evaluating NMPC against AC-based controllers built upon policy gradient algorithms such as the deep deterministic policy gradient (DDPG) and the twin delayed deep deterministic policy gradient (TD3). The proposed method was experimentally validated using a temperature control laboratory (TCLab) testbed featuring long and varying delays. Results demonstrate that while the NMPC–AC hybrid approach maintains tracking control performance comparable to NMPC, the proposed technique acquires adaptability while tracking and further strengthens robustness in the presence of uncertainties and disturbances under dynamic system conditions. These findings highlight the benefits of integrating DRL with NMPC to enhance reliability in thermal process control and optimize resource efficiency in thermal applications.

Future vehicle localisation technologies enable major enhancements of vehicle dynamics control. This study proposes a novel vehicle stability control paradigm, based on pre-emptive control that considers the curvature profile of the expected path ahead in the computation of the reference direct yaw moment and braking control action. The additional information allows pre-emptive trail braking control, which slows down the vehicle if the predicted speed profile based on the current torque demand is deemed incompatible with the reference trajectory ahead. Nonlinear model predictive control is used to implement the approach, in which also the steering angle and reference yaw rate provided to the internal model are varied along the prediction horizon, to account for the expected vehicle path. Two pre-emptive stability control configurations with different levels of complexity are proposed and compared with the passive vehicle, and two state-of-the-art nonlinear model predictive stability controllers, one with and one without non-pre-emptive trail braking control. The performance is assessed along obstacle avoidance tests, simulated with a high-fidelity model of an electric vehicle with in-wheel motors. Results show that the pre-emptive controllers achieve higher maximum entry speeds – up to ∼34% and ∼60% in high and low tyre-road friction conditions – than the formulations without preview.

In this paper, the parameterized dynamical model of the diesel engine intake and exhaust system using a data-based method, namely a Gain-Scheduled model is proposed and designed based on the data from a virtual engine test bench under normal load conditions. In the first step, the Multiple Input Multiple Output model structure is defined with five inputs and two outputs. Using the constructed model, it is possible to establish the relations between intake Manifold Pressure, Air Mass Flow, the control signals, and changes of the load. Then, the model is further used to design a Nonlinear Model Predictive Control controller, aimed at optimizing the efficiency of the combustion system in terms of the control reference value tracking with respect to emission reduction. This paper follows a model-based design approach to construct the Nonlinear Model Predictive Control objective function for the engine intake Manifold Pressure and Air Mass Flow nonlinear control problem. The proposed data-based dynamical modeling method is shown to increase the flexibility for the modeling of nonlinear plant at a low cost in computational requirements. The experimental results illustrate that the optimized nonlinear control approach significantly improve the control reference tracking performance and the exhaust emissions against the standard decentralized Single Input Single Output control in the standard production Engine Control Unit.

Learning affine predictors for MPC of nonlinear systems via artificial neural networks

Integrated nonlinear model predictive fault tolerant control and multiple model based fault detection and diagnosis

A model predictive optimal control system for the practical automatic start-up of anaerobic digesters