Model Predictive Control Optimization Research Articles

Fast Trajectory Tracking Control Algorithm for Autonomous Vehicles Based on the Alternating Direction Multiplier Method (ADMM) to the Receding Optimization of Model Predictive Control (MPC).

In order to improve the real-time performance of the trajectory tracking of autonomous vehicles, this paper applies the alternating direction multiplier method (ADMM) to the receding optimization of model predictive control (MPC), which improves the computational speed of the algorithm. Based on the vehicle dynamics model, the output equation of the autonomous vehicle trajectory tracking control system is constructed, and the auxiliary variable and the dual variable are introduced. The quadratic programming problem transformed from the MPC and the vehicle dynamics constraints are rewritten into the solution of the ADMM form, and a decreasing penalty factor is used during the solution process. The simulation verification is carried out through the joint simulation platform of Simulink and Carsim. The results show that, compared with the active set method (ASM) and the interior point method (IPM), the algorithm proposed in this paper can not only improve the accuracy of trajectory tracking, but also exhibits good real-time performance in different prediction time domains and control time domains. When the prediction time domain increases, the calculation time shows no significant difference. This verifies the effectiveness of the ADMM in improving the real-time performance of MPC.

Parameter identification and model prediction path following control of underactuated AUV: Methodology and experimental verification

This paper explores the integrated optimal control scheme from the identification of underactuated autonomous underwater vehicle (AUV) system dynamics model parameters to the application of Model Predictive Control (MPC) technology in underactuated AUV motion control, and presents the simulation and field test results. First, the AUV kinematics and dynamics models are introduced to represent the horizontal plane motion characteristics. Based on Computational Fluid Dynamics (CFD) numerical simulation and overset mesh technology, AUV plane motion is simulated to determine the unknown hydrodynamic coefficients in the model, and the accuracy of the mathematical model is validated by comparing the maneuverability simulation and field test results. After that, an adaptive line-of-sight (ALOS) guiding algorithm with exponentially variable forward distance is utilized in the guidance layer to reconcile the rapidity and stability of tracking. The path following problem is formulated as an MPC optimization problem that takes into account multiple realistic constraints and then converted into a standard convex quadratic programming structure, permitting for online real-time optimization. Simulation and field test results indicate that the control algorithm proposed in this paper provides a more effective control strategy than the traditional LOS+PID controller in tracking effect and robustness.

Multivariable discrete MPC with exponential cost function on the automation of the anesthesia process

AbstractThe automation of the delivery of anesthesia infusion rate in a general medical procedure consists of calculating the adequate infusion to regulate a patient's hypnosis state. In this procedure, the patient model has been considered as a Single‐Input Single‐Output system. However, the anesthesiologist introduces other medications, such as analgesics. Therefore, this contribution considers a closed‐loop formulation with two drugs as input control variables: propofol as an anesthetic, and remifentanil as an analgesic. Then, through the mathematical model description, this paper introduces a multiple‐input and multiple‐output (MIMO) model predictive control (MPC) to regulate the deep of hypnosis (DOH) based on the co‐administration of propofol and remifentanil. Since the control variables must be positive during the procedure, the MPC is formulated as a constrained optimization problem. Quadratic programming solves the optimization problem by designing and developing an exponential cost function, which allows the rapid convergence of the MPC optimization algorithm. Finally, the proposed MPC formulation is tested on 12 patients in silico, simulating a 60‐min general surgery. The simulated results verify the performance of the proposed MPC.

