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The 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. [ABSTRACT FROM AUTHOR]

This article presents a robust security‐based model predictive control (MPC) framework for a class of discrete‐time nonlinear cyber‐physical systems (CPSs) suffering random deception attacks and persistent actuator saturation. In CPSs, the attacks can significantly degrade the control performance. Naturally, a larger degree of control is required, prompting the consideration of actuator saturation in CPS's structure. In our work, the cyberattacks on the controller‐actuator (C‐A) channel are described as a stochastic process with specific probability and bounded energy. The security‐related constraint is introduced to improve the resistance and robustness against attacks. Mean‐square quadratic boundedness is derived to estimate the robustly invariant set. By placing the saturated input into a convex hull, a robust security‐based MPC optimization problem is addressed less conservatively with linear matrix inequality technique. Furthermore, the feasibility of the proposed method is proved recursively, and the stability and security of the closed‐loop system are established in mean‐square sense. In the end, the laboratory tank and reactor‐separator process are applied to validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This article proposes a novel event‐triggered economic model predictive control (EMPC) scheme with shrinking prediction horizon of nonlinear systems subject to the constraints on the state and control. Some auxiliary positive‐definite functions at economic optimal equilibrium points are defined for economic performance functions. The optimal value function of the auxiliary function is used to design an adjustable stability constraint, which is imposed on the original EMPC optimization problem. The stability constraint is relaxed to design the triggered scheme avoiding Zeno behavior, while the prediction horizon is shrinked in different degrees by judging whether the last state within the triggered interval is in the terminal region. The involved parameter can be used to achieve a sensible compromise between system performance and computational complexity. The sufficient conditions guaranteeing the recursive feasibility and stability of the EMPC are derived. Finally, the effectiveness of the algorithm is illustrated by a continuously stirred tank reactor example. [ABSTRACT FROM AUTHOR]

We propose a novel robust Model Predictive Control (MPC) scheme for nonlinear multi-input multi-output systems of relative degree one with stable internal dynamics. The proposed algorithm is a combination of funnel MPC, i.e., MPC with a particular stage cost, and the model-free adaptive funnel controller. The new robust funnel MPC scheme guarantees output tracking of reference signals within prescribed performance bounds--even in the presence of unknown disturbances and a structural model-plant mismatch. We show initial and recursive feasibility of the proposed control scheme without imposing terminal conditions or any requirements on the prediction horizon. Moreover, we allow for model updates at runtime. To this end, we propose a proper initialization strategy, which ensures that recursive feasibility is preserved. Finally, we validate the performance of the proposed robust MPC scheme by simulations. [ABSTRACT FROM AUTHOR]

This paper proposes a novel stable economic model predictive control (EMPC) strategy for constrained nonlinear systems with changing economic criteria. The traditional EMPC may lead to infeasibility and even instability of the closed-loop system when the criterion has been changed. Firstly, a generalised terminal constraint is introduced to ensure the recursive feasibility of the economic optimisation problem, which enforces the terminal states to converge to an arbitrary equilibrium state rather than a predetermined fixed one at the initial time. Then the stability constraint is constructed by solving an auxiliary optimisation problem online, which is the key to guaranteeing the asymptotic stability of the closed-loop system. Finally, sufficient conditions for feasibility and asymptotic stability are derived in the context of changing economic criteria. The main feature of the proposed strategy is that it does not need to know the changes of economic criterion in advance, and its properties and effectiveness are exemplified by simulations on a nonlinear chemical process example. [ABSTRACT FROM AUTHOR]

Featured Application: For the controllable pitch propeller control system, existing control algorithms still have limitations regarding timeliness. A control law based on a model predictive control (MPC) algorithm is designed in this paper. The results of this paper have potential application value in embedded control of ship controllable pitch propeller. The controllable pitch propeller hydraulic system has high constraints and nonlinearity. Due to these inherent deficiencies, the proportional–integral–derivative (PID) control algorithm cannot meet the control accuracy requirements of nonlinear systems. A control law based on a model predictive control (MPC) algorithm is designed in this paper. The gain parameters of the predictive control are optimized. The MPC and PID control systems are compared and simulated to verify the MPC controller's effectiveness. Subsequently, the embedded controller of a controllable pitch propeller is developed. The support package for the embedded circuit board target containing an underlying driver for each interface is written by introducing the C-MEX S-Function and TLC programming language. A semi-physical simulation experiment is performed. The results show that the established controllable pitch propeller with an embedded controller displays reliable running performance, good anti-interference, and the capacity to fulfill the control function of the pitch propeller under various working conditions. [ABSTRACT FROM AUTHOR]

Summary: Ensuring nominal asymptotic stability of the nonlinear model predictive control (NMPC) controller is not trivial. Stabilizing ingredients such as terminal penalty term and Terminal Region (TR) are crucial in establishing the asymptotic stability. Approaches available in the literature provide limited degrees of freedom for the characterization of the TR for the discrete time quasi infinite horizon NMPC formulation. Current work presents alternate approaches namely arbitrary controller based approach and linear quadratic regulator (LQR) based approach, which provide larger degrees of freedom for enlarging the TR. Both the approaches are scalable to system of any dimension. Approach from the literature provides a scalar whereas proposed approaches provide two additive matrices as tuning parameters for shaping of the TR. Proposed approaches involve solving modified Lyapunov equations to compute terminal penalty term, followed by explicit characterization of the TR. Efficacy of the proposed approaches is demonstrated using benchmark two state system. TR obtained using the arbitrary controller based approach and LQR based approach are approximately 10.4723 and 9.5055 times larger by area measure when compared to the largest TR obtained using the approach from the literature. As a result, there is significant reduction in the prediction horizon length while retaining the feasibility of the controller. [ABSTRACT FROM AUTHOR]

