ABSTRACT This study proposes a novel adaptive approach for fractional data‐driven control of nonlinear systems subject to disturbances. The robust stability of the control system is demonstrated, ensuring bounded tracking error under disturbances. To enhance disturbance mitigation, a data‐driven control strategy is developed, incorporating a radial basis function neural network (RBFNN) based disturbance observer. This design improves system resilience to uncertainties and external perturbations. By integrating fractional‐order dynamics with adaptive neural techniques, the proposed methodology offers enhanced performance over traditional integer‐order controllers. Simulation results demonstrate the approach's effectiveness in tracking accuracy, disturbance rejection, and system stability.
ABSTRACT Quadcopters are four‐motor robots that rely on the thrust generated by their motors to move. Thanks to their maneuverability, vertical takeoff and landing, and hover capabilities, they have become increasingly popular. Due to this popularity, over the years, significant advancements have been made in quadcopter maneuvers from a control perspective. With the objective of real‐time implementation of a model predictive controller (MPC) by reducing the time required for generating control signals, this research investigates the design of a controller for quadcopters to track complicated paths and contributes to regulating the predictive controller's cost. To this end, two methods are tailored: data‐driven regulation based on empirical tests and physics‐based regulation by incorporating human intuition. The developed controller is put to the test with various disturbances and parameter uncertainties, and stability analysis is conducted. A regulated predictive controller achieves high levels of accuracy in real‐time tracking complicated paths, whereas a standard predictive controller fails while reducing energy consumption, as demonstrated in test results.
ABSTRACT This paper considers constrained systems subject to input delays, polytopic uncertainties, and external disturbances, focusing on the core challenge of accurate set‐point tracking and robustness. A robust model predictive tracking control scheme is proposed to address these issues. First, to meet the set‐point tracking requirements of multiple outputs, an augmented state‐space model incorporating state increments and tracking errors is introduced, transforming the original system's tracking control problem into a robust stabilization problem for the augmented system. Next, a state feedback predictive controller is designed. In this case, a worst‐case performance objective function is defined, and a corresponding minimax optimization problem is constructed. The resulting auxiliary problem is then solved via the cone complementarity linearization (CCL) algorithm to handle non‐convex constraints and obtain the controller gain. Finally, a case study of an islanded DC microgrid with two distributed generation units is conducted via simulation. The method achieves set‐point tracking and disturbance rejection of voltage, which verifies its effectiveness.
ABSTRACT This study proposes a robust model predictive controller (RMPC) for the 5 MW fatigue, aerodynamics, structures, and turbulence (FAST) model, a popular wind turbine model developed by the National Renewable Energy Laboratory, to cope with fluctuations and uncertainties associated with the wind more effectively than existing controllers, such as the standard MPC. In line with other model‐based controllers, the proposed RMPC relies on linear control design models obtained by linearizing the high‐fidelity nonlinear aeroelastic FAST model. As with standard MPC, no prior information on the wind speed is given, and the wind speed is considered a disturbance. Robustness against wind disturbances and modeling errors that arise between the control design model and the process (i.e., the simulation model) is ensured by computing a feedback law and a robust invariant set through linear matrix inequalities. The resulting feedback control law is incorporated into the standard MPC, yielding the RMPC, which is thoroughly tested and analyzed by application to the FAST model, compared to the standard MPC, PI control, and light detection and ranging (LiDAR) based feedforward MPC under various realistic wind conditions. The results demonstrate that the proposed controller, which operates without relying on LiDAR measurements, achieves performance nearly comparable to that of a feedforward controller that relies on costly LiDAR technology.
This paper studies the irregular linear quadratic (LQ) optimal control problem involving multiple control inputs and time delays. The distinctive feature of this problem is its integration of multiple control inputs and time delays, leading to a more intricate irregular Riccati equation. This complexity stems from transforming the problem into solving time-delayed forward-backward differential equations (D-FBDEs). This is the crucial issue addressed in this paper. Based on the irregular theory, by constructing coupled irregular Riccati equations, the existence conditions and analytical expressions of the irregular LQ optimal control are presented. Finally, the feasibility of the results is verified through two numerical examples.
