Horizon Model Predictive Control Research Articles

Online learning MPC for switched systems with performance dependent mixed switching law

This paper explores online learning model predictive control (MPC) for switched systems with stable terminal constraints. In order to reduce the computational burden, we decompose the infinite horizon MPC into n finite horizons, and adopt adaptive dynamic programming (ADP) to assist MPC in online solving the optimal control problem in each finite horizon. Further, we use a set of stable terminal constraints to ensure both the convergence of online learning MPC in each finite horizon and the connection of adjacent finite horizons. In addition, in order to ensure the uniform ultimate boundedness (UUB) of the triggered switched systems, on the one hand, a novel performance dependent mixed switching law (PD-MSL) is proposed to both avoid frequent switching and take advantage of performance dependent decision-making; on the other hand, an analytical framework of the coupling between mode switching and event-triggering is proposed. Finally, the validity of the presented approach is demonstrated through simulations.

Quasi-Infinite Horizon Model Predictive Control with Fixed-Time Disturbance Observer for Underactuated Surface Vessel Path Following

As a flexible, autonomous and intelligent motion platform, underactuated surface vessels (USVs) are expected to be an ideal means of transport in dangerous and complex marine environments. The success and efficiency of maritime missions performed by USVs depend on their ability to accurately follow paths and remain robust against wind and wave disturbances. To this end, this paper focuses on accurate and robust path following control for USVs under wave disturbances. Model predictive control with a quasi-infinite horizon is proposed which converts the objective function from an infinite horizon to an approximate finite horizon, providing the convergence performance in long prediction horizons and reducing the computation load explicitly. To enhance robustness against disturbances, a fixed-time disturbance observer is applied to estimate the time-varying and bounded disturbances. The estimated value is provided to the controller input to form a robust control framework with disturbance feedforward compensation and predictive control feedback correction, which is substantially different from existing works. The convergence and optimality of the proposed algorithm are presented mathematically. Finally, we demonstrate the advantages of the algorithm in both theory and simulation.

Minimizing total annualized cost per tonne of feed processed of a semicontinuous distillation process utilizing data-driven model predictive control

Semicontinuous distillation is a separation technique used to purify multicomponent mixtures with low to medium throughput. This research addresses the problem of designing a Data-driven Model Predictive Control (MPC) approach that enables minimizing the Total Annualized Cost (TAC) of the semicontinuous process per tonne of feed processed while maintaining the required product purity. In lieu of typically unavailable first principles models, the manuscript demonstrates the implementation of data-driven technique using data collected from an Aspen Plus Dynamics simulation as a test bed. A subspace model identification technique is adapted to develop a multi-model framework to capture the dynamic behavior of the process and then utilized within a Shrinking Horizon MPC (SHMPC) scheme, to achieve the required objective. The simulation results demonstrate a lowering of the TAC/tonne of feed by 11.4% compared to the traditional PI setup used in the previous studies.

An optimization algorithm based on forward recursion with applications to variable horizon MPC

We consider optimization algorithms designed for variable horizon model predictive control. Traditionally, such problems are considered intractable for real-time applications that require fast computations, as they need to solve multiple optimal control problems with varying horizons at each sampling instance. The main contribution is an algorithm that efficiently solves multiple optimal control problems with different prediction horizons in a recursive manner. This algorithm has been successfully implemented and integrated into the OSQP solver, resulting in a real-time controller that is both fast and reliable. To assess the effectiveness of the approach, we conducted evaluations in both a realistic simulation environment and on real hardware during outdoor flight experiments. Specifically, we focused on two distinct rendezvous maneuvers for autonomous landings of unmanned aerial vehicles. The results obtained from these evaluations further validate the practicality and efficacy of the proposed algorithm.