Enhancing Autonomous Vehicle Lateral Control: A Linear Complementarity Model-Predictive Control Approach

Model-predictive control (MPC) offers significant advantages in addressing constraint-related challenges and plays a pivotal role in self-driving car technology. Its primary goal is to achieve precise trajectory tracking while prioritizing vehicle stability and safety. However, real-time operations often face challenges related to computational demands and low computational efficiency. To address these challenges, this paper introduces a novel lateral control algorithm for self-driving vehicles, which utilizes the linear complementarity problem (LCP) instead of the conventional quadratic programming (QP) method as the MPC optimization solution. This innovative approach incorporates the electric steering system into the vehicle dynamics model, allowing for precise torque regulation of the steering motor and enhancing control accuracy. The MPC algorithm adopts the LCP solution method to calculate control signals based on the vehicle’s state, ensuring both rapid and stable vehicle control. Simulation results demonstrate that the proposed MPC algorithm, utilizing the LCP solution method, effectively addresses efficiency issues in the lateral motion of self-driving cars. This leads to improvements in both driving stability and real-time performance. Overall, this innovative approach lays a solid foundation for the practical implementation of self-driving cars.

Reproducible estimations of internal corrosion distribution from surface cracks using MPC-RBSM

Rebar corrosion estimation is essential for maintenance of reinforced concrete structures against deterioration. Currently available non-destructive methods of evaluating corrosion do not clearly indicate the internal corrosion condition along the rebar and its effect within the concrete. In prior research, an inverse analysis scheme has been proposed in which the model predictive control (MPC) optimization method is utilized within a rigid body spring model (RBSM) to estimate the corrosion-induced expansion distribution along the rebar from corresponding surface crack width data. In this study, an innovative approach is introduced to verify the precision of MPC-RBSM outcomes and systematically examine the major contributing factors. To facilitate this verification, target cracking is generated by precisely controlling the corrosion expansion within the RBSM framework. In total, three sets of simulations are considered: two cases with varied expansive strain distribution profile along a straight rebar, and third in which a bent rebar arrangement is subject to corrosion. The simulated expansion distribution is compared against the original expansion used to generate the crack width data to validate the reproducibility of the MPC-RBSM results. The inverse analysis results show that the automated expansion scheme in MPC-RBSM successfully reproduces the target surface cracking. In the inverse analysis process, the necessity to account for corrosion distribution is identified. When appropriate corrosion distribution criterion is used to estimate corrosion-induced expansive strain levels along the reinforcement, the results are in good agreement with the assumed corrosion-induced expansive strain profiles (including both uniform and non-uniform profiles). Additionally, simulations of bent rebar corrosion are performed. The results indicate that surface cracking local to the bent region is mainly influenced by corrosion-induced stresses along the straight lengths of the rebar, which complicates the corrosion analysis of bent rebars via this form of inverse analysis.

PDE‐constrained model predictive control of open‐channel systems

AbstractA PDE‐constrained model predictive control (MPC) algorithm for open‐channel systems based on the Saint‐Vevant(S‐V) equations is investigated in this paper. The S‐V equations, which precisely model the dynamics of open‐channel systems, are quasi‐linear hyperbolic partial differential equations (PDEs) without analytical solutions. Directly applying the S‐V equations to an MPC controller design becomes sophisticated. In this work, the calculus of variation is used to obtain the adjoint equations and the adjoint analysis method is utilized to deduce the gradients of the MPC optimization problem. Particularly, the physical constraints involving both the state and control variables are also considered. A gradient‐based optimization algorithm in combination with the numerical computation of Preissmann implicit scheme is proposed to solve the constrained MPC optimization problem. The control performances of the developed PDE‐constrained MPC algorithm with respect to the controlled water levels and gate openings are compared with those of the MPC controller designed for the linearized model. All the simulation tests are carried out on an aqueduct reach in Yehe Irrigation District in Hebei Province, China. The results show that the proposed PDE‐constrained MPC algorithm is a promising method in dealing with the constraints in terms of hyperbolic PDEs, control variables and state variables simultaneously.

