Optimal Control Input Research Articles

Dynamic event‐triggered‐based adaptive frequency control of microgrids under cyber‐attacks via adaptive dynamic programming

AbstractThe increasing penetration of renewable energy sources (RES) and the development of the cyber‐physical microgrids (CPMs) make greater demands for frequency control of microgrids. The common approach for frequency control is controlling the micro‐turbine to compensate for frequency deviations, with energy storage systems serving as an auxiliary approach. This article proposes an online adaptive frequency control method to control the governor and energy storage to realize the frequency recovery of microgrid, subject to the external unknown disturbances caused by wind turbine, power load and false data injection (FDI) attacks. First, the non‐zero sum (NZS) games of the considered system are modeled in this work, where the unknown disturbances are also taken into account. For the sake of estimating the unknown disturbances, a disturbance observer (DOB) for the microgrid system is introduced. Then, on the basis of the estimated results of the applied DOB, the disturbance compensation input is derived to offset the interference of the unknown disturbance. Meanwhile, the adaptive dynamic programming (ADP) approach is employed to derive the adaptive optimal control input for the NZS games of microgrid system. Besides, the dynamic event‐triggered (DET) control is introduced, reducing the occupation of computing resources. By utilizing the Lyapunov's method, the stability of the closed‐loop system, the convergence of the estimation weight, the estimation disturbances and the system state are guaranteed. The effectiveness of the proposed method is ultimately verified by the simulation results.

Enhancing ride comfort and driving safety in urban autonomous buses: A data-driven hierarchical longitudinal motion planning using approximate and stochastic MPCs

This paper presents an advanced hierarchical longitudinal motion planning strategy for autonomous buses (ABs), specifically designed to enhance ride comfort and ensure driving safety – key challenges in contemporary autonomous vehicle technologies. ABs typically face limitations due to a narrower perception range and heterogeneous motion profiles compared to human drivers. To tackle these issues, our study employs a dual-phase motion planning framework utilizing both approximate and stochastic Model Predictive Controls (MPCs). In the long time-horizon planning phase, we aim to enhance ride comfort by optimizing a reference motion profile that covers the full perception range of the ABs. This optimization is facilitated by leveraging deep neural networks to approximate the MPC policy, ensuring efficient real-time computational performance. The short time-horizon planning phase focuses on driving safety by determining optimal control inputs, considering vehicle dynamics, and integrating safety-related chance constraints with stochastic MPC. Additionally, this phase fine-tunes the weights in the MPC’s objective function based on risk indices derived from human driving data, balancing the priorities of safety in hazardous situations and maintaining ride comfort. Our hierarchical motion planning strategy ensures both consistent ride comfort and safety in critical scenarios. Through comprehensive evaluations using computer simulations and vehicle tests in actual urban bus-only lanes, the proposed method has proven to significantly enhance ride comfort while maintaining driving safety. This approach contributes to the ongoing improvement of the operational quality of ABs, supporting public transportation goals and meeting passenger expectations effectively.

NN-Based Reinforcement Learning Optimal Control for Inequality-Constrained Nonlinear Discrete-Time Systems With Disturbances.

Based on actor-critic neural networks (NNs), an optimal controller is proposed for solving the constrained control problem of an affine nonlinear discrete-time system with disturbances. The actor NNs provide the control signals and the critic NNs work as the performance indicators of the controller. By converting the original state constraints into new input constraints and state constraints, the penalty functions are introduced into the cost function, and then the constrained optimal control problem is transformed into an unconstrained one. Further, the relationship between the optimal control input and worst-case disturbance is obtained using the Game theory. With Lyapunov stability theory, the control signals are ensured to be uniformly ultimately bounded (UUB). Finally, the effectiveness of the control algorithms is tested through a numeral simulation using a third-order dynamic system.

Experimental study of data-driven model predictive control on transcritical CO2 thermal system in electric vehicles

The transcritical CO2 thermal system has been considered an effective and completable candidate for providing space/battery cooling and heating in electric vehicles. For a realistic system, the optimal performance relies on an effective control strategy. This paper presents a model predictive control approach to optimize the real-time operation of the transcritical CO2 thermal system and conduct a complete experimental investigation. A data-driven control-oriented model is first developed to predict the next steps in system behaviours in a finite time domain. The model predictive controller is designed to provide the optimal inputs based on the control-oriented model and the designed objective function, in which optimal system COP can be achieved provided that the cooling/heating capacity is maintained. Then, a complete test rig is built in a psychrometric test room to experimentally investigate the operating performance using the proposed model predictive control strategy. The experiments are conducted under fixed and variable ambient temperatures for both cooling and heating conditions. The experimental results indicate that the model predictive control strategy can accurately forecast system states and determine optimal control inputs for the transcritical CO2 thermal system to achieve the highest operating COP with the required cooling/heating capacity in electric vehicles.