A Warm-Start Strategy in Interior Point Methods for Shrinking Horizon Model Predictive Control With Variable Discretization Step

For optimal control problems with random external disturbances, offline algorithms may not perform well because the state cannot be predicted. To solve the problems online, the model predictive control is frequently used, where a series of subproblems with different initial conditions are solved. These convex subproblems could be solved by using interior point methods after discrete approximations. To obtain a solution as accurately as possible under limited computing resources, the variable discretization step is usually considered. To improve efficiency, warm-start methods are considered, which utilize the similarity of subproblem structures. Specifically, the information obtained by solving earlier subproblems is used to solve subsequent subproblems. However, the discretization steps and the sampling numbers of subproblems may be different, and the initial states vary greatly, resulting in poor performance of existing warm-start strategies for interior point methods. In this paper, we present a new warm-start strategy for interior-point methods. In the strategy, a convex combination of components of the earlier optimal solution is used to construct an interpolation point, and we use the convex combination of the modified interpolation point and the cold-start point to obtain a warm-start point. We prove that the worst-case iteration complexity of our strategy is better than that of the cold-start. In the numerical experiment of fuel-optimal planetary powered-descent guidance problems, our strategy reduces the number of iterations of second-order cone programming by about <inline-formula><tex-math notation="LaTeX">$80\%$</tex-math></inline-formula> with the number of samples available in practical applications.

Energy-efficient predictive control for trams incorporating disjunctive time constraints from traffic lights

Tram operations are often blocked by traffic lights, leading to frequent decelerations and re-accelerations that increase operational energy consumption. This paper focuses on tram energy-efficient control problem incorporating time constraints from traffic lights that have multiple feasible green time windows (GTWs). We formulate the problem as a mixed-integer nonlinear program (MINLP), where binary variables are assigned to model disjunctive time constraints of the GTWs. To address computational challenge of solving the MINLP, we reformulate it as a tractable nonlinear program (NLP). Specifically, an equivalent NLP is first presented by replacing the integrality constraint with nonlinear constraints, and then the nonlinear constraints are relaxed and penalized into cost functions. To recover a solution of the MINLP, we propose a computationally efficient sequential quadratic programming algorithm in a shrinking horizon model predictive control framework, which updates the penalty parameter and quadratic programming subproblems in parallel. The solution obtained from the subproblem is feasible in each iteration, and convergence of the feasibility iterations can be enforced by the updated penalty. The performance of the proposed approach is investigated on different scenarios using real-life tram data. Results show that the method is able to generate energy-efficient driving trajectories in a dynamic environment, while crossing traffic lights in effective GTWs without unnecessary decelerations and re-accelerations.

Advanced process control system with MPC as a new approach for layer of protection analysis

Layer of protection analysis (LOPA) is a widely used method to support process safety in the chemical industries. In the LOPA, the process is classified into many layers, one of such layers considers the basic process control system (BPCS) which commonly uses PID controllers. This kind of controllers cannot deal with constraints. For this reason, the main purpose of this work is to provide a framework to enhance the control layer in the LOPA, which consists of a model predictive control (MPC) with safety features. These features include: sublayers in the controller system (such as real time optimization, target calculation, and MPC), safety constraints, and guarantee of stability by adopting an Infinite Horizon MPC (IHMPC). Here, we propose an approach for control-inspired view to process safety, replacing the BPCS by an Advanced Process Control System (APCS). Moving forward with these concepts, first, a literature review emphasizes the content, showing two perspectives for the APCS. The APCS is designed for two varieties of controllers, a basic IHMPC and IHMPC with zone control to compare the performance. In this framework, the first sublayer consists of a real time optimization (RTO) structure, that calculates the optimal operating condition for the process controller, which computes the control action. Besides, RTO has an additional constraint called the safety index, based on the protection of process operational. RTO and basic IHMPC communicate directly, while for IHMPC with zone control there is an inner sublayer called Target Calculation, it computes a feasible target to the controller, working as another safety strategy in APCS. After that, we demonstrate both structures applied to a CSTR reactor. From the case study, we compared both controllers, and evaluated the effect that the safety index constraint causes in the setpoints, outputs, and control actions. The use of safety constraint in RTO proved to be a safe strategy for the control layer, as well as IHMPC with zone control presented a safer profile than basic IHMPC. Furthermore, the results show that safety constraint affect the economic goal, decreasing its value.