This paper introduces a novel data‐driven approach to develop a fault‐tolerant model predictive controller (MPC) for non‐linear systems. By adopting a Koopman operator‐theoretic perspective, the proposed method leverages historical data from the system to construct a data‐driven model that captures the non‐linear behaviour and fault characteristics. The fault influence is addressed through an online estimation of a time‐varying Koopman predictor, which allows for adjusting the MPC control law to counteract the fault effects. This estimation is performed in a higher dimensional Koopman feature space, where the dynamics behave linearly. As a result, the non‐linear fault‐tolerant MPC optimization problem can be replaced with a more practical and feasible linear time‐varying one using the approximated Koopman predictor. Moreover, by incorporating the online update procedure, the time‐varying Koopman predictor can represent the dynamics of the faulty system. Hence, the controller can adapt and compensate for the faults in real‐time, integrating the fault diagnosis module in the MPC framework and eliminating the need for a separate fault detection unit. Finally, the efficacy of the proposed approach is demonstrated through case study results, which highlight the ability of the controller to mitigate faults and maintain desired system behaviour. [ABSTRACT FROM AUTHOR]

This paper aims to establish a new event-triggered model predictive control (MPC) strategy for perturbed nonlinear systems working in a networked environment, which can effectively save the computation and communication resources while ensuring control performance. The core of the framework is a new event-triggered mechanism, which is built by combining the differential and integral (D-I) information of the error between the optimal state and the actual state in a pre-specified time horizon. Based on such a triggering mechanism, a D-I based event-triggered robust MPC algorithm is proposed to stabilise the system and reduce the computation/communication resource consumption. In addition, sufficient conditions to ensure the feasibility and stability of the proposed MPC algorithm and avoid Zeno behaviour are obtained through rigorous theoretical analysis. Finally, the proposed control framework is implemented in the nonlinear cart-damper-spring and autonomous underwater vehicle systems to verify its effectiveness. [ABSTRACT FROM AUTHOR]

The centrosome plays a crucial role in regulating the flow field of a continuous wind tunnel, and its positioning precision directly impacts the control accuracy of the Mach number. A high‐precision positioning control algorithm for the wind tunnel centrosome is proposed based on a model predictive control framework. Since that the centrosome is a typical non‐linear system with a Hammerstein structure comprising an input backlash and a linear dynamic block in series, a parameterized least‐squares identification method is constructed based on an adaptive forgetting factor strategy and a centrosome position prediction model with input backlash is established. To counteract the weakening effect of the backlash non‐linear block on the control signal, a compensator is constructed to compensate for the non‐linear input block. Considering that the input undetectable disturbance signal in the actuator may lead to unpredictable responses, an intermediate state observer is designed and the stable convergence of the observer algorithm is also proved. Finally, the closed‐loop stability of the proposed control algorithm is analyzed by constructing a Lyapunov function. Experimental testing verifies the superiority and applicability of the proposed algorithm. This study proposes a parameterized least‐squares identification method based on an adaptive forgetting factor strategy and establishes a centrosome position prediction model with input backlash. The closed‐loop stability of the proposed control algorithm is analyzed through the construction of a Lyapunov function. Experimental testing verifies the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the issue of Robust Fuzzy Model Predictive Control (RFMPC) of nonlinear discrete‐time systems in the presence of disturbance. To this end, Takagi‐Sugeno (T‐S) fuzzy model is adopted in order to characterize uncertain nonlinear systems and facilitate providing controller for such systems. Non‐parallel distributed compensation (non‐PDC) technique is applied to design improved RFPMC with better performance. The optimization problem of RFMPC is represented in terms of linear matrix inequalities (LMIs) so as to decrease online computational burden. Besides, feasibility and stability which are decisive factors in MPC theory are investigated for the proposed method. Ultimately, two examples including cart‐damper‐spring system are simulated to evaluate the results of this research work. [ABSTRACT FROM AUTHOR]

This work develops a new robust multi‐objective model predictive control (MoMPC) strategy for constrained non‐linear systems with bounded disturbances. The multiple objectives are always contradictory, and the presence of disturbances may result in the violation of state constraints and instability of the controlled system. Firstly, the conflict between multiple objectives is reconciled by minimizing the distance of the cost function vector to the vector of independently minimised objectives obtained by solving a set of steady‐state optimisation problems. Then the contractive state set, which takes into account the effect of disturbances on system states, is constructed to guarantee the robust satisfaction of state constraints. Finally, a stability constraint updated online by solving an auxiliary optimization problem is established to ensure the robust stability of the system under MoMPC. An isothermal chemical reactor system is employed to verify the effectiveness of the controller proposed here. [ABSTRACT FROM AUTHOR]

This study examined the control problem of continuous‐time nonlinear systems under a sample‐and‐hold control structure. A new integral‐type double self‐triggered (ST) model predictive control (MPC) approach is developed by combining a novel ST strategy with MPC, which significantly decreases the sampling frequency of the system, saving computation/communication resources. In contrast to the traditional ST strategy, two integral‐type self‐triggering mechanisms are designed based on the mode of the state and the integral of the difference between the optimal and actual states. In addition, the integral‐type double ST‐MPC algorithm is developed, and the feasibility and stability of the closed‐loop system are rigorously demonstrated. Finally, the effectiveness and superiority of the proposed algorithm are verified by comparing the simulation results with those of existing ST‐MPC methods. [ABSTRACT FROM AUTHOR]

This paper studies the three‐dimensional (3‐D) dynamic trajectory tracking control of an autonomous underwater vehicle (AUV). As AUV is a typical nonlinear system, each degree of freedom is strongly coupled, so the traditional control method based on the nominal model of AUV cannot guarantee the accuracy of the control system. To solve this problem, we first propose a prediction model based on a radial basis function neural network (RBF‐NN). The nonlinearity of AUV is learned and modeled offline by RBF‐NN based on previous data. This model can reflect the time sequence state and control variables of AUV. Secondly, to avoid the overfitting problem in network training based on the traditional gradient descent method, a new adaptive chaotic sparrow search algorithm (ACSSA) is proposed to optimize the network parameters, to improve the full approximation ability of RBF‐NN to nonlinear systems. To eliminate the steady‐state error caused by external interference during AUV trajectory tracking, a nonlinear optimizer is designed by updating the deviation of the NN model output layer. In each sampling period, the predictive control law is calculated online according to the deviation between the predicted value and the actual value. In addition, the stability analysis based on the Lyapunov method proves the asymptotic stability of the controller. Finally, the 3‐D dynamic trajectory tracking the performance of AUV under different external disturbances is verified by MATLAB/Simulink, and the results show that the proposed controller is more efficient and robust than the standard model predictive controller (MPC) controller and the standard NN model predictive controller (NNPC). [ABSTRACT FROM AUTHOR]