A novel bi-level temporally-distributed MPC approach: An application to green urban mobility

Model predictive control (MPC) has been widely used for traffic management, such as for minimizing the total time spent or the total emissions of vehicles. When long-term green urban mobility is considered including e.g. a constraint on the total yearly emissions, the optimization horizon of the MPC problem is significantly larger than the control sampling time, and thus the number of the variables that should be optimized per control time step becomes very large. For systems with dynamics that involve nonlinear, non-convex, and non-smooth functions, including urban traffic networks, this results in optimization problems that are computationally intractable in real time. In this paper, we propose a novel bi-level temporal distribution of such complex MPC optimization problems, and we develop two mathematically linked short-term and long-term MPC formulations with small and large control sampling times that will be solved together instead of the original complex optimization problem. The resulting bi-level control architecture is used to solve the two MPC formulations online for real-time control of urban traffic networks with the objective of long-term green mobility. In order to assess the performance of the bi-level control architecture, we perform a case study where a rough version of the model of the urban traffic flow, S-model, is used by the long-term MPC level to estimate the states of the urban traffic networks, and a detailed version of the model is used by the short-term MPC level. The results of the simulations prove the effectiveness (with respect to the objective of control, as well as computational efficiency) of the proposed bi-level MPC approach, compared to state-of-the-art control approaches.

Machine learning aided model predictive control with multi-objective optimization and multi-criteria decision making

Model predictive control (MPC) is a well-established control methodology in chemical engineering, but the increasing complexity of chemical processes necessitates the consideration of multiple objectives in the MPC optimization step. To address this research gap, this work proposes a comprehensive machine learning (ML) aided MPC with multi-objective optimization (MOO) and multi-criteria decision making (MCDM) methodology (abbreviated as ML-aided MPC-MOO-MCDM) for chemical process control. The proposed methodology is evaluated on a continuous stirred tank reactor (CSTR), and the results demonstrate its capability to achieve intended optimization considering multiple objectives in MPC without compromising the closed-loop stability of the controlled system. The present work also reinforces the viability of using ML models as surrogates for first-principles models in process control and optimization. Overall, this work exhibits the effectiveness of the proposed ML-aided MPC-MOO-MCDM methodology and its applicability to complex chemical processes.

Standoff Tracking Using DNN-Based MPC With Implementation on FPGA

This work studies the standoff tracking problem to drive an unmanned aerial vehicle (UAV) to slide on a desired circle over a moving target at a constant height. We propose a novel Lyapunov guidance vector (LGV) field with tunable convergence rates for the UAV’s trajectory planning and a deep neural network (DNN)-based model predictive control (MPC) scheme to track the reference trajectory. Then, we show how to collect samples for training the DNN offline and design an integral module (IM) to refine the tracking performance of our DNN-based MPC. Moreover, the hardware-in-the-loop (HIL) simulation with a field-programmable gate array (FPGA) at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$200$</tex-math> </inline-formula> MHz demonstrates that our method is a valid alternative to embedded implementations of MPC for addressing complex systems and applications which is impossible for directly solving the MPC optimization problems.

Hierarchical MPC for a dynamic process system employing parametric global optimization strategy

The hierarchical decision making in process industries has been traditionally viewed as having a common objective, such as the overall cost, which needs to be optimized. However, a more appropriate approach is to formulate and solve hierarchical optimization and control problems. The solution algorithms for hierarchical optimization problems have been reported in the literature. The idea is to recast each optimization sub-problem in the hierarchy into a multiparametric programming problem, considering the variables of upper-level problems as unknown parameters. In this paper, explicit Model Predictive Control (MPC) and hierarchical optimization techniques, employing multiparametric programming, are combined for hierarchical MPC. The solution algorithm for hierarchical MPC is described in detail. Note that the solution to a hierarchical MPC problem is challenging, even for the simplest case of linear-quadratic objectives. Closed-loop simulations of a thermal mixing process, under two different hierarchical MPC formulations, are performed and the control performance is studied.