An event-triggered trajectory planning and tracking scheme for automatic berthing of unmanned surface vessel

This study proposes a trajectory planning and tracking scheme for the fully actuated USV's automatic berthing. First, a three-degree-of-freedom model (3-DOF) of USV is employed, considering model uncertainty, actuator saturation, and environmental disturbances. Moreover, an A* algorithm with the Bezier curve (AB) approach is proposed to plan the smooth berthing trajectory. To make the velocity of the USV converge to zero at the berth, an interpolation method is proposed to densify the waypoints at the end of the berthing trajectory. Most of the previous studies about USV's tracking control pay little attention to real-time performance, which may increase the computational cost of the control system and affect its stability. Therefore, to improve the computational performance during the USV's berthing, an event-triggered adaptive horizon model predictive control (ETAHMPC) method is proposed. Comparative simulation experiments are performed in two scenarios to verify the effectiveness and superiority of the proposed ETAHMPC scheme. The results show that the proposed scheme can effectively reduce computational costs while ensuring control performance.

Predictive tracking of an object by a pan–tilt camera of a robot

Moving-object tracking using a pan–tilt camera setup is quite a well-known task in robotics. However, the presented research addresses specific properties of the tracked object and introduces novel features to the pan–tilt camera control strategy. Pan–tilt camera control does not operate in an isolated environment. It is a part of the visual servoing system with specific goals. The system has to fulfill certain purposes, which affect its configuration and functionality. The pan–tilt system aims at keeping the visually tracked object within the middle of the image. At the same time, the overall visual servoing efficiently recognizes and tracks the object enabling its grasping by the robot arm. It uses a predictive strategy utilizing specific second-order linear models for pan and tilt joints. Model predictive control (MPC) introduces into the system the ability to predict camera operation over the specific horizon according to the predefined tracking goals. As the system anticipates future positions over the horizon of operation, the setpoint prediction of the future tracked system positions is required. Visual object recognition and tracking system use particular strategies for preparing online tracked object extrapolation over MPC horizon. Therefore, the pan–tilt camera system is intrinsically coupled to camera-based recognition and tracking. Predictive pan–tilt positioning keeps the tracked system in the middle of the image, while the visual system extrapolation improves the tracking performance. The proposed approach is thoroughly tested in the dedicated Gazebo-based robot simulator. Finally, the system is implemented and validated on the Velma robot. The results and their comparison with other control strategies confirm the initial assumptions, allowing further visual servoing system development.

Global sensitivity analysis for design and operation of distributed energy systems: A two-stage approach

Distributed Energy Systems (DES) can play a vital role as the energy sector faces unprecedented changes to reduce carbon emissions by increasing renewable and low-carbon energy generation. However, current operational DES models do not adequately reflect the influence of uncertain inputs on operational outputs, resulting in poor planning and performance. This paper details a methodology to analyse the effects of uncertain model inputs on the primary output, the total daily cost, of an operational model of a DES. Global Sensitivity Analysis (GSA) is used to quantify these effects, both individually and through interactions, on the variability of the output. A Mixed-Integer Linear Programming model for the DES design is presented, followed by the operational model, which incorporates Rolling Horizon Model Predictive Control. A subset of model inputs, which include electricity and heating demand, and solar irradiance, is treated as uncertain using data from a case study. Results show reductions of minimum 25% in the total annualised cost compared to a traditional design that purchases electricity from the centralised grid and meets heating demand using boilers. In terms of carbon emissions, the savings are much smaller, although the dependency on the national grid is drastically reduced. Limitations and suggestions for improving the overall DES design and operation are also discussed in detail, highlighting the importance of incorporating GSA into the DES framework.

Cooperative game-based multi-objective optimization of cargo transportation with floating partial space elevator

This paper develops a dual-phase control strategy based on the piecewise cooperative game method to balance the multiple competing objectives for cargo transportation by a partial space elevator in terms of orbital state stability and cargo transport efficiency and ensure final state stability. The cargo transportation is performed in the libration-free mode to facilitate the control implementation, where all libration motions are kept at zero. The new control strategy is split into phases I and II. Phase I focuses on cargo transportation and covers most cargo transfer distances. Multiple competing control objectives in this phase are balanced by the newly proposed piecewise cooperative game method. Once the remaining distance meets the preset threshold, the transportation enters phase II, which focuses on bringing the state of the partial space elevator to a stable equilibrium state. A shrinking horizon model predictive control method is used to ensure the state converges to the equilibrium point by the end of transportation. The simulation results reveal that the newly proposed dual-phase control scheme effectively balances multiple competing control objectives in the cargo transfer period. Moreover, by introducing phase II, the system can achieve a stable equilibrium state by the end of the transfer period.

