Stabilizing Model Predictive Control Research Articles

Application of a stabilizing model predictive controller to path following for a car‐like agricultural robot

AbstractThis work addresses the problem of path following for a car‐like agricultural robot by means of a finite control set model predictive control (FCS‐MPC) strategy that considers the control actions in a set composed of a limited amount of elements. Recent results on a stabilizing MPC formulation that replaces the classical control invariant set by a pair of inner‐outer sets are extended to preserve stability properties with different control and prediction horizons and are then used for the aforementioned application. Being particularly simple, the presented approach can explicitly deal with nonlinearities and constraints at the expense of resolution in the vehicle steering system, which in practice does not affect the controller performance as will be shown. In addition to describing the control method, simulations and a comparison with another nonlinear MPC strategy are presented to illustrate the advantages of the proposed scheme.

Flexible development and evaluation of machine‐learning‐supported optimal control and estimation methods via HILO‐MPC

AbstractModel‐based optimization approaches for monitoring and control, such as model predictive control and optimal state and parameter estimation, have been used successfully for decades in many engineering applications. Models describing the dynamics, constraints, and desired performance criteria are fundamental to model‐based approaches. Thanks to recent technological advancements in digitalization, machine‐learning methods such as deep learning, and computing power, there has been an increasing interest in using machine learning methods alongside model‐based approaches for control and estimation. The number of new methods and theoretical findings using machine learning for model‐based control and optimization is increasing rapidly. However, there are no easy‐to‐use, flexible, and freely available open‐source tools that support the development and straightforward solution to these problems. This article outlines the basic ideas and principles behind an easy‐to‐use Python toolbox that allows to solve machine‐learning‐supported optimization, model predictive control, and estimation problems quickly and efficiently. The toolbox leverages state‐of‐the‐art machine learning libraries to train components used to define the problem. Machine learning can be used for a broad spectrum of problems, ranging from model predictive control for stabilization, set point tracking, path following, and trajectory tracking to moving horizon estimation and Kalman filtering. For linear systems, it enables quick generation of code for embedded model predictive control applications. HILO‐MPC is flexible and adaptable, making it especially suitable for research and fundamental development tasks. Due to its simplicity and numerous already implemented examples, it is also a powerful teaching tool. The usability is underlined, presenting a series of application examples.

Decomposition of Equations of Nonlinear Affine Control Systems and its Application to the Synthesis of Regulators

The article deals with the decomposition of nonlinear differential equations based on the group-theoretic approach. At the beginning, the decomposition of differential equations of linear systems using a transition matrix of state is presented, and then, based on the theory of continuous groups (Lie groups), the process of decomposition of differential equations of nonlinear systems is shown. The decomposition approach is based on the isomorphism theorem of the space of vector fields and Lie derivatives, which allows us to consider vector fields as differential operators of smooth functions. A formula is derived about the adjoin representation of a Lie group in its Lie algebra, which actually determines the finding of a vector field that characterizes the interaction of two or more vector fields. The Lie algebra of derivatives makes it possible to determine the infinitesimal action of the Lie group, i.e. the linearization of this action is carried out (transformation of the points of the trajectory space of the original system in a small neighborhood). Decomposition allows, as in the linear case, to separate the finding of an action (only locally) of a group of transformations from the transformed points themselves. For linear systems, this separation is global. It is also shown that the decomposition of linear equations is a particular case of the decomposition of nonlinear equations. An algorithm of the method of model predictive control with Gramian weighting using this decomposition is presented. A practical example of decomposition and application of the model predictive control for stabilization of a nonstationary nonlinear system is considered.

A Novel Control Architecture Based on Behavior Trees for an Omni-Directional Mobile Robot

Robotic systems are increasingly present in dynamic environments. This paper proposes a hierarchical control structure wherein a behavior tree (BT) is used to improve the flexibility and adaptability of an omni-directional mobile robot for point stabilization. Flexibility and adaptability are crucial at each level of the sense–plan–act loop to implement robust and effective robotic solutions in dynamic environments. The proposed BT combines high-level decision making and continuous execution monitoring while applying non-linear model predictive control (NMPC) for the point stabilization of an omni-directional mobile robot. The proposed control architecture can guide the mobile robot to any configuration within the workspace while satisfying state constraints (e.g., obstacle avoidance) and input constraints (e.g., motor limits). The effectiveness of the controller was validated through a set of realistic simulation scenarios and experiments in a real environment, where an industrial omni-directional mobile robot performed a point stabilization task with obstacle avoidance in a workspace.

