Model Predictive Control Formulation Research Articles

3DoF-KF HMPC: A Kalman filter-based Hybrid Model Predictive Control Algorithm for Mixed Logical Dynamical Systems

This paper presents the formulation, design procedure, and application of a hybrid model predictive control (HMPC) scheme for hybrid systems that is embedded in a mixed logical dynamical (MLD) framework. The proposed scheme adopts a three degrees-of-freedom (3DoF) tuning method to accomplish precise setpoint tracking and ensure robustness in the face of disturbances (both measured and unmeasured) and uncertainty. Furthermore, the HMPC algorithm employs setpoint and disturbance anticipation to proactively enhance controller performance and potentially reduce control effort. Slack variables in the objective function prevent the mixed-integer quadratic problem from becoming infeasible. The effectiveness of the proposed algorithm is demonstrated through its application in three distinct case studies, which include control of production–inventory systems, time-varying behavioral interventions for physical activity, and management of epidemics/pandemic prevention. These case studies indicate that the HMPC algorithm can effectively manage hybrid dynamics, setpoint tracking and disturbance rejection in diverse and demanding circumstances, while tuned to perform well in the presence of nonlinearity and uncertainty.

Model Predictive Control Used in Passenger Vehicles: An Overview

The following article presents a high-level overview of how Model Predictive Control (MPC) is leveraged in passenger vehicles and their subsystems for improved performance. This overview presents the fundamental concepts of MPC algorithms and their common variants. After building some understanding of MPC methods, the paper discusses state-of-the-art examples of how MPC methods are leveraged to perform low- to high-level tasks within a typical passenger vehicle. This review also aims to provide the reader with intuition in formulating MPC systems based on the strengths and weaknesses of the different formulations of MPC. The paper also highlights active areas of research and development.

Artificial Neural Networks for Energy Demand Prediction in an Economic MPC‐Based Energy Management System

ABSTRACTMicrogrids are a development trend and have attracted a lot of attention worldwide. The control system plays a crucial role in implementing these systems and, due to their complexity, artificial intelligence techniques represent some enabling technologies for their future development and success. In this paper, we propose a novel formulation of an economic model predictive control (economic MPC) applied to a microgrid designed for a faculty building with the inclusion of a predictive model to deal with the energy demand disturbance using a recurrent neural network of the long short‐term memory (RNN‐LSTM). First, we develop a framework to identify an RNN‐LSTM using historical data registered by a smart three‐phase power quality analyzer to provide feedforward power demand predictions. Next, we present an economic MPC formulation that includes the prediction model for the disturbance within the optimization problem to be solved by the MPC strategy. We carried out simulations with different scenarios of energy consumption, available resources, and simulation times to highlight the results obtained and analyze the performance of the energy management system. In all cases, we observed the correct operation of the proposed control scheme, complying at all times with the objectives and operational restrictions imposed on the system.

Computation of feedback control laws based on switched tracking of demonstrations

A common approach in robotics is to learn tasks by generalizing from special cases given by a so-called demonstrator. In this paper, we apply this paradigm and present an algorithm that uses a demonstrator (typically given by a trajectory optimizer) to automatically synthesize feedback controllers for steering a system described by ordinary differential equations into a goal set. The resulting feedback control law switches between the demonstrations that it uses as reference trajectories. In comparison to the direct use of trajectory optimization as a control law, for example, in the form of model predictive control, this allows for a much simpler and more efficient implementation of the controller. The synthesis algorithm comes with rigorous convergence and optimality results, and computational experiments confirm its efficiency.

Time-efficient model predictive control for autonomous tugs with adaptive input constraints

The marine autonomous surface ship (MASS) has gained significant attention because of its wide application in waterborne transportation in recent years. The trajectory control of the MASS is crucial in ensuring safety, particularly in narrow navigation areas and urgent encounter situations. Model predictive control (MPC) is well known as a sufficient method to solve the tracking problem considering the actuator saturation with model uncertainties and environmental disturbances. However, due to the constraints on computing resources and hardware limits, the controller may fail to find a feasible solution for MPC within a reasonable amount of time, especially when the system models are coupled and complex. To improve the solution efficiency, this paper introduces adaptive constraints to reduce search space for optimization, i.e., the current tracking point’s speed is transformed into input constraints in the MPC formulation to decrease the computation burden, as well as reduce mechanical wear on the thrusters with smaller amplitudes of control actions. Simulations are carried out to evaluate the effectiveness of the proposed method with different MPC forms.

