Traditional State Feedback Research Articles

MPC-Based Asynchronous Attack Tolerant Control for Uncertain Markov Jump Cyber-Physical Systems.

The model predictive control (MPC)-based asynchronous attack tolerant control scheme is investigated in this article for uncertain Markov jump cyber-physical systems (MJCPSs) under the Denial-of-Service (DoS) attack. To tackle the problem of the system running mode may not be observed in the control center, an asynchronous model predictive controller is proposed. Specifically, a dynamic controller, which can tune the performance online, is designed besides a traditional state feedback one. Even though such a combination may cause possible degradation of system performance, it can expand the initial feasible region and relieve the online computation burden efficiently. In addition, a decision variable is introduced to alleviate limitations on the feasible region generated by the constraints in the traditional MPC method. A series of solvable optimal problems are further constructed to achieve the desired performances. Finally, an application of the proposed method is given to demonstrate its effectiveness.

Optimizing inverted pendulum control: Integrating neural network adaptability

This study explores the implementation and efficacy of a neural network controller for an inverted pendulum system, contrasting it with traditional state feedback control. Initially, state feedback control exhibited limitations in managing complex system dynamics. Subsequently, a neural network controller was developed, trained using datasets from both uncontrolled and refined state space models. The refined model yielded lower training loss and superior control performance. This research demonstrates the neural network controllers enhanced adaptability and precision, offering significant improvements over traditional methods in controlling dynamic systems like inverted pendulums.

State-restricted adaptive control of a multilevel rotating electromagnetic mechanical flexible device using electromagnetic actuators

This work presents the development of a multilevel electromagnetic actuation system that controls the shape of a flexible rotatory robotic structure. An array of electromagnets is used as the set of actuators that regulate the position of permanent magnets within the flexible device. The primary outcome of this study is the design and experimental validation of the multilevel rotating device. In addition, the theoretical description of the system motion under electromagnetic actuation is formulated using Euler–Lagrange and electromagnetic theories. Given the developed model, a theoretical study leads to designing an adaptive control that considers motion restrictions in the flexible device. The controller aims to modify the current applied to the electromagnets, which changes the interaction forces between the electromagnet and the permanent magnets in the robotic flexible structure. A set of numerical simulations confirms the proposed controller’s effectiveness compared to the traditional state feedback approach that does not consider the state restrictions, which is implemented in devices that also operate under an electromagnetic approach. Furthermore, an experimental version of the flexible device allows for testing of the developed controller. The experimental results show the suitability of the proposed control to generate non-oscillatory controlled motion during the regulation of the flexible mechanic device shape.

Finite-time interval stabilization for time-varying stochastic delayed systems via interval matrix method by piecewise controllers

This paper presents a comprehensive study addressing the problem of finite-time interval stabilization (FTIS) for two distinct types of systems: linear time-invariant stochastic delayed systems (LTISDSs) and linear time-varying stochastic delayed systems (LTVSDSs). To begin, the definition of FTIS is established, which is based on employing piecewise state feedback controllers. Subsequently, a time-varying Lyapunov-Krasovskii functional (LKF) is proposed and a novel optimization algorithm is designed to address the challenge of FTIS for LTISDSs. Additionally, this paper investigates the equivalence of LTVSDSs to uncertain stochastic delayed systems with interval parameters, represented as a series of convex combinations. Notably, both the optimization algorithm and the linear matrix inequalities (LMIs) technique are employed to establish sufficient conditions for achieving FTIS in LTVSDSs. Furthermore, when compared to traditional state feedback controllers, the piecewise controllers not only enhance the precision of system control but also lead to reduced control gains and fewer control effort requirements. Finally, the findings are substantiated through the presentation of two numerical examples, providing practical validation for the proposed methodologies and their effectiveness.

State Feedback Control for Vehicle Electro-Hydraulic Braking Systems Based on Adaptive Genetic Algorithm Optimization

In traditional state feedback control, the difficulty in determining the coefficient matrix is a significant factor that prevents achieving optimal control. To address this issue, this paper proposes the integration of adaptive genetic algorithms with state feedback control. The effectiveness of the proposed algorithm is validated via an electro-hydraulic braking system. Firstly, a model of the electro-hydraulic braking system is introduced. Next, a state feedback controller optimized by parameter-adaptive genetic algorithm is designed. Additionally, a penalty term is introduced into the fitness function to suppress overshoots. Finally, simulations are conducted to compare the convergence speed of parameter-adaptive genetic algorithm with genetic algorithm, ant colony optimization, and particle swarm optimization. Furthermore, the performance of the proposed algorithm, the state feedback control, and the proportional-integral control are also compared. The comparison results show that the proposed algorithm effectively accelerates the settling time of the electro-hydraulic braking system and suppresses the overshoots.