Hybrid iLQR Model Predictive Control for Contact Implicit Stabilization on Legged Robots

Hybrid iLQR Model Predictive Control for Contact Implicit Stabilization on Legged Robots

Stabilizing model predictive control synthesis using integral quadratic constraints and full‐block multipliers

SummaryIn this paper, we discuss how to synthesize stabilizing model predictive control (MPC) algorithms based on convexly parameterized integral quadratic constraints (IQCs), with the aid of general multipliers. Specifically, we consider Lur'e systems subject to sector‐bounded and slope‐restricted nonlinearities. As the main novelty, we introduce point‐wise IQCs with storage in order to accordingly generate the MPC terminal ingredients, thus enabling closed‐loop stability, strict dissipativity with regard to the nonlinear feedback, and recursive feasibility of the optimization. Specifically, we consider formulations involving both static and dynamic multipliers, and provide corresponding algorithms for the synthesis procedures. The major benefit of the proposed approach resides in the flexibility of the IQC framework, which is capable to deal with many classes of uncertainties and nonlinearities. Moreover, for the considered class of nonlinearities, our method yields larger regions of attraction of the synthesized predictive controllers (with reduced conservatism) if compared to the standard approach to deal with sector constraints from the literature.

A Practically Stabilizing Model Predictive Control Scheme for Switched Affine Systems

This letter presents the design and analysis of a practically stabilizing model predictive control (MPC) scheme for a class of discrete-time switched affine systems with at least one stable subsystem. A pruning algorithm with cost approximation is proposed to ensure the practical stability of the MPC scheme while reducing the online computations. A criterion for selecting the pruning parameters to ensure the feasibility of the MPC scheme is presented, which is formulated as a convex optimization problem. With the proposed pruning, the value function of the MPC scheme becomes a practical-Lyapunov function which guarantees global practical stability of the switched affine system for arbitrary prediction horizons. The MPC scheme is applied to switching power converters and simulation results are given for a buck converter which is a DC-DC converter.

Handling model uncertainty in control of a pressure swing adsorption unit for syngas purification: A multi-model zone control scheme-based robust model predictive control strategy

The application of a robustly stabilizing model predictive control (MPC) strategy to a pressure swing adsorption (PSA) unit, hitherto unexplored in the literature, is addressed in this work. Here, a set of linear models to handle model uncertainties describes the PSA nonlinear dynamic behaviour. Each model represents a different operating condition of the PSA, generating a multi-model uncertainty description. In addition to incorporating the multi-model uncertainty, the proposed MPC control law deals with a controlled output zone tracking scheme to systematically accommodate typical cyclic steady states of a PSA process. From the industrial standpoint, economic targets on process variables (controlled outputs, manipulated inputs, or both) are also incorporated into the robust control method. A Real-Time Optimizer usually defines these targets, making up a two-layer control scheme. The effectiveness of the robust MPC is evaluated in a syngas purification process via a single bed, six-step PSA unit composed of a porous amino-functionalized titanium terephthalate MIL-125-type MOF adsorbent.

Model Predictive Control for Stabilization of DC Microgrids in Island Mode Operation

DC microgrid (DCMG) is a promising technology for integrating distributed resources, such as solar generation and energy storage devices, that are intrinsically DC. Recently, model predictive control (MPC) is one of the control techniques that has been widely used in microgrid applications due to its advantages, such as transient response and flexibility to nonlinearity inclusion. MPC applications can be centralized, distributed, or decentralized based on the communication architecture. A major disadvantage of the centralized model predictive control (CMPC) is the high computational effort. This paper proposes a CMPC for DCMG stabilization that uses the admittance matrix of a reduced DCMG in the prediction equation and the one-step prediction horizon to decrease the computational effort. The proposed CMPC also replaces the hierarchical architecture primary and secondary controls, achieving voltage or power regulation. A hardware-in-the-loop (HIL) tool, known as RT-Box 2, has been used to emulate an 8-node DC microgrid with versatile buck–boost converters at the supply and power consumption nodes. The proposed predictive control exhibited better performance in comparison with the averaged voltage control in the HIL experiments.

A hybrid deep-Q-network and model predictive control for point stabilization of visual servoing systems

Major difficulties and challenges of visual servoing point stabilization focus on how to design controllers to efficiently complete the task while satisfying various constraints. This paper designs a hybrid control scheme that combines reinforcement learning and model predictive control to handle the point stabilization problem for image-based visual servoing systems of wheeled mobile robots with the visibility and input constraint. The image plane is divided into two parts: the deep-Q-network (DQN) part and the model predictive control (MPC) part. In the DQN part, a DQN controller incorporating two deep networks is designed and activated to pull the image coordinates of the feature into the MPC part. In the MPC part, a simplified-dual-neural-network-based MPC scheme (SDN-MPC) is proposed to precisely guide the robot to the desired position. The asymptotic stability of the SDN-MPC is proven for the point stabilization task. Finally, simulations and experiments are provided to verify the effectiveness, efficiency and robustness of the proposed hybrid controller by comparing with the MPC-only controller and DQN-only controller.