This work focuses on enhancing the operational safety, cybersecurity, computational efficiency, and closed-loop performance of large-scale nonlinear time-delay systems. This is achieved by employing a decentralized model predictive controller (MPC) with encrypted networked communication. Within this decentralized setup, the nonlinear process is partitioned into multiple subsystems, each controlled by a distinct Lyapunov-based MPC. These controllers take into account the interactions between subsystems by utilizing full state feedback, while computing the control inputs only corresponding to their respective subsystem. To address the performance degradation associated with input delays, we integrate a predictor with each LMPC to compute the states after the input delay period. The LMPC model is initialized with these predicted states. To cope with state delays, the LMPC model is formulated using differential difference equations (DDEs) that describe the state-delays in the system. Further, to enhance cybersecurity, all signals transmitted to and received from each subsystem are encrypted. A stability analysis is carried out for the encrypted decentralized MPC when it is utilized in a time-delay system. Bounds are set up for the errors arising from encryption, state-delays, and sample-and-hold implementation of the controller. Guidelines are established to implement this proposed control structure in any nonlinear time-delay system. The simulation results, conducted on a nonlinear chemical process network, illustrate the effective closed-loop performance of the decentralized MPCs alongside the predictor with encrypted communication when dealing with input and state delays in a large-scale process. • Feedback control under state and input delays. • Encrypted decentralized model predictive control architecture. • Predictor scheme for input delay handling. • Application to a chemical process network. [ABSTRACT FROM AUTHOR]

This paper presents a novel control strategy that provides active disturbance rejection predictive control on constrained systems with no nominal identified model. The proposed loop relaxes the modelling requirement to a fixed discrete-time state–space realisation of a first-order plus integrator plant despite the nature of the controlled process. A third-order discrete Extended State Observer (ESO) estimates the model mismatch and assumed plant states. Moreover, the constraints handling is tackled by incorporating the compensation term related to the total perturbation in the definition of the optimisation problem constraints. The proposal merges in a new way state–space Model Predictive Control (MPC) and Active Disturbance Rejection Control (ADRC) into an architecture suitable for the servo-regulatory operation of linear and non-linear systems, as shown through validation examples. • Active disturbance rejection is merged with state–space model predictive control. • System information is relaxed to a second-order general integral assumed plant. • The compensation term is used to reformulate the optimisation problem constraints. • Suitable for linear and nonlinear benchmarks with no nominal model. • System constraints are satisfied, and disturbance rejection is enhanced. [ABSTRACT FROM AUTHOR]

Hydrobatic autonomous underwater vehicles (AUVs) can be efficient in range and speed, as well as agile in maneuvering. They can be beneficial in scenarios such as obstacle avoidance, inspections, docking, and under‐ice operations. However, such AUVs are underactuated systems—this means exploiting the system dynamics is key to achieving elegant hydrobatic maneuvers with minimum controls. This paper explores the use of model predictive control (MPC) techniques to control underactuated AUVs in hydrobatic maneuvers and presents new simulation and experimental results with the small and hydrobatic SAM AUV. Simulations are performed using nonlinear model predictive control (NMPC) on the full AUV system to provide optimal control policies for several hydrobatic maneuvers in Matlab/Simulink. For implementation on AUV hardware in robot operating system, a linear time varying MPC (LTV‐MPC) is derived from the nonlinear model to enable real‐time control. In simulations, NMPC and LTV‐MPC shows promising results to offer much more efficient control strategies than what can be obtained with PID and linear quadratic regulator based controllers in terms of rise‐time, overshoot, steady‐state error, and robustness. The LTV‐MPC shows satisfactory real‐time performance in experimental validation. The paper further also demonstrates experimentally that LTV‐MPC can be run real‐time on the AUV in performing hydrobatic maneouvers. [ABSTRACT FROM AUTHOR]

In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics of the slow and fast subsystems. Machine learning techniques are utilized to approximate the dynamics of both subsystems. Specifically, a recurrent neural network (RNN) and a feedforward neural network (FNN) are used to predict the slow and fast state vectors, respectively. Moreover, we investigate the generalization error bounds for these machine learning models approximating the dynamics of two-time-scale systems. Next, under the assumption that the fast states are asymptotically stable, our focus shifts toward designing a Lyapunov-based model predictive control (LMPC) scheme that exclusively employs the RNN to predict the dynamics of the slow states. Additionally, we derive sufficient conditions to guarantee the closed-loop stability of the system under the sample-and-hold implementation of the controller. A nonlinear chemical process example is used to demonstrate the theory. In particular, two RNN models are constructed: one to model the full two-time-scale system and the other to predict solely the slow state vector. Both models are integrated within the LMPC scheme, and we compare their closed-loop performance while assessing the computational time required to execute the LMPC optimization problem. [ABSTRACT FROM AUTHOR]

We propose a robust nonlinear model predictive control design with generalized zone tracking (ZMPC) in this work. The proposed ZMPC has guaranteed convergence into the target zone in the presence of bounded disturbance. The proposed approach achieves this by modifying the actual target zone such that the effect of disturbances is rejected. A control invariant set (CIS) inside the modified target zone is used as the terminal set, which ensures the closed-loop stability of the proposed controller. Closed-loop stability analysis is presented. Simulation studies based on a continuous stirred tank reactor (CSTR) are performed to validate the effectiveness of the proposed ZMPC. • A robust nonlinear model predictive control design with generalized zone tracking. • Rigorious analysis showing the closed-loop stability. • Extensive simulation results showing the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This work develops a transfer learning (TL) framework for modeling and predictive control of nonlinear systems using recurrent neural networks (RNNs) with the knowledge obtained in modeling one process transferred to another. Specifically, transfer learning uses a pretrained model developed based on a source domain as the starting point, and adapts the model to a target process with similar configurations. The generalization error for TL‐based RNN (TL‐RNN) is first derived to demonstrate the generalization capability on the target process. The theoretical error bound that depends on model capacity and the discrepancy between source and target domains is then utilized to guide the development of pretrained models for improved model transferability. Subsequently, the TL‐RNN model is utilized as the prediction model in model predictive controller (MPC) for the target process. Finally, the simulation study of chemical reactors via Aspen Plus Dynamics is used to demonstrate the benefits of transfer learning. [ABSTRACT FROM AUTHOR]