A Novel MPC Formulation for Dynamic Target Tracking with Increased Area Coverage for Search-and-Rescue Robots

Robots are increasingly deployed for search-and-rescue (SaR), in order to speed up rescuing the victims in the aftermath of disasters. These robots require effective mission planning approaches to determine time and space-efficient trajectories that steer them faster towards (moving) victims, while dealing with uncertainties. Model predictive control (MPC) is an effective optimization-based control approach that has been used to steer robots along reference trajectories determined by higher level controllers. Determining the trajectory of the robots directly via MPC has the advantage of optimizing multiple SaR criteria while handling the constraints. We, thus, introduce a path planning approach based on MPC for indoor SaR robots that allows the robot to systematically chase the moving victims, when no reference trajectory is provided. The proposed approach combines target-oriented and coverage-oriented search, and allows for systematic handling of environmental uncertainties, by deploying a robust tube-based version of the introduced MPC formulation. In addition, we model the movements of the victims for MPC, by adopting an existing evacuation model. We present a case study, using Gazebo, MATLAB, and ROS, where the performance of the proposed MPC controller is evaluated compared to four state-of-the-art methods (two target-oriented methods based on MPC and A* and two heuristic algorithms for area coverage). The results show that, while robust to uncertainties, our approach overall outperforms the other methods, with regards to victim detection, area coverage, and mission time.

Nonlinear scenario‐based model predictive control for quadrotors with bidirectional thrust

AbstractThe control of quadrotor vehicles under state and parameter uncertainty is a well studied problem that is vitally important to the deployment of these systems under real world conditions. In this article, we propose a linearization‐based extension to nonlinear systems of the existing scenario model predictive control (MPC) framework, which quantifies the impact of uncertainty on the vehicle dynamics through repeated sampling of the uncertainty space. Given the computational costs of such an approach, we also propose two simplifications of the scenario MPC algorithm that are significantly more tractable. In order to evaluate the performance of the algorithms, the specific problem of the control of a bidirectionally actuated quadrotor vehicle is considered. Simulations are carried out for each scenario MPC scheme as well as for a reference deterministic MPC scheme. When a sufficiently large sample count is considered, each of the scenario MPC algorithms achieves safer performance than the deterministic formulation without sacrificing any optimality. Additionally, the approximate solution techniques conclusively outperform the original nonlinear scenario MPC formulation for the same computational cost.

Image based Modeling and Control for Batch Processes

This manuscript addresses the problem of leveraging thermal images for modeling and feedback control, specifically tailored for terminal quality control of batch processes. The primary objective, common in many batch processes, is to produce products with quality variables aligning with user specifications, available for measurement only at batch termination, precluding the direct use of classical control strategies. Furthermore, in many instances, traditional online sensors such as thermocouples may not be available, but instead spectral inputs like thermal images or acoustic data may be more readily available for feedback control. The challenge is to not only use the non-traditional sensor data for building a dynamic model but also to use that model for terminal quality control. The proposed approach involves a multi-layered modeling strategy. Initially, a dimensionality reduction technique is employed to condense the high-dimensional image into a set of representative outputs. Subsequently, subspace identification (SSID) is applied to develop a Linear Time-Invariant (LTI) State Space (SS) model between the inputs and the reduced outputs. Finally, a Partial Least Squares (PLS) model is constructed linking the terminal states of a batch (identified using SSID) with the product qualities obtained for that specific batch. This model is then incorporated into a Model Predictive Control (MPC) formulation. The effectiveness of the MPC is illustrated by showcasing its capability to generate products of high quality by deploying the MPC on a bi-axial lab-scale rotational molding setup.

Self-stabilizing economic nonlinear model predictive control applied to modular systems

Recent advances have been made in self-stabilizing Economic Nonlinear Model Predictive Control (eNMPC) formulation without pre-calculated setpoints, which leverages norm-based steady-state optimality conditions to enhance system robustness. To enable practical implementation, a generalized time-domain formulation is proposed, accommodating the discrete-time nature of control instrumentation and the continuous-time nature of first-principles models. A case study involving a modular membrane reactor illustrates the applicability of self-stabilizing eNMPC in real-world industrial scenarios.

Novel terminal region computation method for quasi-infinite horizon NMPC

An algorithm for invariant region characterization for a nonlinear system controlled by an LQR is proposed. The quasi-infinite horizon nonlinear model predictive controller formulation is extended for zone control with optimizing targets. The novel invariant region characterization proposed promotes hypervolume gains of up to two orders of magnitude for an unstable CSTR. Extension of the NMPC formulation to the case of zone control with optimizing targets improves the formulation’s practical deployment capability. A comparison between QIH-NMPC and NMPC with a terminal equality constraint is drawn, showing considerable closed-loop performance loss when employing a terminal equality constraint. The proposed invariant region shows feasibility set gains from the proposed invariant region characterization, when compared to a recent approach. Closed-loop simulations of both controllers from the enlarged feasibility set show how sensible the closed-loop performance is to one infeasible controller iteration.