Learning‐based tracking control of AUV: Mixed policy improvement and game‐based disturbance rejection

AbstractA mixed adaptive dynamic programming (ADP) scheme based on zero‐sum game theory is developed to address optimal control problems of autonomous underwater vehicle (AUV) systems subject to disturbances and safe constraints. By combining prior dynamic knowledge and actual sampled data, the proposed approach effectively mitigates the defect caused by the inaccurate dynamic model and significantly improves the training speed of the ADP algorithm. Initially, the dataset is enriched with sufficient reference data collected based on a nominal model without considering modelling bias. Also, the control object interacts with the real environment and continuously gathers adequate sampled data in the dataset. To comprehensively leverage the advantages of model‐based and model‐free methods during training, an adaptive tuning factor is introduced based on the dataset that possesses model‐referenced information and conforms to the distribution of the real‐world environment, which balances the influence of model‐based control law and data‐driven policy gradient on the direction of policy improvement. As a result, the proposed approach accelerates the learning speed compared to data‐driven methods, concurrently also enhancing the tracking performance in comparison to model‐based control methods. Moreover, the optimal control problem under disturbances is formulated as a zero‐sum game, and the actor‐critic‐disturbance framework is introduced to approximate the optimal control input, cost function, and disturbance policy, respectively. Furthermore, the convergence property of the proposed algorithm based on the value iteration method is analysed. Finally, an example of AUV path following based on the improved line‐of‐sight guidance is presented to demonstrate the effectiveness of the proposed method.

A Data-Driven Predictive Control Method for Modeling Doubly-Fed Variable-Speed Pumped Storage Units

In this study, a data-driven model predictive control (MPC) method is proposed for the optimal control of a doubly-fed variable-speed pumped storage unit. This method combines modern control theory with the dynamic characteristics of the pumped storage unit to establish an accurate dynamic model based on actual operating data. In each control cycle, the MPC uses the system model to predict future system behavior and determines the optimal control input sequence by solving the constrained optimization problem, thereby effectively dealing with the nonlinearity, time-varying characteristics, and multivariable coupling problems of the system. When compared with a traditional PID control, this method significantly improves control accuracy, response speed, and system stability. The simulation results show that the proposed MPC method exhibits better steady-state error, overshoot, adjustment time, and control energy under various operating conditions, demonstrating its advantages in complex multivariable systems. This study provides an innovative solution for the efficient control of doubly-fed variable-speed pumped storage units and lays a solid foundation for the efficient utilization of new energy sources.

Nonlinear model predictive control of a conductance-based neuron model via data-driven forecasting

Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control, which employs a dynamical model of the system to find optimal control inputs, has promise for dealing with the nonlinear dynamics, high levels of exogenous noise, and limited information about unmeasured states and parameters that are common in a wide range of neural systems. However, the challenge still remains of selecting the right model, constraining its parameters, and synchronizing to the neural system.Approach. As a proof of principle, we used recent advances in data-driven forecasting to construct a nonlinear machine-learning model of a Hodgkin-Huxley type neuron when only the membrane voltage is observable and there are an unknown number of intrinsic currents.Main Results. We show that this approach is able to learn the dynamics of different neuron types and can be used with model predictive control (MPC) to force the neuron to engage in arbitrary, researcher-defined spiking behaviors.Significance.To the best of our knowledge, this is the first application of nonlinear MPC of a conductance-based model where there is only realistically limited information about unobservable states and parameters.

Model-free aperiodic tracking for discrete-time systems using hierarchical reinforcement learning