This article is motivated by the pressing need to robustly automate clinical interventions for trauma‐induced coagulopathy (TIC). TIC occurs after severe trauma and shock, and has poor outcomes and about 30% mortality. Although modulating the blood proteins that drive TIC can improve patient outcomes, no practical control‐oriented methodology exists to accurately capture biochemical process dynamics and satisfactorily regulate clotting. Hence, we propose a nonlinear dynamic coagulation model that distills the complex biochemical reactions of clotting and also simultaneously generalizes an existing linear phenomenological model. Using our new nonlinear model, we demonstrate the feasibility of model predictive control (MPC) to automate clinical treatments, first in a single‐input case that is similar to current open‐loop clinical practice, and second in a multi‐input case that administers three blood proteins as system inputs to attain satisfactory TIC treatment. The output in both cases is the key clotting protein thrombin. To test robustness, we confirm that both single‐input and multi‐input MPC are suitable for TIC treatment in the presence of an experimentally observed nonlinearity, an unknown state‐dependent power law input delay. Thus, this article provides a strong foundation to transition current open‐loop clinical approaches to closed‐loop process control. [ABSTRACT FROM AUTHOR]

We propose a design of data-driven Model Predictive Control (MPC) using a suboptimal trajectory and the linear time-varying (LTV) models from data-driven trajectory optimisation that achieves offset-free tracking. Data-driven constrained differential dynamic programming (CDDP) is exploited to improve the trajectory iteratively without the knowledge of the nonlinear model. A trajectory is divided to the transient and steady state regions, controlled by the Linear time-varying MPC (LTVMPC) and the offset-free linear MPC (LMPC), respectively. We prove the feasibility of the proposed LTVMPC in the transient region, and the offset-free tracking property of LMPC. The proposed scheme is validated to a continuous stirred tank reactor (CSTR) process. Simulation studies show that the suboptimal trajectory and LTV models are generated by CDDP, and the proposed MPC achieves offset-free tracking and disturbance rejection for a set of initial conditions and set points in the operating region. [ABSTRACT FROM AUTHOR]

We present a Model Predictive Control (MPC) framework to simulate movement in interaction with computers, focusing on mid-air pointing as an example. Starting from understanding interaction from an Optimal Feedback Control (OFC) perspective, we assume that users aim at minimizing an internalized cost function, subject to the constraintsimposed by the human body and the interactive system. Unlike previous approaches used in HCI, MPC can compute optimal controls for nonlinear systems. This allows to use state-of-the-art biomechanical models and handle nonlinearitiesthat occurin almost any interactive system. Instead of torque actuation, our model employs second-order muscles acting directly at the joints. We compare three different cost functions and evaluate the simulation against user movements in a pointing study. Our results show that the combination of distance, control, and joint acceleration cost matches individual users’ movements best, and predicts movements with an accuracy that is within the between-user variance. To aid HCI researchers and designers in applying our approach for different users, interaction techniques, or tasks, we make our SimMPC framework, including CFAT, a tool to identify maximum voluntary torques in joint-actuated models, publicly available, and give step-by-step instructions. [ABSTRACT FROM AUTHOR]

A gas-lifted system in a mature oil well can experience casing-heading instability, which reduces the mean oil production and it is not healthy for the downstream equipment. This instability was removed by implementing a terminal equality-constrained nonlinear model predictive control (NMPC) having input targets with control zones in the system. The input-dependent stability behaviour of the gas-lifted system was visualised through the bifurcation diagram and the step responses of the linearised model at various operating points. The controller was then presented. Then, the close-loop feasibility, as well as the convergence, were discussed. The controller stabilised the undisturbed gas-lifted system, improving production by 5.63% compared to the open-loop operation when the system was in casing-heading instability. For the two input case, the steady-state production, aided by the high-input target, reached 12.25 kg/s, which was far more than 9.57 kg/s for the one input case. This controller showed a 3.76% improvement over the PI controller for the same purpose. [ABSTRACT FROM AUTHOR]

In this work, a predictive control framework is presented for feedback stabilisation of nonlinear systems. To achieve this, we integrate Koopman operator theory with Lyapunov-based model predictive control (LMPC). The main idea is to transform nonlinear dynamics from state-space to function space using Koopman eigenfunctions -- for control affine systems this results in a bilinear model in the (lifted) function space. Then, a predictive controller is formulated in Koopman eigenfunction coordinates which uses an auxiliary Control Lyapunov Function (CLF) based bounded controller as a constraint to ensure stability of the Koopman system. Remarkably, the feedback control design proposed in this work remains completely data-driven and does not require any explicit knowledge of the original system. Furthermore, due to the bilinear structure of the Koopman model, seeking a CLF is no longer a bottleneck for LMPC. Benchmark numerical examples demonstrate the utility of the proposed feedback control design. [ABSTRACT FROM AUTHOR]

In this paper centralized and distributed model predictive control methods are used for the consensus problem of nonlinear multi-agent systems in the presence of fixed and time-varying obstacles. The distributed method is implemented in two ways: serial and parallel. Contractive constraints are applied to establish stability, and the convergence of agents to a consensus point is guaranteed. Obstacles are considered as the constraints of the optimization control problem. Using the proposed methods, the need for designing terminal ingredients that are essential parts of designing the conventional MPC for establishing stability is eliminated. Terminal ingredients are usually hard to design and have been used for low-order systems but the proposed methods reduce the complexity of the design and can be applied for higher-order systems. To show the effectiveness of the proposed methods, the simulation is provided for the consensus of a group of wheeled mobile robots for both centralized and distributed methods and the results are reported. • CMPC and DMPC are used for consensus of nonlinear multi-agent systems in the presence of fixed and time-varying obstacles. • The proposed distributed method is implemented in two ways: serial and parallel. • Contractive constraints are used to establish stability and the convergence of agents to a consensus point is guaranteed. • Parallel DMPC scheme in the presence of exogenous disturbances is studied. [ABSTRACT FROM AUTHOR]