A model predictive control for attitude stabilization and spin control of a spacecraft with a flexible rotating payload

Many Earth Observation missions, implementing space-based microwave sensing techniques for collecting surface information, employ spinning sensors to cover large swaths of terrestrial areas, thus improving the rate at which global maps of those measured data are generated. These spacecraft (as Soil Moisture Active Passive (SMAP) developed by NASA or Copernicus Imaging Microwave Radiometer (CIMR) currently under development by Thales Alenia Space) consist of a main non-spun platform and a rotating part composed of an antenna boom, a deployable reflector and a rotation mechanism. As the reflector is designated to rotate about the nadir axis producing conically scanned antenna beams with precise surface incidence angle, the payload pointing accuracy needs to be addressed at both spin subsystem and platform level. In this work, a representative model of the dynamic behaviour of SMAP satellite is developed as a study case to design the proposed control strategies; in particular, a SMAP-like payload structural model is built using FEM commercial codes. The spacecraft is equipped with a Reaction Wheels Assembly (RWA) to accomplish both momentum compensation for the spun element and three-axis attitude control and a motor for the spin mechanism. The objective of the study is to develop the spacecraft control architecture in the frame of Model Predictive Control (MPC) theory. MPC refers to a class of algorithms in which the control action is obtained by computing an open-loop optimal sequence of control moves over a predefined time horizon; moreover, the ability to set constraints on process inputs and outputs directly in the problem formulation allows to account for actuators’ limits. In the study two operative phases of the satellite are addressed: the Spin-up, in which the 6-meter diameter antenna is spun-up to the operative condition of 14.6 RPM, and the Science Phase, in which precise nadir pointing and stability of the flexible system must be kept for acquiring high-resolution measurements. To this purpose, control–structure interaction between attitude/spin control system and flexible dynamics, as well as system’s imbalances, are carefully addressed by the proposed control architecture. The nonlinear in-orbit dynamics of the flexible spacecraft is then used to evaluate the performance of the MPC controller in terms of pointing accuracy and robustness to uncertainties.

Development of a Nonlinear Model Predictive Control for Stabilization of a Gas-Lift Oil Well

Development of a Nonlinear Model Predictive Control for Stabilization of a Gas-Lift Oil Well

A Stabilizing Model Predictive Control Scheme With Arbitrary Prediction Horizon for Switched Linear Systems

This letter deals with the design and analysis of a stabilizing model predictive control (MPC) scheme for discrete-time switched linear systems with at least one stabilizable subsystem. An approach for pruning the switching sequences is proposed which is used for reducing the online computation and ensuring stability of the MPC scheme. With the pruning approach, the value function of the MPC scheme becomes an exponential Lyapunov function (ELF). Consequently, the MPC scheme results in globally exponentially stable (GES) closed-loop dynamics for switched linear systems for all prediction horizons. Feasibility of the MPC scheme is discussed and simulation results are given for illustrating the effectiveness of the MPC scheme.

A One-Layer Stabilizing Model Predictive Control Strategy of Integrating Systems with Repeated Poles

A One-Layer Stabilizing Model Predictive Control Strategy of Integrating Systems with Repeated Poles

Closed‐loop dynamic real‐time optimization with stabilizing model predictive control

AbstractDynamic real‐time optimization (DRTO) is a supervisory strategy at the upper level of the industrial process automation architecture that computes economically optimal set‐point trajectories that are in turn passed on to the lower‐level model predictive control (MPC) for tracking. The economically optimal solution, in several process industries, could lead to operating the plant at or around an unstable steady state. The present article accounts for this by developing a closed‐loop DRTO (CL‐DRTO) formulation that enables handling unstable operating points via an underlying MPC with stability constraints. To this end, a stabilizing MPC that handles trajectory tracking for unstable systems is embedded within the upper‐level DRTO. The resulting CL‐DRTO problem is reformulated by applying a simultaneous solution approach. The economic benefits realized by the proposed strategy are illustrated through applications to both linearized and nonlinear dynamic models for single‐input single‐output and multi‐input multi‐output continuous stirred tank reactor case studies.