Time-distributed optimization for shrinking horizon MPC

This paper proposes a strategy for implementing shrinking horizon Model Predictive Control (MPC) using a limited number of optimization iterations at each timestep. Offline and online certification methods are presented for determining a time-varying bound on the number of optimization iterations that ensures the closed-loop system satisfies a specified terminal constraint. An axisymmetric spacecraft spin stabilization example is reported to demonstrate the certification procedure.

A Novel Framework for Trajectory Planning and Safe Navigation of Satellite Swarms

This paper proposes a new framework for near-optimal, collision-free navigation of a swarm of identical satellites from an initial formation to a desired final formation. The framework combines a centralized optimization problem for location assignment with collision avoidance constraints, a decentralized fuel-optimal trajectory planner, a decentralized Artificial Potential Field (APF)-based real-time controller to ensure robustness, and a Shrinking Horizon Model Predictive Control logic to prevent deadlocks and livelocks and to improve robustness. To ensure high performance and low fuel cost, a novel optimization problem is formulated to tune the APF parameters based on mission requirements. The proposed framework provides a balance between optimality and scalability while keeping computational requirements low. The effectiveness of the frame work is demonstrated using numerical simulations.

Performance Evaluation of Energy-Optimal Adaptive Cruise Control in Simulation and on a Test Track

This paper presents a comprehensive evaluation of energy-optimal adaptive cruise control (EACC) based on model predictive control (MPC) in comparison to standard adaptive cruise control (ACC) which is equipped for mass-produced cars of a German car maker. First, a simulation study is made in this work to compare the performance of PID-based control and MPC. Afterwards, a prototype of EACC is installed in an electric vehicle (EV), which is tested as the host car and follows a preceding car on a test track. In the test cycles, which represent urban and rural driving scenarios, EACC reduces the energy consumption of the host car by up to 13% in comparison with the standard ACC. The results of the vehicle tests not only demonstrate a significant energy reduction by EACC, but also show that EACC can reduce the risk of rear-end collisions by reacting earlier to rapid deceleration of the vehicle in front. Furthermore, the passengers feel more comfortable as the vehicle speed trajectory is smoothened by EACC. Finally, to investigate the real-time implementation capability of the optimization algorithms, this paper also examines the computation time of the MPC-based EACC function with different lengths of the MPC horizon.

An Improvement of Model Predictive for Aircraft Longitudinal Flight Control Based on Intelligent Technique

This paper introduces a new intelligent tuning for the model predictive control (MPC) based on an effective intelligent algorithm named the bat-inspired algorithm (BIA) for the aircraft longitudinal flight. The tuning of MPC horizon parameters represents the main challenge to adjust the system performance. So, the BIA algorithm is intended to overcome the tuning issue of MPC parameters due to conventional methods, such as trial and error or designer experience. The BIA is adopted to explore the best parameters of MPC based on the minimization of various time domain objective functions. The suggested aircraft model takes into account the aircraft dynamics and constraints. The nonlinear dynamics of aircraft, gust disturbance, parameters uncertainty and environment variations are considered the main issues against the control of aircraft to provide a good flight performance. The nonlinear autoregressive moving average (NARMA-L2) controller and proportional integral (PI) controller are suggested for aircraft control in order to evaluate the effectiveness of the proposed MPC based on BIA. The proposed MPC based on BIA and suggested controllers are evaluated against various criteria and functions to prove the effectiveness of MPC based on BIA. The results confirm that the accomplishment of the suggested BIA-based MPC is outstanding to the NARMA-L2 and traditional PI controllers according to the cross-correlation criteria, integral time absolute error (ITAE), system overshoot, response settling time, and system robustness.