This work develops a model predictive control (MPC) scheme using online learning of recurrent neural network (RNN) models for nonlinear systems switched between multiple operating regions following a prescribed switching schedule. Specifically, an RNN model is initially developed offline to model process dynamics using the historical operational data collected in a small region around a certain steady‐state. After the system is switched to another operating region under a Lyapunov‐based MPC with suitable constraints to ensure satisfaction of the prescribed switching schedule policy, RNN models are updated using real‐time process data to improve closed‐loop performance. A generalization error bound is derived for the updated RNN models using the notion of regret, and closed‐loop stability results are established for the switched nonlinear system under RNN‐based MPC. Finally, a chemical process example with the operation schedule that requires switching between two steady‐states is used to demonstrate the effectiveness of the proposed RNN‐MPC scheme. [ABSTRACT FROM AUTHOR]

A design of adaptive model predictive control (MPC) based on adaptive control Lyapunov function (aCLF) is proposed in this article for nonlinear continuous systems with part of its dynamics being unknown at the starting time. Specifically, to guarantee the convergence of the closed‐loop system with online predictive model updating, a stability constraint is designed. It limits the aCLF of the system under the MPC to be less than that under an online updated auxiliary adaptive control. The auxiliary adaptive control which implements in a sampling‐hold fashion can guarantee the convergence of the controlled system. The sufficient conditions that guarantee the states to be steered to a small region near the equilibrium by the proposed MPC are provided. The calculation of the proposed algorithm does not depend on the model mismatch at the starting time. And it does not require the Lyapunov function of the state of the real system always to be reduced at each time. These provide the potential to improve the performance of the closed‐loop system. The effectiveness of the proposed method is illustrated through a chemical process example. [ABSTRACT FROM AUTHOR]

This paper aims to address a finite-horizon model predictive control (MPC) for non-linear drum-type boiler-turbine system using a system-identification method. Considering that the strong state coupling of a non-linear mechanism model, the subspace identification method is first utilized to obtain a linear state-space model, and transformed into an input–output model. By taking the inputs and outputs of the input–output model as system states, an augmented non-minimal state-space (NMSS) model of state measurable is constructed. In order to reduce the computation burden, the augmented NMSS model is further transformed into a canonical formulation by adopting a Kalman decomposition. Based on the minimal realization state-space model, the MPC controller is parameterized as a finite-horizon optimization problem. Finally, simulations are performed and evaluated the performance of the proposed method, and the simulation results show that: the linear model approximate the non-linear system accurately; the proposed MPC method can achieve a satisfactory stable control performance; and the computation time 18.388 s for the overall optimization problem also illustrates the real-time performance effectively. [ABSTRACT FROM AUTHOR]

We show that Funnel MPC, a novel model predictive control (MPC) scheme, allows tracking of smooth reference signals with prescribed performance for nonlinear multi-input multioutput systems of relative degree one with stable internal dynamics. The optimal control problem solved in each iteration of funnel MPC resembles the basic idea of penalty methods used in optimization. To this end, we present a new stage cost design to mimic the high-gain idea of (adaptive) funnel control. We rigorously show initial and recursive feasibility of funnel MPC without imposing terminal conditions or other requirements like a sufficiently long prediction horizon. [ABSTRACT FROM AUTHOR]

Due to the occurrence of over-fitting at the learning phase, the modeling of chemical processes via artificial neural networks (ANN) by using corrupted data (i.e., noisy data) is an ongoing challenge. Therefore, this work investigates the effect of both Gaussian and non-Gaussian noise on the performance of process-structure based recurrent neural networks (RNN) models, which take the form of partially-connected RNN models in this work, that are used to approximate a class of multi-input-multi-outputs nonlinear systems. Furthermore, two different techniques, specifically Monte Carlo dropout and co-teaching, are utilized in the development of partially-connected RNN models. These two techniques are employed to reduce the over-fitting in ANNs when noisy data is used in the training process and, hence, to improve the open-loop accuracy as well as the closed-loop performance under a Lyapunov-based model predictive controller (MPC). Aspen Plus Dynamics, a well-known high-fidelity process simulator, is used to simulate a large-scale chemical process application in order to demonstrate the anticipated improvements in both open-loop approximation and closed-loop controller performance in the presence of Gaussian and non-Gaussian noise in the data set using physics-informed RNNs. • ML model structure is determined by process structure. • Measurement data noise is handled via data dropout in training. • ML model is used in model predictive control. • Comparisons with existing approaches are carried out to evaluate the approach. [ABSTRACT FROM AUTHOR]

One of the difficulties in practical implementations of the classic Real-Time Optimization (RTO) strategy is the integration between optimization and control layers, mainly due to the differences between the models used in each layer, which may result in unreachable setpoints coming from optimization to the control layer. In this context, Economic Model Predictive Control (EMPC) is a strategy where optimization and control problems are solved simultaneously. However, this strategy is based on the assumption that a nonlinear dynamic model is available, which may not be valid. Also, when considering a first-principles nonlinear model, the computational cost and convergence may be relevant issues. The present work presents an RTO framework based on an EMPC structure considering a Hammerstein model for the plant. This modeling approach can be applied even in the absence of first-principles models. The proposed EMPC considers the minimization of the economic objective function gradient calculated through a steady-state model based on a Gaussian Process. This strategy was applied to the Willians–Otto Reactor benchmark and presented superior results than the classic RTO and Hybrid RTO (H-RTO) approaches in closed-loop and a lower average iteration time than these other approaches. • An EMPC framework applied in the absence of any first-principles model is presented. • The EMPC framework tracks the first-order Necessary Optimality Condition. • The framework presents full compatibility between optimization and control layers. • The framework presents better results than classic RTO and H-RTO in closed loop. [ABSTRACT FROM AUTHOR]