Extremum seeking control for the trajectory tracking of a skid steering vehicle via averaged sub-gradient integral sliding-mode theory

This study introduces the development of a novel extremum-seeking controller designed to stabilize the tracking trajectory of a fully actuated four-wheeled skid steering vehicle. The controller design employs a class of averaged sub-gradient optimization strategies for a suitable convex function that depends on the enforced tracking trajectory achieved through an integral sliding mode implementation. The application of this controller necessitates a nonlinear coordinate transformation of the skid steering vehicle dynamics, resulting in a perturbed multi-input–multi-output linear system. Using the proposed controller, a multidimensional sliding surface remains remarkably stable despite tracking errors. The surface design defines a manifold that aligns with the sub-gradient of a convex function, contingent upon the integral of the tracking error. This connection establishes a link between the extremum-seeking problem and the sliding mode control design. Employing the cascade design strategy, commonly referred to as backstepping, enables the calculation of torques for the four wheels of the mobile vehicle using a sequence of auxiliary sliding surfaces, each with its corresponding complementary function for every stage. The dynamic formulation for the wheel torques is derived from the integral sliding mode methodology. A series of numerical evaluations are conducted to assess the controller’s effectiveness in terms of functional performance. A comparison between the control action based on sliding mode and the traditional state feedback formulation validates the efficacy of the proposed design. This comparison demonstrates advancements in robustness in the face of modeling uncertainties and optimization of the performance function, which are theoretically supported by the suggested control design. Implementing the proposed controller in an experimental platform for a wheeled skid steering vehicle reaffirms the control design methodology presented in this study. This platform includes the application of an image processing algorithm to determine the non-inertial position of the autonomous vehicle using integral sliding mode control. This information completes the necessary data for implementing the on-site version of the proposed controller.

Adaptive controller based on barrier Lyapunov function for a composite Cartesian-delta robotic device for precise time-varying position tracking

This study presents the design of an adaptive event-driven controller for solving the trajectory tracking problem of a composite robotic device made up of a three-dimensional Cartesian and a parallel Delta robot. The proposed composite device has a mathematical model satisfying a standard Lagrangian structure affected by modeling uncertainties and external perturbations. The adaptive gain of the controller is considered to enforce the convergence of the tracking error while the state bounds are satisfied. The barrier Lyapunov function addresses the preconceived state constraints for both robotic devices by designing a time-varying gain that guarantees the ultimate boundedness of the tracking error under the effect of external perturbations. The event-driven approach considers that the Cartesian robot is moving into a predefined invariant zone near to the origin. In contrast, the delta robot can complete the tracking problem once the end-effector is inside the given zone. The suggested controller was evaluated using a virtual representation of the composite robotic device showing better tracking performance (while the restrictions are satisfied) than the performances obtained with the traditional linear state feedback controllers. Analyzing the mean square error and its integral led to confirming the benefits of using the adaptive barrier control.

Sliding-Mode Control of Full-State Constraint Nonlinear Systems: A Barrier Lyapunov Function Approach

This study presents the design of a robust control based on the sliding-mode theory to solve both; the stabilization and the trajectory tracking problems of nonlinear systems subjected to a class of full-state restrictions. The selected nonlinear system satisfies a standard Lagrangian structure affected by nonparametric uncertainties. A barrier Lyapunov function is used to ensure the state constraints by designing a time-varying gain, which guarantees the fulfillment of the predefined state constraints even under external perturbations. The proposed design methodology for the barrier sliding-mode control (BSMC) ensures the convergence of the sliding surface in finite time to the origin. Consequently, the asymptotic convergence of the states to the corresponding equilibrium point is achieved. The finite-time stability of the origin in the closed-loop system with the proposed controller has been demonstrated using the second Lyapunov stability method. The suggested controller was evaluated on a two-link robotic manipulator. Then, the obtained results showed better stabilization and tracking performances (while the restrictions are satisfied) than the traditional first-order sliding-mode or linear state feedback controllers.