Synchronization control of blanket remote maintenance robot based on MPC-CCC algorithm

AbstractThis paper studies the synchronization control of the blanket remote maintenance robot (BRMR) of the China fusion engineering test reactor (CFETR). First, the general state space mathematical model of BRMR was established by using a physical-based method. Second, based on the receding horizon optimization of model predictive control (MPC) and cross-coupling error reduction in cross-coupling control (CCC), the innovative MPC-CCC controller was proposed to realize the single-system and multisystem error convergence and high accuracy transportation of blanket through the high accuracy synchronization control of BRMR. Third, to verify the control effectiveness of the MPC-CCC controller, two types of simulations and experiments were implied compared with the original proportional-integral (PI) controller in Mover. Results showed that simulation and experiments were highly consistent. It is found that the use of an MPC-CCC controller can result in up to a 70% reduction in displacement error and up to a 59% reduction in synchronization error compared to the PI controller. And the accuracy of the MPC-CCC controller satisfies the real requirement of the maintenance process of the blanket. This work provides the theoretical basis and practical experience for the highly stable, safe, and efficient maintenance of blankets in the future.

Deep learning-based model predictive control for real-time supply chain optimization

This paper presents a deep learning-based model predictive control (MPC) method for operational supply chain optimization in real time. The method follows an offline-online procedure. In the offline phase, the state-space model of a supply chain system is developed and the MPC problem for supply chain operation is formulated. Then, the MPC problem is solved for a set of initial states to obtain the corresponding optimal inputs. A deep neural network (DNN) is built and trained by using the optimal state-input pairs as training data to approximate the optimal MPC law. In the online phase, the DNN controller is employed to provide real-time decisions. In this paper, the MPC problem for supply chain operation is formulated as a mixed-integer linear program. A deep learning-based MPC method is proposed to accommodate time delays in the system. Moreover, a heuristic method is proposed for feasibility recovery with the binary decision variables taken into account. The training set for the DNN controller contains two subsets, one formed from MPC solutions corresponding to random initial states, and the other formed from optimal state-input pairs in closed-loop simulations. The deep learning-based MPC is validated via two case studies through closed-loop simulation. The first case study involves a linear MPC, and the second case study involves a more complicated mixed-integer linear MPC. Results show that deep learning-based MPC can achieve a high accuracy in approximating the MPC decisions and a significant reduction in the online computation time. Compared with MPC, the average performance loss of using deep learning-based MPC in the two cases is 0.43% and 1.8%, respectively.

Dynamic Optimization Fabrics for Motion Generation

Optimization fabrics are a geometric approach to real-time local motion generation, where motions are designed by the composition of several differential equations that exhibit a desired motion behavior. We generalize this framework to dynamic scenarios and nonholonomic robots and prove that fundamental properties can be conserved. We show that convergence to desired trajectories and avoidance of moving obstacles can be guaranteed using simple construction rules of the components. In addition, we present the first quantitative comparisons between optimization fabrics and model predictive control and show that optimization fabrics can generate similar trajectories with better scalability, and thus, much higher replanning frequency (up to 500 Hz with a 7 degrees of freedom robotic arm). Finally, we present empirical results on several robots, including a nonholonomic mobile manipulator with 10 degrees of freedom and avoidance of a moving human, supporting the theoretical findings.

Cautious Bayesian MPC: Regret Analysis and Bounds on the Number of Unsafe Learning Episodes

This paper investigates the combination of model predictive control (MPC) concepts and posterior sampling techniques and proposes a simple constraint tightening technique to introduce cautiousness during explorative learning episodes. The provided theoretical analysis in terms of cumulative regret focuses on previously stated sufficient conditions of the resulting ‘Cautious Bayesian MPC’ algorithm and shows Lipschitz continuity of the future reward function in the case of linear MPC problems. In the case of nonlinear MPC problems, it is shown that commonly required assumptions for nonlinear MPC optimization techniques provide sufficient criteria for model-based RL using posterior sampling. Furthermore, it is shown that the proposed constraint tightening implies a bound on the expected number of unsafe learning episodes in the linear and nonlinear case using a soft-constrained MPC formulation. The efficiency of the method is illustrated using numerical examples.