Concentrated Solar Power plants (CSP) have the energy storage capability to generate electricity when sunlight is scarce. However, due to the highly non-linear dynamics of these systems, a simple linear controller will not be able to overcome the variable dynamics and multiple disturbance sources affecting it. In this paper, a deep Model Predictive Control (MPC) based on the Koopman operator is proposed and applied to control the Heat Transfer Fluid (HTF) temperature of a distributed-parameter model of the ACUREX solar collector field located at Almería, Spain. The Koopman operator is an infinite-dimensional linear operator that fully captures a system's non-linear dynamics through the linear evolution of functions of the state-space. However, one of the major problems is identifying a Koopman linear model for a non-linear system. Koopman eigenfunctions are involved in converting a non-linear model to a Koopman-based linear model. In this paper, a deep Long Short-Term Memory (LSTM) autoencoder is designed to calculate Koopman eigenfunctions of the solar collector field. The Koopman linear model is then used to design a linear MPC with terminal components to ensure closed-loop stability guarantees. Simulation results are utilized to show the satisfactory tracking performance of the proposed approach. [ABSTRACT FROM AUTHOR]

A novel pseudo-spectral method is proposed to tackle the non-linear control problem of a wave energy converter (WEC) integrated with an all-electrical power-take-off (PTO). The WEC hydrodynamic model is constructed using linear wave theory together with a non-linear viscous damping term. The PTO model encompasses a permanent magnet synchronous generator (PMSG) whose local field weakening mechanism imposes non-linear operational constraints on the WEC's motion and PTO torque. The energy-maximizing control problem of this wave-to-wire model is non-linear and has not been investigated before. In comparison to pseudo-spectral methods previously studied, the proposed pseudo-spectral method is exempt from the assumption of ideal incoming wave prediction. This is made possible by the introduction of a novel mapping function to convert the finite control horizon onto the Gaussian quadrature interval. This mapping function increases more slowly with time at the beginning of the control horizon where wave prediction attains greater precision. As a result, the collocation points are utilized to the advantage of the better approximation of the objective function, thus better overall control performance. • A novel model predictive control (MPC) for wave energy converters (WEC) is proposed. • The case study involves a WEC integrated with an electric power take-off model. • Non-linear dynamics and constraints can be handled explicitly and optimally. • The novel MPC controller is robust against. wave prediction errors. [ABSTRACT FROM AUTHOR]

The model predictive control (MPC) scheme funnel MPC enables output tracking of smooth reference signals with prescribed error bounds for nonlinear multi-input multi-output systems with stable internal dynamics. Earlier works achieved the control objective for system with relative degree restricted to one or incorporated additional feasibility constraints in the optimal control problem. Here we resolve these limitations by introducing a modified stage cost function relying on a weighted sum of the tracking error derivatives. The weights need to be sufficiently large and we state explicit lower bounds. Under these assumptions we are able to prove initial and recursive feasibility of the novel funnel MPC scheme for systems with arbitrary relative degree — without requiring any terminal conditions, a sufficiently long prediction horizon or additional output constraints. [ABSTRACT FROM AUTHOR]

Due to the strong nonlinearities of the boiler-turbine system, feasibility and high response capability are hard to realize using traditional linear controllers. Advanced controllers that can ensure stability and feasibility without violating system constraints, and enhance the system’s dynamic output performance, are needed. Therefore, this paper proposes a stable input/output feedback linearization (IOFL) model predictive controller (MPC) technique for the boiler-turbine system. This nonlinear system is decoupled using the IOFL method into a novel linearized model, which is then used for constituting the proposed stable IOFL MPC problem. The proposed scheme uses a constraint mapping method that converts actual input limits into limits on the basis of the control output variable to ensure a feasible solution over the whole prediction horizon. Moreover, a min-max MPC technique in the form of linear matrix inequality with the realization of the input rate-of-change constraints is utilized to ensure the boiler-turbine unit’s stability. The process model and proposed control scheme are executed using MATLAB and the simulation results demonstrate that the proposed controller has an enhanced dynamic output performance compared with an advanced control scheme under various load variations. [ABSTRACT FROM AUTHOR]

Privacy preservation in data-driven modeling of a heterogeneous nonlinear system with multiple subsystems has become vitally important since communication data is vulnerable to cyber-attacks. This work develops a federated learning (FL) modeling and model predictive control (MPC) method for heterogeneous nonlinear systems with multiple subsystems to address privacy preservation and heterogeneity issues. The FL framework with two different neural network structures is developed to aggregate the submodels trained locally for the subsystems into a global model without sharing the local data with each other. Subsequently, a theoretical bound on the generalization error of the FL models is established using information theory. The closed-loop stability criteria of heterogeneous nonlinear systems under the FL-based MPC scheme are developed in an information-theoretical manner. Finally, a chemical process network is applied to demonstrate the effectiveness of the proposed FL modeling and FL-based MPC methods. • Privacy-preserving federated machine learning frameworks for distributed systems. • Guaranteed data privacy through distribution of learning process. • Theoretical results on generalization performance of federated learning models. • Desired modeling accuracy and data privacy shown in a chemical process example. [ABSTRACT FROM AUTHOR]

The accuracy of the underlying model predictions is crucial for the success of model predictive control (MPC) applications. If the model is unable to accurately analyze the dynamics of the controlled system, the performance and stability guarantees provided by MPC may not be achieved. Learning-based MPC can learn models from data, improving the applicability and reliability of MPC. This study develops a nonlinear sparse variational Bayesian learning based MPC (NSVB-MPC) for nonlinear systems, where the model is learned by the developed NSVB method. Variational inference is used by NSVB-MPC to assess the predictive accuracy and make the necessary corrections to quantify system uncertainty. The suggested approach ensures input-to-state stability (ISS) and the feasibility of recursive constraints in accordance with the concept of an invariant terminal region. Finally, a PEMFC temperature control model experiment confirms the effectiveness of the NSVB-MPC method. [ABSTRACT FROM AUTHOR]

We present differentiable predictive control (DPC) as a deep learning-based alternative to the explicit model predictive control (MPC) for unknown nonlinear systems. In the DPC framework, a neural state-space model is learned from time-series measurements of the system dynamics. The neural control policy is then optimized via stochastic gradient descent approach by differentiating the MPC loss function through the closed-loop system dynamics model. The proposed DPC method learns model-based control policies with state and input constraints, while supporting time-varying references and constraints. In embedded implementation using a Raspberry-Pi platform, we experimentally demonstrate that it is possible to train constrained control policies purely based on the measurements of the unknown nonlinear system. We compare the control performance of the DPC method against explicit MPC and report efficiency gains in online computational demands, memory requirements, policy complexity, and construction time. In particular, we show that our method scales linearly compared to exponential scalability of the explicit MPC solved via multiparametric programming. • Data-driven differentiable parametric optimization approach to optimal control problem. • Learning of neural state-space dynamics models and predictive constrained control policies. • Linear scalability in terms of the problem complexity. • Significantly improved computational and memory footprints compared to explicit MPC. • Experimental demonstration using embedded hardware. [ABSTRACT FROM AUTHOR]