This study proposes a novel mathematical model that integrates key epidemiological features, including vertical transmission, saturated incidence, and nonlinear treatment into the dynamics of infectious diseases in a human population. The mathematical and epidemiological relevance of the model is established through the theory of positivity and boundedness of solutions. The basic reproduction number, a key metric for assessing disease spread, is calculated using the next-generation matrix approach, and the existence of model equilibria is established under specific conditions. Bifurcation analysis and long-term behavior are investigated using centre manifold theory and Lyapunov functions, respectively. Two time-dependent control strategies are considered: prevention (blocking mother-to-child transmission) and treatment (using effective drugs), which are analyzed using Pontryagin's maximum principle. The study highlights the impact of implementing each control individually and in combination on reducing disease spread within a community. Key epidemiological properties and optimal control scenarios are quantitatively examined using MATLAB simulations. The results provide valuable insights into curbing vertically transmitted diseases and promoting recovery, emphasizing the importance of combining prevention and treatment strategies to effectively control infectious disease spread.
This paper investigates the data-driven optimal guaranteed cost control problem for a class of uncertain nonlinear systems subject to bounded parameter perturbations and input constraints. To relax the stringent existence conditions of the controller, an auxiliary system with a modified cost function is reformulated. Through this transformation, the original robust control problem is converted into equivalent optimal control problems under restricted actuator outputs. Subsequently, a neural network-based reinforcement learning algorithm is developed to approximately solve the complex Hamilton-Jacobi-Bellman equation. By utilizing real system data within a model-free iterative learning framework, the parameterized representation of the optimal policy is achieved, strictly avoiding the identification of unknown model dynamics. Furthermore, a rigorous convergence analysis of the proposed iterative algorithm is provided. Finally, simulation examples are presented to illustrate the feasibility and effectiveness of the proposed theoretical results.
In Hamilton-Jacobi reachability analysis, reachable sets are characterized by sublevel sets of the value function of an optimal control problem. Although grid-based approaches provide a general-purpose means of numerically computing this value function, the curse-of-dimensionality often limits their use in all but simple applications. In this article, inner approximations of the backward reachable set are characterized through the design of a feedback control law for feedback linearizable systems subject to input constraints. This structure is exploited to propose a selection of control gains via an optimization problem. For a fixed sampling/discretization choice, the computational cost and memory requirement of the proposed scheme are tied to the number of system states and inputs in a polynomial manner. Thus, the proposed approximation scheme is computationally tractable for feedback linearizable systems of relatively high dimension.
In this paper, we focus on a kind of mean-field doubly stochastic optimal control problems described by mean-field delayed backward doubly stochastic differential equations. To begin with, we obtain the existence and uniqueness result of the solution for mean-field delayed backward doubly stochastic differential equations (MFDBDSDEs, for short) and mean-field anticipated backward doubly stochastic differential equations (MFABDSDEs, for short) by the contraction mapping principle, respectively. Then, under the convexity condition, we deduce the stochastic maximum principle of the mean-field delayed backward doubly stochastic control systems by utilizing the classical variational theory. After that, we give the sufficient conditions for the stochastic control systems by using the duality relation between the state equations and the corresponding adjoint equations. Finally, we give the application to the mean-field delayed doubly stochastic linear quadratic optimal control problems.
In this paper, an adaptive optimized control strategy based on deep neural networks (DNNs) and an accelerated gradient method is developed for a class of nonlinear strict-feedback systems to achieve prescribed tracking performance via a dynamic-memory event-triggered mechanism (DMETM). Initially, DNNs are applied to approximate both the unknown dynamic functions and the combined unknown functions that contain the performance index. Subsequently, an accelerated gradient adaptive strategy based on the first-order Taylor series is employed to estimate the DNN weights in real-time, and auxiliary weight estimation is introduced through the first adaptive law to couple with the second adaptive law. Although the coupled adaptive structure increases the complexity of the analysis, it achieves significantly faster learning convergence and improves transient tracking performance while maintaining stability. Moreover, the virtual controller and the actual controller are constructed using optimized backstepping technology, with two -class functions introduced to meet the prescribed accuracy tracking. Lastly, the DMETM is used to reduce the communication burden while ensuring uniform boundedness of all signals. Simulation results are provided to verify the effectiveness of the control strategy.
This article presents a comprehensive overview of optimization-based modeling and control strategies in robotics, highlighting their evolution over the past three decades. Robotic systems are increasingly designed and controlled through optimization frameworks that integrate dynamic and kinematic analyses, enabling efficient performance across diverse tasks. A key focus is formulating optimal control problems that incorporate nonlinear dynamics, contact interactions, and a wide range of system constraints. The general optimal control problem is formalized using differential-algebraic equations to capture both continuous dynamics and discrete constraints, providing a unified structure for motion planning. To address the problem, we establish an explicit expression for the Riemann-Liouville fractional integral operational matrix of Mittag-Leffler polynomials for the first time, utilizing the Fourier Transform. By utilizing the operational matrix in conjunction with the Galerkin method, the problem is converted into a system of algebraic equations. Ultimately, the effectiveness and precision of the proposed numerical algorithm are demonstrated through several illustrative case studies.