An implementable stabilizing model predictive controller applied to a rotary flexible link: An experimental case study

This work addresses the application of implementable stabilizing model predictive control (MPC) strategies to a rotary flexible link (RFL). Despite their practice usefulness and design simplicity, the implementation of these stable MPC controllers with guaranteed feasibility in a real experiment, and dedicated to dynamic features of RFL systems, have not yet been documented by the literature. In contrast to conventional finite-horizon MPC strategies, infinite-horizon MPC (IHMPC) techniques ensure nominal closed-loop stability irrespective of the cost function parameters. Also, if these IHMPC strategies have feasible-optimization problem based formulations, such as implementable ones investigated here, their applicability naturally becomes attractive to the industry. Simulation and experimental results illustrate the usefulness of the implementable stabilizing MPC controllers when compared to non-feasible in practice ones, such as a classical infinite-horizon MPC and a conventional finite-horizon generalized predictive controller, thus ensuring their benefits in terms of performance and computational burden in the context of constrained RFL mechatronic systems.

Novel Switch Stabilizing Model Predictive Control Strategy Applied in the Control of a Simulated Moving Bed for the Separation of Bi-Naphthol Enantiomers

The control of cyclic processes is an open issue in the literature because of their very peculiar dynamic behavior. Thus, deeper studies about this problem are necessary in order to promote an efficient operation of these processes at the industrial level. This work presents a nominally stabilizing MPC controller, also known as infinite horizon model predictive control (IHMPC) applied in the control of a simulated moving bed (SMB) process where bi-naphthol enantiomers are separated. A novel advanced control strategy is presented in the field of SMB process control, while grounds are provided for further developments in the field of cyclic process dynamics and control. The IHMPC performance is evaluated in terms of feasibility and robustness in a realistic nonlinear plant-model mismatch scenario. It is tested in terms of both unmeasured disturbance rejection and conflicting output-tracking scenarios. The results presented indicate that even though the conventional finite horizon-based MPC controller is able to control the process around its optimal point, far from this condition, the conventional MPC loses the process track. On the other hand, the IHMPC controller performed well the process control in all conditions evaluated, far and close to the design conditions. This demonstrates the ability of an IHMPC-like stabilizing control law not only for controlling the system but also for improving the robustness in plant-model mismatch scenarios by considering an infinite prediction horizon.

Koopman Lyapunov‐based model predictive control of nonlinear chemical process systems

AbstractIn this work, we propose the integration of Koopman operator methodology with Lyapunov‐based model predictive control (LMPC) for stabilization of nonlinear systems. The Koopman operator enables global linear representations of nonlinear dynamical systems. The basic idea is to transform the nonlinear dynamics into a higher dimensional space using a set of observable functions whose evolution is governed by the linear but infinite dimensional Koopman operator. In practice, it is numerically approximated and therefore the tightness of these linear representations cannot be guaranteed which may lead to unstable closed‐loop designs. To address this issue, we integrate the Koopman linear predictors in an LMPC framework which guarantees controller feasibility and closed‐loop stability. Moreover, the proposed design results in a standard convex optimization problem which is computationally attractive compared to a nonconvex problem encountered when the original nonlinear model is used. We illustrate the application of this methodology on a chemical process example.

Robust MPC with recursive model update

Robust constrained control of linear systems with parametric uncertainty and additive disturbance is addressed. The main contribution is the introduction of a mathematically rigorous and computationally tractable framework for stabilizing model predictive control with online parameter estimation to improve performance and reduce conservatism. Requirements for closed-loop stability and provable constraint satisfaction are considered separately, resulting in the use of online set-membership system identification combined with homothetic prediction tubes for robust constraint satisfaction, and an H∞ optimal point estimate of the unknown parameters to achieve a finite closed-loop gain from the disturbance to the state. Extensions to time-varying parameters and persistently exciting inputs to guarantee parameter convergence are presented. A numerical example illustrates the proven properties and efficacy of the approach.

A hybrid model predictive control for traffic flow stabilization and pollution reduction of freeways

In this work a control system is developed and analyzed for the suppression of moving jamwaves and the reduction of pollutant concentrations near motorways. The system is based on the second-order macroscopic freeway traffic model METANET, joined by an emission dispersion model, introduced in a previous work of the authors. For the control tasks dedicated controllers are designed, both using the nonlinear model predictive control method. The control objectives require a distinction in the utilized control measures, thus different controllers are designed and used in predefined control modes. The first mode of the controller is responsible for keeping pollutant concentrations below prescribed limits under stable conditions. The second mode of the controller is working in case of a shockwave threat, aiming for traffic stabilization. Between the control modes switching is based on an appropriate rule set that satisfies the stability of the controlled system. The hybrid controller structure is realized by a finite automata. A complex case study is presented for the evaluation of the suggested controller.