Embedded predictive controller based on fuzzy linear parameter-varying model: A hardware-in-the-loop application to an ESP-lifted oil well system

This work addresses the development of a fuzzy infinite horizon model predictive control (FIHMPC) strategy and its application to an ESP-lifted oil well system in an embedded hardware. The proposed scheme is based on a fuzzy model to approximate the nonlinear system to a linear parameter-varying model and incorporate it into the proposed MPC law. Slacked terminal constraints and zone control scheme are incorporated to the FIHMPC controller assuring optimization feasibility to handle ESP time-varying operation envelope. The implementable zone FIHMPC controller is applied through an ESP32 micro-controller to ESP-lifted oil well system equations, executed in MATLAB, composing a hardware-in-the-loop (HIL) simulation scheme. Nonlinear mismatch scenarios with unmeasured disturbances show the effectiveness of the proposed controller over multiple operating conditions. Computational memory and processing analysis over simulations also validates the controller application.

Libration-free cargo transfer of floating space elevator

This paper studies the libration-free cargo transfer control of a partial space elevator where the main satellite may change its orbital state in the transfer period. The orbital motion of the main satellite in the climber transfer period is first studied. Then, a reduced-order libration-free dynamics of the partial space elevator is derived. Accordingly, a novel libration-free switching control strategy is proposed to stabilize cargo transportation with two alternating controllers. The Controller I controls the cargo speed in the libration-free mode by a shrinking horizon model predictive control based on the reduced-order libration-free dynamic mode of the partial space elevator. It leads to high computational efficiency in control. Once the libration is induced by the cargo transfer, the control turns off the Controller I and activates the Controller II to suppress the libration to zero within one time step of the Controller I by a novel prescribed-time control law based on the fixed-time control scheme. The stability of the control is proved in the Lyapunov framework. The validity and effectiveness of the proposed control strategy are demonstrated by computation simulation. Simulation results reveal that the proposed control strategy is effective in keeping stable cargo transportation while ensuring the equilibrium state at the end of transportation.

Stability of finite horizon optimisation based control without terminal weight

This paper presents a stability analysis tool for model predictive control (MPC) where control action is generated by optimising a cost function over a finite horizon. Stability analysis of MPC with a limited horizon but without terminal weight is a well-known challenging problem. We define a new value function based on an auxiliary one-step optimisation related to stage cost, namely optimal one-step value function (OSVF). It is shown that a finite horizon MPC can be made to be asymptotically stable if OSVF is a (local) control Lyapunov function (CLF). More specifically, by exploiting the CLF property of OSFV to construct a contractive terminal set, a new stabilising MPC algorithm (CMPC) is proposed. We show that CMPC is recursively feasible and guarantees stability under the condition that OSVF is a CLF. Checking this condition and estimation of the maximal terminal set are discussed. Numerical examples are presented to demonstrate the effectiveness of the proposed stability condition and corresponding CMPC algorithm.

A fast equivalent scheme for robust constrained-input min–max finite horizon model predictive control via model-free critic-only Q-learning

A fast equivalent scheme for robust constrained-input min–max finite horizon model predictive control via model-free critic-only Q-learning

Trajectory-tracking control of an underactuated unmanned surface vehicle based on quasi-infinite horizon model predictive control algorithm

The method of a designed trajectory tracking for an underactuated unmanned surface vehicle (USV) in the presence of ocean disturbances is addressed in this paper; the differential flatness theory is applied to get the reference inputs and speed states at the reference position trajectory. Second, a transition process is arranged for the reference trajectory to reduce the overshoot of the actuator, which caused by the large deviation in the initial tracking. Third, the nonlinear disturbance observer is designed to obtain the estimated values of unknown disturbances in the ocean. Then, a controller-based model predictive control (MPC) and terminal cost function is designed for the nominal system. The inherent robustness of the controller and estimates of the observer are used to resist and compensate disturbances. Finally, the simulation experiments of linear trajectory and sinusoidal trajectories are carried out to prove the effectiveness and reliability of the control algorithm designed.