Predictive Control of a Human–in–the–Loop Network System Considering Operator Comfort Requirements

We propose a model-predictive control (MPC)-based approach to solve a human-in-the-loop control problem for a network system lacking sensors and actuators to allow for a fully automatic operation. The humans in the loop are, therefore, essential; they travel between the network nodes to provide the remote controller with measurements and to actuate the system according to the controller’s commands. Time instant optimization MPC is utilized to compute when the measurement and actuation actions are to take place to coordinate them with the network dynamics. The time instants also minimize the burden of human operators by tracking their energy levels and scheduling the necessary breaks. Fuel consumption related to the operators’ travel is also minimized. The results in a digital twin of the Dez Main Canal illustrate that the new algorithm outperforms previous methods in terms of meeting operational objectives and taking care of human well-being, but at the cost of higher computational requirements.

Multi-Objective Adaptive Optimization Model Predictive Control: Decreasing Carbon Emissions from a Zinc Oxide Rotary Kiln

The zinc oxide rotary kiln, as an essential piece of equipment in the zinc smelting industrial process, is presenting new challenges in process control. China’s strategy of achieving a carbon peak and carbon neutrality is putting new demands on the industry, including green production and the use of fewer resources; thus, traditional stability control is no longer suitable for multi-objective control tasks. Although researchers have revealed the principle of the rotary kiln and set up computational fluid dynamics (CFD) simulation models to study its dynamics, these models cannot be directly applied to process control due to their high computational complexity. To address these issues, this paper proposes a multi-objective adaptive optimization model predictive control (MAO-MPC) method based on sparse identification. More specifically, with a large amount of data collected from a CFD model, a sparse regression problem is first formulated and solved to obtain a reduction model. Then, a two-layered control framework including real-time optimization (RTO) and model predictive control (MPC) is designed. In the RTO layer, an optimization problem with the goal of achieving optimal operation performance and the lowest possible resource consumption is set up. By solving the optimization problem in real time, a suitable setting value is sent to the MPC layer to ensure that the zinc oxide rotary kiln always functions in an optimal state. Our experiments show the strength and reliability of the proposed method, which reduces the usage of coal while maintaining high profits.

Parameter Optimization of Model Predictive Direct Motion Control for Distributed Drive Electric Vehicles Considering Efficiency and the Driving Feeling.

This paper presents a novel motion control strategy based on model predictive control (MPC) for distributed drive electric vehicles (DDEVs), aiming to simultaneously control the longitudinal and lateral motion while considering efficiency and the driving feeling. Initially, we analyze the vehicle's dynamic model, considering the vehicle body and in-wheel motors, to establish the foundation for model predictive control. Subsequently, we propose a model predictive direct motion control (MPDMC) approach that utilizes a single CPU to directly follow the driver's commands by generating voltage references with a minimum cost function. The cost function of MPDMC is constructed, incorporating factors such as the longitudinal velocity, yaw rate, lateral displacement, and efficiency. We extensively analyze the weighting parameters of the cost function and introduce an optimization algorithm based on particle swarm optimization (PSO). This algorithm takes into account the aforementioned factors as well as the driving feeling, which is evaluated using a trained long short-term memory (LSTM) neural network. The LSTM network labels the response under different weighting parameters in various working conditions, i.e., "Nor", "Eco", and "Spt". Finally, we evaluate the performance of the optimized MPDMC through simulations conducted using MATLAB and CarSim software. Four typical scenarios are considered, and the results demonstrate that the optimized MPDMC outperforms the baseline methods, achieving the best performance.