This work provides a mathematical model that allows us to evaluate the dynamics of Chlamydia trachomatis infections and examine the optimal strategies to control this disease. The model classifies the population of humans into four classes: susceptible, exposed, infected and recovered, and includes biological and behavioral dynamics. Stability analysis for the proposed model is performed. This analysis shows that the disease-free equilibrium is locally and globally asymptotically stable when , while an endemic equilibrium occurs when . Recruitment rate and transmission parameters have been identified via sensitivity analysis as the most important factors for spreading disease, while recovery and mortality rates significantly decrease the potential of transmitting the disease. A framework for optimal control has been developed that considers three different types of control (time-dependent) measures: promoting safe sexual practices, periodic screening, and effective treatment. The maximum principle of Pontryagin and forward-backward sweep computational techniques are used to analyze and evaluate multiple intervention strategies. The findings show that using all three controls leads to a larger reduction of persons either exposed or infected than the comparison of paired interventions. Among the partial strategies, the combination of screening and treatment is the most successful method of controlling the disease; however, the combination will never equal the total control method. A full cost-effectiveness analysis using multiple different measures (e.g., the number of infections that have been avoided and the incremental cost effectiveness ratio) shows that the three-control method, although higher cost is extremely cost-effective. Furthermore, Strategy III (prevention + treatment) dominates Strategy IV (prevention + screening), indicating that screening without treatment is economically inefficient. Numerical simulations confirm that comprehensive, simultaneous application of all controls significantly mitigates infection prevalence and accelerates disease reduction.
This article proposes an accelerated gradient-based parameter estimation for generalized time-varying systems. A momentum term is incorporated into the parameter adaptation law to accelerate convergence and suppress oscillatory behavior. In addition, the data filtering technique is applied to preprocess the input and output signals, effectively attenuating the influence of colored noise on parameter estimation. The proposed algorithm is further validated through its application to a DC motor system.
In this paper we propose a model-free reinforcement learning framework for adaptive control of continuous-time linear systems without requiring prior system knowledge. By estimating system states from measurable outputs and iteratively minimizing the optimal cost function, both optimal and suboptimal output feedback control policies are derived. An integral reinforcement learning approach with an actor-critic structure enables real-time estimation of Q-function parameters, thereby facilitating adaptive policy optimization. In particular, the proposed approach can outperform traditional LQR-based output-feedback control by delivering superior results in complex systems, while maintaining good performance in simple scenarios. Simulation results on a Multi-agent Network with Eliminated Constraints and an active vibration control system validate the framework's effectiveness and robustness under uncertainty.
This article studies a linear-quadratic mixed leadership stochastic differential game with overlapping information, where each player simultaneously acts as the follower in one strategy and the leader in the other. A distinctive feature of this paper is that the information available to the two players overlaps only partially, with neither being a subset of the other. At the follower layer, the players engage in a linear-quadratic non-zero-sum stochastic differential Nash game with overlapping information. At the leader layer, they participate in a similar game, whose state dynamics are governed by a conditional mean-field forward-backward stochastic differential equation. By applying the maximum principle with partial information and the completion of the square technique, this paper derives the open-loop Stackelberg-Nash equilibrium with overlapping information. It is shown that this equilibrium admits a state feedback representation, provided that an associated system of Riccati equations is solvable. As an application, this model is used to study a continuous-time principal-agent problem.
An optimal control problem with state and control constraints is addressed using a barrier function approach adapted from an interior-point method. A closed-form approximate Linear Quadratic Regulator (LQR) control law has been derived to achieve stabilizing behavior in a state and control constrained environment. The closed-form control law provides automatic controller caution and safe steering. The controller caution is achieved by auto-tuning and to adjust the system's transient response, and the safe steering is achieved by an automatic shift in the target point to avoid converging on an infeasible state. This work demonstrates the results on linear and non-linear systems in comparison with the widely used Artificial Potential Field (APF) Method and the state-of-the-art Control Barrier Function (CBF) method, both paired with the stabilizing LQR law. The proposed law also attains the guidance attribute in the proposed law by integrating range sensors for state constraint feedback. This is supported by the ROS-Gazebo simulation results on a linear omnidirectional autonomous mobile robot with range sensor feedback for navigation in a structured environment.