In the operation of practical systems, it is often a challenging task to deal with limited knowledge of the system dynamics, therefore, it is needed to obtain a framework for the simultaneous learning and control of dynamic systems, able to cope with uncertain dynamics. This paper proposes a model-free aperiodic tracking control method based on MAXQ hierarchical reinforcement learning for unknown dynamics in discrete-time systems. Firstly, a MAXQ hierarchical framework is developed for aperiodic tracking control that decomposes the task into pre-control and accurate control subtasks. The former achieves sub-optimal tracking which prompts the implementation of accurate control. The latter implements aperiodic tracking based on the pre-control result to reduce resource occupation. The structure of the MAXQ framework simplifies the complexity of the tracking task, and the incorporation of pre-control accelerates the learning process in the formal control stage. Secondly, considering the disparities between the control inputs and the control update instants, pre-control is decomposed to learn the triggering strategy and control policy, respectively. Meanwhile, the control policy learns optimal control inputs by minimizing the cost function. Similarly, the triggering strategy and control policy are also separately learned in accurate control. In contrast to traditional aperiodic triggering mechanisms, in accurate control stage, the triggering strategy is developed based on the cumulative error of the pre-control result, thus avoiding the influence of accidental factors and the cumulative effects of errors, enhancing system robustness. Thirdly, the proposed tracking control is derived by using only the input, output, and reference signal data from the system, without relying on system dynamics. It is applicable to both linear and nonlinear systems, demonstrating strong generalizability. Finally, simulation examples are provided to validate the effectiveness and superiority of the proposed method.

Machine learning-based input-augmented Koopman modeling and predictive control of nonlinear processes

Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original state-space to a lifted state space. In this work, we propose an input-augmented Koopman modeling and model predictive control approach. Both the states and the known inputs are lifted using two deep neural networks (DNNs), and a Koopman model with nonlinearity in inputs is trained within the higher-dimensional state space. A Koopman-based model predictive control problem is formulated. To bypass non-convex optimization induced by the nonlinearity in the Koopman model, we further present an iterative implementation algorithm, which approximates the optimal control input via solving a convex optimization problem iteratively. The proposed method is applied to a chemical process and a biological water treatment process via simulations. The efficacy and advantages of the proposed modeling and control approach are demonstrated.

Cooperative control of virtually coupled trains considering train-to-train communication cycle: a tube-based model predictive control approach

In this paper, a distributed tube-based model predictive control (TMPC) method is proposed to address the cooperative control of virtually coupled high-speed train (HSTs), which consists of an optimisation control part and a feedback control part. The novelty of this work lies in its pioneering consideration of the inconsistency between the train-to-train (T2T) communication cycle and the train operation control cycle in the cooperative control of virtually coupled trains. Firstly, for the optimisation control part, a distributed MPC scheme is designed based on the nominal train dynamics model to address the cooperative control of trains with different initial states, state constraints and control input constraints. By solving the optimisation control problem of the MPC, the optimal control input sequence and operating state sequence of the train for the next T2T communication cycle can be obtained. Secondly, the recursive feasibility and convergence of the MPC are analysed theoretically. Thirdly, for the feedback control part, an adaptive feedback control law is designed based on the actual train dynamics model, auxiliary dynamic system (ADS) and neural network techniques. In the train operation control cycle, the feedback control part utilises the optimal state sequence from the MPC as a reference for feedback control to deal with the external disturbance and train dynamics modelling inaccuracy. Fourthly, it is theoretically proved that the actual operating state of the train can converge to a small region around the optimal state of the MPC in a finite time. Finally, the effectiveness of the proposed distributed cooperative control scheme is verified by simulations.

Energy-Oriented Hybrid Cooperative Adaptive Cruise Control for Fuel Cell Electric Vehicle Platoons.

Given the complex powertrain of fuel cell electric vehicles (FCEVs) and diversified vehicle platooning synergy constraints, a control strategy that simultaneously considers inter-vehicle synergy control and energy economy is one of the key technologies to improve transportation efficiency and release the energy-saving potential of platooning vehicles. In this paper, an energy-oriented hybrid cooperative adaptive cruise control (eHCACC) strategy is proposed for an FCEV platoon, aiming to enhance energy-saving potential while ensuring stable car-following performance. The eHCACC employs a hybrid cooperative control architecture, consisting of a top-level centralized controller (TCC) and bottom-level distributed controllers (BDCs). The TCC integrates an eco-driving CACC (eCACC) strategy based on the minimum principle and random forest, which generates optimal reference velocity datasets by aligning the comprehensive control objectives of the platoon and addressing the car-following performance and economic efficiency of the platoon. Concurrently, to further unleash energy-saving potential, the BDCs utilize the equivalent consumption minimization strategy (ECMS) to determine optimal powertrain control inputs by combining the reference datasets with detailed optimization information and system states of the powertrain components. A series of simulation evaluations highlight the improved car-following stability and energy efficiency of the FCEV platoon.