State‐dependent dynamic tube MPC: A novel tube MPC method with a fuzzy model of model of disturbances

AbstractMost real‐world systems are affected by external disturbances, which may be impossible or costly to measure. For instance, when autonomous robots move in dusty environments, the perception of their sensors is disturbed. Moreover, uneven terrains can cause ground robots to deviate from their planned trajectories. Thus, learning the external disturbances and incorporating this knowledge into the future predictions in decision‐making can significantly contribute to improved performance. Our core idea is to learn the external disturbances that vary with the states of the system, and to incorporate this knowledge into a novel formulation for robust tube model predictive control (TMPC). Robust TMPC provides robustness to bounded disturbances considering the known (fixed) upper bound of the disturbances, but it does not consider the dynamics of the disturbances. This can lead to highly conservative solutions. We propose a new dynamic version of robust TMPC (with proven robust stability), called state‐dependent dynamic TMPC (SDD‐TMPC), which incorporates the dynamics of the disturbances into the decision‐making of TMPC. In order to learn the dynamics of the disturbances as a function of the system states, a fuzzy model is proposed. We compare the performance of SDD‐TMPC, MPC, and TMPC via simulations, in designed search‐and‐rescue scenarios. The results show that, while remaining robust to bounded external disturbances, SDD‐TMPC generates less conservative solutions and remains feasible in more cases, compared to TMPC.

A Precise Temperature Control Method for Lithium-ion Battery Pack based on the Nonlinear Model Predictive Control Algorithm

Abstract To utilize the maximum performance of the battery while ensuring its thermal safety, a battery thermal management system is used to control the battery maximum temperature within a safe range. This paper centres on the establishment of a temperature prediction model and the development of the nonlinear-based model predictive control (MPC) strategy. First, to address the need of predicting battery temperature, this paper develops a distributed parameter thermal resistance model to predict battery temperature quickly and accurately. Secondly, the open-loop formulation of the nonlinear-based MPC is derived based on the established state space equations. Then the soft and hard constraints of the model are established based on the actual current conditions, pump conditions, temperature difference and temperature rise indexes, so as to establish the objective function of the MPC algorithm. Finally, the established temperature nonlinear MPC algorithm is embedded on the board and the hardware platform of battery liquid cooling system is established. The experiment test result shows that the maximum error of temperature control is less than 0.1°C, and the effectiveness of the temperature control strategy of lithium-ion battery is verified through experiments.

Modeling of Cooperative Robotic Systems and Predictive Control Applied to Biped Robots and UAV-UGV Docking with Task Prioritization.

This paper studies a cooperative modeling framework to reduce the complexity in deriving the governing dynamical equations of complex systems composed of multiple bodies such as biped robots and unmanned aerial and ground vehicles. The approach also allows for an optimization-based trajectory generation for the complex system. This work also studies a fast-slow model predictive control strategy with task prioritization to perform docking maneuvers on cooperative systems. The method allows agents and a single agent to perform a docking maneuver. In addition, agents give different priorities to a specific subset of shared states. In this way, overall degrees of freedom to achieve the docking task are distributed among various subsets of the task space. The fast-slow model predictive control strategy uses non-linear and linear model predictive control formulations such that docking is handled as a non-linear problem until agents are close enough, where direct transcription is calculated using the Euler discretization method. During this phase, the trajectory generated is tracked with a linear model predictive controller and addresses the close proximity motion to complete docking. The trajectory generation and modeling is demonstrated on a biped robot, and the proposed MPC framework is illustrated in a case study, where a quadcopter docks on a non-holonomic rover using a leader-follower topology.

Cable shaping with MPC: A reliable, fast, and real-time feasible formulation

Cable shaping remains a challenge for robotic automation in various industrial applications. While recent studies have demonstrated the potential of using learned interaction models combined with feedback controllers, there is still significant room for improvement, especially concerning reliability and execution speed. In light of this, we propose combining a learned interaction model with model predictive control, an effective approach for controlling constrained dynamical systems. To achieve real-time feasibility, we introduce a suitable approximation into the model predictive control formulation. When compared to the state-of-the-art, our approach achieves substantially improved reliability and execution speed.

Stability of Progressively Tightening Model Predictive Control in Continuous Time

We consider a continuous-time nonlinear model predictive control formulation that is progressively tightening in path costs and constraints. Under standard assumptions, we prove asymptotic stability of the origin for the corresponding closed-loop system and extend this result to formulations employing an auxiliary dynamic system. The theoretical results are illustrated on a numerical example.