Modelling and Control Tank Testing Validation for Attenuator Type Wave Energy Converter - Part I: Experiment Setup and Control-Oriented Modelling

Advanced non-causal optimal control strategies have been demonstrated to significantly improve the energy output of a scale physical model of an attenuator type wave energy converter (WEC) by tank testing experiments using FloWave tank facilities in Edinburgh supported by Wave Energy Scotland's control project. The results are reported in a series of three papers, summarizing the tank testing setup, dynamic modelling, and validation of both linear non-causal optimal control (LNOC) and model predictive control (MPC) in regular and irregular waves. Compared with an optimally tuned passive damping control, both LNOC and MPC can significantly improve the energy output, by between 10% to 460%, using irregular waves with low to medium magnitude and peak periods ranging from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.7~\mathrm{s}$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2.8~\mathrm{s}$</tex-math></inline-formula> at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1/20^{th}$</tex-math></inline-formula> scale, as shown in Part II and Part III papers. These controllers also show robust performance in spread waves and side waves which are normally encountered in real sea conditions. Furthermore, the control technologies can be transferred to other types of WECs. The results pave the way for the sea trial testing and full control system validation involving the electricity generation stage and power conditioning stage. This Part I paper will focus on the tank testing setup, the passive damping control experimental results, and the control-oriented models for the WEC. Two state-space models derived respectively from the hydrodynamic model and system identification of experimental data, are validated and compared for use on the controller designs to be presented in Part II and Part III.

Centralized MPC for Home Energy Management With EV as Mobile Energy Storage Unit

Electric vehicle (EV) is commonly considered as an electric load in a residential energy network. However, the large capacity EV battery can be used as electric storage when the EV is plugged in at home. While model predictive control (MPC) offers an efficient and reliable control mechanism for a home energy management system (HEMS), the uncertainty related to the availability of an EV at home poses an interesting challenge for the MPC optimization strategy. In this article, the thermal comfort and energy management performance of a centralized MPC-based HEMS is presented for such a scenario where an EV is used as a mobile energy storage unit in a home energy network. The MPC-based HEMS simultaneously controls the zone-based heating system consisting of a heat pump and baseboard units along with the energy flow among the different components of the home energy network. This network comprises the home baseload, charging and discharging of the home-battery and the EV battery, in-house solar energy generation and storage. The MPC-based HEMS optimizes the buying/selling of energy from/to the grid based on time of use electricity rates. A Monte-Carlo based uncertainty analysis is presented here to estimate the robustness of the MPC against the randomness in the EV arrival and departure schedule. Finally, the responsiveness of the centralized MPC is showcased using a vehicle to home communication scenario where the owner notifies the home network regarding their arrival within a short interval, along with the preferred indoor temperature upon arrival.

Balancing CO[formula omitted] emissions and economic cost in a microgrid through an energy management system using MPC and multi-objective optimization

In this work, the energy production of a microgrid is managed to satisfy the demand while simultaneously minimizing two objectives: CO2 emissions and the economic cost of operating the microgrid. To this end, a novel energy management system (EMS) that combines a Model Predictive Control (MPC), a multi-objective optimization algorithm and a decision-tool, has been developed. This EMS takes advantage of the individual strengths of these components to address the changes that frequently appear in the microgrid operating conditions. Unlike traditional optimization, MPC applies the concept of receding horizon, so that the optimization problem covers a prediction horizon instead of the entire simulation time. In addition, it is rerun at each simulation sample time with updated information, so that the controller can adapt to changes. The multi-objective optimization algorithm optimizes the CO2 emissions and the economic cost (these two objectives are in conflict objectives and need to be optimized simultaneously) and generates a set of solutions, each of which is a trade-off between the two objectives. These solutions are called Pareto optimal solutions, and they form the Pareto front. The decision-tool automates the process by managing the Pareto front obtained from the multi-objective optimization. It acts as an expert and selects, among those equally suitable solutions, the one that best fits the current priorities. To test the performance and robustness of the MPC and to demonstrate that the decreasing horizon actually helps to mitigate the uncertainties in the predictions, two simulations are performed. In the first one, the forecasting variables are assumed to be predicted without errors, while in the second one, a prediction error is added to these variables. For each experiment, the decision-tool has been adjusted to select, from the Pareto front provided by the multi-objective algorithm, different solutions satisfying various requirements.