A Compartmental Approach to Modeling the Measles Disease: A Fractional Order Optimal Control Model

Measles is the most infectious disease with a high basic reproduction number (R0). For measles, it is reported that R0 lies between 12 and 18 in an endemic situation. In this paper, a fractional order mathematical model for measles disease is proposed to identify the dynamics of disease transmission following a declining memory process. In the proposed model, a fractional order differential operator is used to justify the effect and success rate of vaccination. The total population of the model is subdivided into five sub-compartments: susceptible (S), exposed (E), infected (I), vaccinated (V), and recovered (R). Here, we consider the first dose of measles vaccination and convert the model to a controlled system. Finally, we transform the control-induced model to an optimal control model using control theory. Both models are analyzed to find the stability of the system, the basic reproduction number, the optimal control input, and the adjoint equations with the boundary conditions. Also, the numerical simulation of the model is presented along with using the analytical findings. We also verify the effective role of the fractional order parameter alpha on the model dynamics and changes in the dynamical behavior of the model with R0=1.

Tracking control of non-minimum phase systems: a kernel-based approach

Feedforward control with model inversion is a widely-used solution for high-precision output tracking. However, because inverting a non-minimum phase model generates unbounded control input, model-inversion only applies to limited types of systems. This paper presents a new non-parametric pseudo-inversion approach to design bounded optimal control input with desirable properties for arbitrary types of systems. Closed-form equations are presented for the batch (full preview) and recursive (limited preview) implementations of this approach, and its performance is compared against existing pseudo-inversion methods in benchmark numerical examples. Furthermore, the practical implementation of the proposed method is demonstrated by designing a feedforward controller for a commercial 3-Dimensional (3D) printer. The results show that the proposed approach effectively compensates for the structural vibrations of the printer, preventing layer-shifting errors that usually happen during high-speed printing.

New Equilibria and Dynamic Structures Under Continuous Optimal Feedback Control

In this paper, the new equilibria realized by continuous optimal control inputs and the dynamic structure around them are studied. Using the Euler–Lagrange equation, which is a necessary condition for optimal control problems, the equations of motion of a dynamic system with optimal control inputs that minimize the quadratic cost function are described in terms of state and adjoint variables. Based on the equations of motion, equilibrium conditions are derived, and the properties of equilibria are analyzed for the two-body and Hill three-body problems. The stability and dynamic structure around unstable equilibria are also characterized to get insights into the properties of optimal trajectories.

Optimal Range Capabilities for Low-Lift-to-Drag Ratio Mars Entry Vehicles

Optimal solutions for maximizing the range of low-lift-to-drag ratio entry vehicles at Mars are explored. Optimal control problems are formulated to consider both vehicles using bank-angle steering as well as alpha-beta steering during entry. Both the maximum downrange and maximum crossrange problems are considered. Results are combined to determine an overall range capability and facilitate comparison to suboptimal constant bank or angle-of-attack and sideslip-angle commands. The resulting optimal control inputs often differ significantly between bank-angle steering and alpha-beta steering vehicles, the latter of which can extend range by lowering drag through sideslip-angle reversals during entry. While control over the in-plane and out-of-plane motion is found to be more decoupled for alpha-beta steering than bank-angle steering, control over the longitudinal and lateral motion is still not completely decoupled for vehicles using alpha-beta steering.

Modeling and control of COVID-19 disease using deep reinforcement learning method.

The prevalence of epidemics has been studied by researchers in various fields. In the last 2 years, the outbreak of COVID-19 has affected the health, economy, and industry of communities around the world and has caused the death of millions of people. Therefore, many researchers have tried to model and control the prevalence of this disease. In this article, the new SQEIAR model for the spread of the COVID-19 disease is provided, which, compared to previous models, explores the effects of additional interventions on the outbreak and incorporates a wider range of variables and parameters to enhance its accuracy and alignment with reality. These modifications in the model lead to a more rapid eradication and control of the disease. This model includes six variables of the group of susceptible, quarantined, exposed, symptomatic, asymptomatic, and recovered individuals and includes three control inputs such as quarantine of susceptible, vaccination, and treatments. In order to minimize symptomatic infectious individuals and susceptible individuals and also to reduce treatment, vaccination, and quarantine costs, an optimal control approach using the Deep Deterministic Policy Gradient (DDPG) method has been applied to the system. This algorithm is applied to the model in different cases of control inputs, and for each case, optimal control inputs are obtained. In the following, the number of deaths due to the disease and the total number of symptomatic infectious individuals for each of these optimal control cases has been calculated. The results of the implemented control structure demonstrated a reduction of 60% in the number of deaths and 74% in the number of symptomatically infected individuals compared to the uncontrolled model. Finally, to test the performance of the control system, noise was applied to the system in various ways, including three methods: applying noise to observer variables, applying noise to control inputs, and applying uncertainty to model parameters. Therefore, we found that this control system was robust and performed well in different conditions despite the disturbance.