This paper studies robust fuzzy model predictive control of discrete-time fuzzy Takagi-Sugeno large-scale systems based on hierarchical optimization and H_ ∞ Performance. The considered system in this paper is a large-scale system. So, the Takagi-Sugeno (T-S) fuzzy approach which uses nonlinear local models is applied to estimate the nonlinear system to reduce the burden of modeling. The model predictive control (MPC) is a practical application that is useful for all systems but the problem is the online computational cost. For large-scale systems, this problem is the online computational burden. Besides, it leads to conservative or even no solution. By the proposed method, more relaxed solutions are achieved. First, the T-S system with nonlinear local models is adopted. Second, the hierarchical optimization scheme is considered for the optimization part of the MPC. Third, by inspiring the H ∞ performance, uncertainties and disturbances that are appeared are reduced. Moreover, the linear matrix inequalities (LMIs) are used to solve the proposed method that the computational burden significantly is reduced at the same time. Simulation results are finally presented to show the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, the Nonlinear Model Predictive Control (NMPC) technique is proposed for the control of BrushLess Direct Current (BLDC) motors to address the problem of overexcitation, specifically in Electric Vehicle (EV) applications. This over-excitation increases the overall energy consumption of the machine and eventually reduces the vehicle's driving range. The developed NMPC incorporates a nonlinear model of the BLDC motor with EV load and obtains the optimal current through the optimal voltage applied to the machine to regulate the motor torque. The proposed NMPC is compared with three conventional control techniques, the Field-Oriented Control (FOC), the Direct Torque Control (DTC), and the hybrid (the combination of DTC and FOC) control. It is observed from the simulation results that the proposed NMPC controller is more energy efficient while maintaining performance. This paper also discusses the selection of the motor based on the specified vehicle requirements. This has been done by matching the vehicle speedtorque characteristic curve with the motor's one. [ABSTRACT FROM AUTHOR]

Accurate trajectory tracking is a critical property of unmanned aerial vehicles (UAVs) due to system nonlinearities, under-actuated properties and constraints. Specifically, the use of unmanned rotorcrafts with accuracy trajectory tracking controllers in dynamic environments has the potential to improve the fields of environment monitoring, safety, search and rescue, border surveillance, geology and mining, agriculture industry, and traffic control. Monitoring operations in dynamic environments produce significant complications with respect to accuracy and obstacles in the surrounding environment and, in many cases, it is difficult to perform even with state-of-the-art controllers. This work presents a nonlinear model predictive control (NMPC) with collision avoidance for hexacopters' trajectory tracking in dynamic environments, as well as shows a comparative study between the accuracies of the Euler–Lagrange formulation and the dynamic mode decomposition (DMD) models in order to find the precise representation of the system dynamics. The proposed controller includes limits on the maneuverability velocities, system dynamics, obstacles and the tracking error in the optimization control problem (OCP). In order to show the good performance of this control proposal, computational simulations and real experiments were carried out using a six rotary-wind unmanned aerial vehicle (hexacopter—DJI MATRICE 600). The experimental results prove the good performance of the predictive scheme and its ability to regenerate the optimal control policy. Simulation results expand the proposed controller in simulating highly dynamic environments that showing the scalability of the controller. [ABSTRACT FROM AUTHOR]

This article presents a novel scheme for model-based control of multi-input–multi-output (MIMO) systems considering input nonaffinity, nonlinear dynamical effects, and bounded modeling uncertainty. Commonly, model-based control of a nonaffine system is conducted based on an equivalent pseudo-affine expression. However, validity of this approximation necessitates boundedness of inputs and states. Furthermore, existence of truncation errors is inevitable when obtaining the pseudo-affine model. Therefore, robustness to bounded uncertainty should be ensured even in cases where the original system is deterministic. To address the expressed issues, in this study the boundedness assumptions are incorporated in a constrained robust model predictive control (MPC) algorithm. The corresponding MPC scheme is based on construction of cost according to predicted sliding functions over a finite prediction horizon. It should be noted that for the considered class of uncertain nonlinear nonaffine system, obtaining the perquisite robust stability and feasibility conditions is non-trivial. To attain the aforementioned qualities, it is proposed that sliding functions can be expressed as the sum of input-based terms (using pseudo-affine approximation of input gains based on Taylor expansion) and dynamical variation terms. Subsequently, robust stability is ensured by constructing a Lyapunov-based terminal cost. Constraints satisfaction conditions are determined based on calculation of the corresponding feasible region. Numerical simulations for a nonlinear nonaffine mechanical system indicate efficiency of the presented control model. Comparisons with other applicable schemes highlight significant features of the presented algorithm and the attained improvements regarding stability and control feasibility are discussed. [ABSTRACT FROM AUTHOR]

This paper presents a tracking control scheme for nonlinear systems with input constraints by combining the continuous-time model predictive control and the feedback linearization. Although there are some similar combinations for nonlinear systems presented in literature, their formulations are complex and massive computations are unavoidable. This study aims to simplify the formulations and reduce the computational loads by imposing the Laguerre functions to approximate the control signals. Since the Laguerre functions have the property of orthogonality, the tracking control problem, by applying the combination, leads to a constrained quadratic optimization problem in terms of the coefficients associated with the Laguerre functions, where the input constraints are converted so as to be state-dependent, based on feedback linearization. The Hildreth's quadratic programming algorithm is used to solve the optimization problem, so as to determine the coefficients. Moreover, this study also summarizes some common linearization schemes and shows their pros and cons. Furthermore, the proposed approach is applied to two illustrative examples, and the control performances are compared with those by linear control strategies combined with those linearization schemes. [ABSTRACT FROM AUTHOR]