In this study, we introduce a mathematical model to analyze the dynamics of leprosy transmission, incorporating a novel SEIR framework extended by an additional compartment that accounts for the bacterial load in the environment. The model employs the Caputo-Fabrizio (CF) fractional derivative to better represent memory effects in the disease transmission process. We establish the existence and uniqueness of the solution using the Banach fixed-point theorem and analyze both the local and global stability of the equilibrium states. A comprehensive sensitivity analysis is conducted to identify the key parameters influencing the spread of leprosy. Numerical simulations are performed to demonstrate the model's ability to capture the complex dynamics of leprosy transmission. Additionally, an optimal control strategy is proposed, involving two control variables: raising awareness and administering medical treatment to reduce the number of infected individuals. Results reveal that awareness-raising is more effective than treatment alone, as it promotes early diagnosis and limits further transmission. Simulations confirm that the fractional order serves as a control parameter influencing convergence to equilibrium and infection persistence. Overall, the findings provide valuable insights into leprosy management, highlighting the importance of environmental factors and public health interventions.
This article investigates an advanced control method called the fuzzy adaptive super-twist integral sliding mode (FASISM) controller. It combines adaptive sliding mode control with fuzzy logic to improve stability and effectively handle external disturbances. The uncertainties in the system are integrated into a unified framework, enabling them to be effectively addressed using an adaptive control approach. This controller aims to achieve stabilization and optimal performance in electric vehicles by addressing system uncertainties and mitigating the impact of disturbances, thereby ensuring reliable and efficient operation under varying conditions. To realize efficient control, the EV's battery voltage is utilized as the control input, while the EV speed serves as the system output; both variables are restricted to maintain optimal performance and stability. The proposed strategy combines the Takagi-Sugeno (TS) fuzzy model with a parallel distributed compensation fuzzy controller, incorporating an LMI-based optimal super-twist SMC adaptive scheme. The closed-loop system is proven to attain uniform ultimate boundedness with the implementation of the proposed sliding mode controller. Simulation results in MATLAB demonstrate the robust performance of the FASISM controller, achieving rapid stabilization of EV speed even with the existence of uncertainties and disturbances.
Increasing system reliability and reducing costs for electric vehicle (EV) applications requires reducing sensor dependency in permanent magnet synchronous motors (IPMSMs). Therefore, sensorless operation remains a significant challenge, particularly over a wide speed range. Adaptive vector filters (AVF) and phase-locked loops (PLL) are integrated with a grey relational analysis (GRA)-based model predictive torque control (MPTC) strategy for IPMSMs in the proposed sensorless control framework. The proposed method incorporates an amplitude and phase offset to counteract feedback delay-induced amplitude and phase distortions in the back electromotive force (BEMF) filtered by the AVF. The ideal PLL is implemented using a differential calculation structure that preserves closed-loop dynamics. In comparison, the steady-state position estimation error is effectively eliminated using an open-loop deviation compensator. Incorporating GRA-based optimization enables online adaptation of the weighting factors, achieving an effective trade-off among torque ripple, flux distortion, and switching frequency. An experimental validation of the proposed algorithm is carried out on a Speedgoat real-time hardware-in-the-loop (HIL) platform. The obtained results confirm that the method significantly improves sensorless estimation accuracy, torque response, and robustness against parameter variations, demonstrating its suitability for rail transit applications.
Grid-tied inverters are widely used to integrate renewable energy sources into the electrical grid. In these systems, LCL filters are often utilized as the interface between the inverter and the grid. However, LCL filters present a resonance peak that may turn the system unstable. In addition, as the grid weakens, lower is the frequency of this peak, posing relevant challenges for the control system. In this sense, adaptive controllers emerge as feasible solutions once they can adjust their gains in response to any perturbation. However, the design of an adaptive controller requires plenty of experience due to the high quantity of parameters. This work proposes a systematic parametrization for a robust model reference adaptive proportional integral controller using the whale optimization algorithm, considering controller performance and stability constraints. The optimized controller is applied on a grid-tied inverter with an LCL filter. Simulation results indicate the feasibility of using the proposed automatic procedure to design the controller, obtaining fast current tracking and high robustness to unmodeled dynamics and exogenous disturbances. In addition, significant parametric variations (more than 30 times the nominal value of grid inductance) are imposed during the experiment to evaluate the robustness of the optimized controller, which is able to maintain the closed-loop globally stable and properly controlled even in the face of all adversities. Processor-in-the loop experiments are presented to validate the feasibility and satisfactory performance of the optimized controller. Experimental results are provided to prove the controller's feasibility in real-world application, demonstrating that grid-injected currents comply with the IEEE 1547 standard.