Robust constrained nonlinear Model Predictive Control with Gated Recurrent Unit model

In this paper we propose a robust Model Predictive Control where a Gated Recurrent Unit network model is used to learn the input–output dynamics of the system under control. Robust satisfaction of input and output constraints and recursive feasibility in presence of model uncertainties are achieved using a constraint tightening approach. Moreover, new terminal cost and terminal set are introduced in the Model Predictive Control formulation to guarantee Input-to-State Stability of the closed loop system with respect to the uncertainty term.

Stability Verification of Neural Network Controllers Using Mixed-Integer Programming

We propose a framework for the stability verification of Mixed-Integer Linear Programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be evaluated at a low computational cost, against a fixed baseline policy, which is known to be stable but expensive to evaluate. We provide sufficient conditions for the closed-loop stability of the candidate policy in terms of the worst-case approximation error with respect to the baseline policy, and we show that these conditions can be checked by solving a Mixed-Integer Quadratic Program (MIQP). Additionally, we demonstrate that an outer and inner approximation of the stability region of the candidate policy can be computed by solving an MILP. The proposed framework is sufficiently general to accommodate a broad range of candidate policies including ReLU Neural Networks (NNs), optimal solution maps of parametric quadratic programs, and Model Predictive Control (MPC) policies. We also present an open-source toolbox in Python based on the proposed framework, which allows for the easy verification of custom NN architectures and MPC formulations. We showcase the flexibility and reliability of our framework in the context of a DC-DC power converter case study and investigate its computational complexity.

Lexicographic optimization for economic model predictive control with zone tracking

Tracking model predictive control (MPC) and economic model predictive control (EMPC) are essential techniques in process control. Economic model predictive control with zone tracking offers an effective means of concurrently addressing both tracking MPC and EMPC objectives. However, the aggregated conflicting objectives do not always align with the prioritization of critical tasks, such as safety, stability, quality, and economy. To address this issue, this study introduces a lexicographic approach for EMPC with zone tracking, which aims at balancing the competing zone tracking and economic objectives. The work also explores a generalized lexicographic multi-objective MPC (MoMPC) formulation and presents lexicographic zone economic model predictive control to accommodate multiple tracking and economic objectives. The advantages, disadvantages, and effectiveness of the proposed approach are validated and showcased through extensive simulation experiments.

Distributed Model Predictive Formation Control for a Group of UAVs With Spatial Kinematics and Unidirectional Data Transmissions

This paper proposes a distributed model predictive control (DMPC) algorithm for the formation flight of a group of UAVs modeled by six degree-of-freedom (6-DoF) spatial kinematics. The formation system has a leader-follower structure with the leader cruising at a constant linear velocity during the flight, and the UAVs transmit data in a unidirectional order. The DMPC algorithm utilizes the unidirectional structure through the reception and transmission of an assumed output sequence as the reference trajectory, which is constructed from the solutions to the local DMPC problem and the prediction model. Based on the interactions between UAVs, convergence and stability of the multi-UAV formation are ensured by the terminal constraints and recursive feasibility of the DMPC optimization. Simulations involving time-delays, packet drops and turbulence effect are conducted to verify the effectiveness of the proposed algorithm. Comparisons with non-unidirectional data transmissions further demonstrate that the unidirectional structure plays a critical role in the convergence performance

Risk‐averse perimeter control for alleviating the congestion of an urban traffic network system with uncertainties

AbstractThe perimeter control method is an effective way to alleviate traffic congestion that is based on Macroscopic Fundamental Diagrams (MFDs). However, the strategy may lead to congestion when it ignores the uncertainty of MFDs. To address this problem, this paper presents a risk‐averse perimeter control method. First, the urban traffic network system with uncertainty is modeled using a neural network and scenario tree. Then, this research quantifies the congestion risk caused by uncertainty using an average value‐at‐risk. The next step sees the design of a risk‐averse model predictive control (MPC) controller that takes the multi‐stage risk as the optimization objective and improves robustness by interpolating between the conventional stochastic and worst‐case MPC formulations. Finally, this paper analyzes the risk‐sensitive stability of an urban traffic network system and gives a solvable form of risk‐averse optimal control for this system. Finally, two simulations are conducted to verify the presented method's validity and superiority for an urban traffic network system with uncertainties. The simulation results show that the risk‐averse perimeter control method presented by this paper is superior because it reduces the total travel time by 12.98% compared to Stochastic MPC, by 15.96% compared to bang‐bang control, and by 14.54% compared to proportional‐integral.