Here, decentralized robust interval type-2 (IT2) fuzzy model predictive control (MPC) for Takagi–Sugeno (T-S) large-scale systems is studied. The large-scale system consists of many IT2 fuzzy T–S subsystems. Important necessities that limit the practical application of MPC are the online computational cost and burden of the frameworks. For MPC of T–S fuzzy large-scale systems, the online computational burden is even worse, and in some cases, they cannot be solved timely. Especially for severe, large-scale systems with disturbances, the MPC of T–S fuzzy large-scale systems usually give a conservative solution. So, researchers have many challenges and in finding a reasonable solution in a short time. Although more comfortable results can be achieved by the proposed fuzzy MPC approach, which adopts T–S large-scale systems with nonlinear subsystems, many restrictions are not considered. In this paper, challenges are solved, and the MPC is designed for a nonlinear IT2 fuzzy large-scale system with uncertainties and disturbances. Besides, the online optimization problem is solved, and results are proposed. Consequently, the online computational cost of the optimization problem is reduced considerably. Finally, the effectiveness of the proposed algorithm is illustrated with two practical examples. [ABSTRACT FROM AUTHOR]

We propose a novel sampled-data output-feedback controller for nonlinear systems of arbitrary relative degree that ensures reference tracking within prescribed error bounds. We provide explicit bounds on the maximum input signal and the required uniform sampling time. A key strength of this approach is its capability to serve as a safety filter for various learning-based controller designs, enabling the use of learning techniques in safety-critical applications. We illustrate its versatility by integrating it with two different controllers: a reinforcement learning controller and a non-parametric predictive controller based on Willems et al.'s fundamental lemma. Numerical simulations illustrate effectiveness of the combined controller design. [ABSTRACT FROM AUTHOR]

Koopman operator with numerical approximation method for modelling nonlinear systems has become a popular data-driven approach in the past five years. However, when the system contains time-varying parameters, the data-driven Koopman operator-based model produces deviations between the nominal model and the true one. It affects the control performance when it serves as the nominal model in Model Predictive Control (MPC). To solve this issue, the Koopman operator-based model learned by using a multi-step prediction autoencoder and the strategy of online updating model are proposed. In the first step, a neural network with encoder-decoder structure is trained to search for the optimal lifted functions of the corresponding nonlinear system with fixed parameters. In the second step, an online updating strategy is presented to update the Koopman operator-based model using the collected data, when the nominal model is applied in the closed loop operation of MPC. In order to reduce the additional time consumption on updating the nominal model, the matrix inversion lemma is applied and it leads the strategy of updating to be presented in a recursive form. In general, this paper proposed an iterative MPC algorithm for online updating the Koopman operator-based model in a recursive form based on the optimal lifted function using autoencoder. Numerical simulations on three nonlinear cases with time-varying parameters show good performances on tracking control using the proposed Koopman operator-based model using autoencoder and online updating strategy. • A method based on autoencoder to learn the lifted functions was presented to obtain the approximation of Koopman operator. • The learned nominal model shows good prediction on evolution behaviors of nonlinear systems. • Adaptive model predictive control (MPC) was proposed to address the model mismatch on parameter-varying nonlinear systems. • The proposed Koopman operator-based Adaptive MPC can achieve high computational efficiency and good control performances. [ABSTRACT FROM AUTHOR]

The continuous optimization of the operational performance of chemical plants is of fundamental importance. This research proposes a method that utilizes policy-constrained offline reinforcement learning to learn improved control policies from abundant historical plant data available in industrial settings. As a case study, historical data is generated from a nonlinear chemical system controlled by an economic model predictive controller (EMPC). However, the method's principles are broadly applicable. Theoretically, it is demonstrated that the learning-based controller inherits stability guarantees from the baseline EMPC. Experimentally, we validate that our method enhances the optimality of the baseline controller while preserving stability, improving the baseline policy by 1% to 20%. The results of this study offer a promising direction for the general improvement of advanced control systems, both data-informed and stability-guaranteed. [Display omitted] • Utilizes offline reinforcement learning to optimize operational performance using historical data. • Demonstrates method's effectiveness and stability in a nonlinear chemical system controlled by economic MPC. • Achieves up to 20% improvement in controller optimality while maintaining stability. • Introduces a shift towards learning control policies from historical data, bypassing traditional model updates. [ABSTRACT FROM AUTHOR]

• Integrated autoencoder with RNN to develop reduced-order machine learning models. • Developed probabilistic closed-loop stability results for reduced-order RNN-MPC. • Validated the closed-loop performance via a diffusion-reaction process example. In this work, we develop a model predictive control scheme for nonlinear systems using autoencoder-based reduced-order machine learning models. First, an autoencoder is developed for model order reduction by projecting the process states onto a low-dimensional space using data generated from open-loop simulations of the nonlinear system in the original high-dimensional space. Subsequently, reduced-order recurrent neural networks (RNN) are developed to capture the dominant dynamics of the nonlinear system using the low-dimensional data. Lyapunov-based model predictive control (MPC) scheme using RNN models in low-dimensional space is developed to stabilize the nonlinear system. Finally, a diffusion-reaction process example is used to demonstrate the effectiveness of the proposed reduced-order RNN modeling approach and RNN-based predictive control method. [ABSTRACT FROM AUTHOR]

This article focuses on the design of model predictive control (MPC) for nonlinear systems with slow time‐dynamic change. To avoid frequent updates of the predictive model and guarantee the state always stays inside of a given feasible region, an event‐triggered parametric estimation mechanism is designed. Firstly, a trigger condition is designed to judge if parameters of the predictive model are out of date and differ a lot from their current true values so that there is no feasible solution to regulate the state within the given bound without predictive model parameter update. This condition also depends on the current state and is deduced from a designed Lyapunov constraint, inputs constraints, and the mismatched predictive model. Then the EMPC is designed based on this condition. If the trigger condition is met, the MPC recursively updates the parameters and imposes the Lyapunov constraint. The Lyapunov constraint is based on the mismatched model and the real state does not need to be convergence. Else, the MPC only optimizes the cost function to derive a good profit. We proved that the proposed EMPC promises that the closed‐loop system state is maintained within a predefined stable region when the model mismatch bound can be estimated accurately. A simulation of a chemical process demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]