Safety-critical formation control of switching uncertain Euler-Lagrange systems with control barrier functions

This paper investigates the safety-critical formation control problem with disturbance rejection for switching uncertain EL MASs in the presence of multiple stationary/moving obstacles. A safety-critical control method is proposed for achieving a collision-free formation for a group of EL systems subject to safety constraints, model uncertainties, and external disturbances. Specifically, a distributed adaptive nominal control law is designed to accomplish the formation control task. Then, based on ISSf-CBF derived safety constraints, a distributed quadratic programming problem is established for computing the optimal control input subject to safety constraints. The safety and stability of the closed-loop control system have been demonstrated. Finally, one exemplary application to safety-critical formation control of some practical multiple mechanical systems is provided to illustrate the effectiveness of the main result.

Sliding mode observer-based model predictive tracking control for Mecanum-wheeled mobile robot

This paper proposes a novel adaptive variable power sliding mode observer-based model predictive control (AVPSMO-MPC) method for the trajectory tracking of a Mecanum-wheeled mobile robot (MWMR) with external disturbances and model uncertainties. First, in the absence of disturbances and uncertainties, a model predictive controller that considers various physical constraints is designed based on the nominal dynamics model of the MWMR, which can transform the tracking problem into a constrained quadratic programming (QP) problem to solve the optimal control inputs online. Subsequently, to improve the anti-jamming ability of the MWMR, an AVPSMO is designed as a feedforward compensation controller to suppress the effects of external disturbances and model uncertainties during the actual motion of the MWMR, and the stability of the AVPSMO is proved via Lyapunov theory. The proposed AVPSMO-MPC method can achieve precise tracking control while ensuring that the constraints of MWMR are not violated in the presence of disturbances and uncertainties. Finally, comparative simulation cases are presented to demonstrate the effectiveness and robustness of the proposed method.

Closed-Loop Subspace Predictive Control of Gyroscope

Control moment gyroscope (CMG) is used in many applications, especially related to spacecraft navigation. Hence, the trajectory tracking problem of the CMG control is important and worth researching. To address this problem, a closed-loop subspace predictive control (CSPC) of the gyroscope is presented in this paper. The proposed control technique constructs an auxiliary variable based on the known controller information. The constructed auxiliary variable assists to handle the inherent correlation between control inputs and noises in the closed-loop system. Additionally, an unbiased prediction of the system output is obtained to calculate the optimal control input. The theoretical analysis of the recursive feasibility and stability of the proposed control technique is also provided. Ultimately, the effectiveness of the proposed control technique is verified on a real-time experimental platform of the CMG. The experimental results demonstrate the improved trajectory tracking and predictive performance of the proposed control technique. Overall, this paper provides a solution for the trajectory tracking problem of the CMG control.

Vibration suppression of smart composite beam using model predictive controller

Abstract This work presents an adaptive model predictive control (MPC) strategy to suppress the vibration in a laminated composite beam. The control method incorporates a system identification algorithm to estimate the system parameters online, which provides a precise simulation of system dynamics. A fixed-free cantilever composite beam equipped with piezoelectric actuators was used to evaluate the efficacy of the control method. The sensors and actuators are securely bonded to the upper and lower surfaces at arbitrary locations along the beam’s length. A unified mechanical displacement field is applied to all layers, while displacements are considered independently for each layer. The beam is composed of eight layers of material, each with a thickness of 0.2 mm and orientations specified as (90°/0°/90°/0°). To achieve the best performance, the parameters of the MPC were adjusted numerically. The numerical analysis revealed that placing the actuator near the clamped end at the fixed end resulted in superior control outcomes, with a settling time of approximately 1.8 s. Conversely, the longest settling time occurred when the actuator was positioned at the free end, taking around 4 s. This model could potentially be expanded to address vibration in more intricate beams exhibiting nonlinear characteristics. The deflection readings measured at the end of the beam have been utilized as feedback control signals for predicting future behavior over a predetermined control horizon. The subsequent cost function is minimized through a quadratic equation to determine the sequence of optimal yet constrained control inputs. The suggested active vibration control system is then implemented and assessed numerically to examine the effectiveness of the control method.