Active neck orthosis for musculoskeletal cervical disorders rehabilitation using a parallel mini-robotic device

This work presents the design, construction, simulation, instrumentation, and implementation of a closed chain robotic active neck orthosis with four degrees of freedom satisfying a similar configuration to a four-legged Stewart platform. The dynamics of the device is regulated by a robust control strategy with state restrictions based on a first sliding mode controller with state dependent gains that operates as a divergent function as the states approach the state restrictions. The formal justification about the application of the controller on the proposed orthosis, the finite-time convergence to a sliding surface and the effect of the constraints is proven. The orthosis is also controlled with a traditional state feedback strategy to evaluate the tracking error concerning an external disturbance and compare its performances against the proposed control strategy. A graphical interface based on computer vision is developed to select the type of therapy and assess the patient’s range of motion while wearing the orthosis. The system is tested in some selected volunteers subjects, managing to limit the range of motion within a pre-established area based on the range of motion reported by patients with cervicalgia and whiplash syndrome found in the literature. The developed system offers a novel method to deal with the treatment of neck illnesses based on a novel mechatronic device.

Averaged sub-gradient integral sliding mode control design for cueing end-effector acceleration of a two-link robotic arm

Acceleration tracking is a significant problem in aeronautics, automotive, and biomedical technical areas because its solution may yield effective simulation of motion cues. In the case of aeronautics, the proper solution for the tracking problem improves the in-flight simulations for the training of plane pilots. These simulators can be set up using robotic devices that develop controlled motions with the end-effector following the required three-dimensional reference accelerations robustly. Hence, the primary goal of this study is the effective application of the integral sliding mode controller to solve the acceleration tracking problem for the end-effector of a two-link robotic arm. The control design problem is formulated as an optimization of a convex (non-strict) performance functional depending on the difference between the acceleration of the robotic arm and the desired acceleration using the averaged sub-gradient (ASG) descendant method. A novel sliding surface considers the sensitiveness threshold for acceleration dynamics, inspired by the limit of detection in the pilot vestibular apparatus. The proposed controller was analyzed in terms of the finite-time convergence of the sliding surface and the practical stability analysis for the tracking error dynamics. Our main contribution is the design of the online averaged sub-gradient optimization controller based on integral SMCs. The controller solves the end-effector acceleration tracking for a two-link robotic arm, which implements a simplified version of a flight simulator that is considered to be operated under uncertain scenarios and assumes the presence of perturbations and modeling errors. The controller considers the case of incomplete knowledge of the robotic arm model, which adds an extra degree of robustness to the control design. The numerical evaluations demonstrate the attributes of the ASG formulation compared to traditional state feedback control, using the performance functional, the norm of the acceleration tracking error, and the control input variation

Output feedback robust control for teleoperated manipulator robots with different workspace

This article solves the tracking trajectory problem of teleoperated robotic systems with different workspaces. The overall robotic system satisfies a regular master–slave structure with a delta-robot as the master device and a planar manipulator attached to a Cartesian robot with five degrees of freedom (DOFs) as the slave device. A forward kinematics analysis describes the workspace for the delta-robot and the five-DOFs manipulator. A coordinate transformation based on sigmoidal functions establishes the relation between the workspaces for both robotic devices. The obtained transformation yields a feasible workspace for the slave robot. Then, an inverse kinematics analysis provides the desired reference trajectories. The tracking trajectory control implements a robust strategy based on Barrier Lyapunov functions. The barrier controller does not allow the slave robot to reach non-attainable configurations. State-dependent gains characterized the obtained controller taking into account the different workspaces for each device. Numerical results describe the suggested controller applied in a virtual teleoperated robot and a real robotic system platform. The obtained results confirm the improvements (measured in terms of the mean square error and the l2 norm of the applied controls) of the proposed controller against a traditional state feedback realization. Furthermore, the results show that the trajectories of the slave robot do not leave the valid workspace.

Adaptive terminal sliding mode control of a regulated multidimensional electrospinning device for polymeric structures

This study intends to present an automatic control design for a Cartesian electrospinning system with a dual moving platforms for the collector and the syringe subsystems which are mobilized using linear actuators. The proposed device is including a set of dual robotized structures, that is also carrying a structure to create the Taylor cone that regulates the nano-fiber deposition over the supporting platform. The suggested control form considers the synchronization between the syringe tip and the collector using a cascade tracking structure. A class of distributed state-dependent terminal sliding mode control form solves the tracking problem that yields the syringe-collector pair moves in a synchronized form tracking a bidimensional design that should be reproduced with the fibers deposition made of polyvinyl acid–based polymer. This controller also considers the working space restrictions in the Cartesian electrospinning system device using state-dependent gains which are obtained using a control barrier Lyapunov function. The application of the second stability method of Lyapunov serves to both design the state-dependent gains and prove that the tracking error trajectory is ultimate bound. The proposed controller is evaluated using a cyber-physical representation of the Cartesian electrospinning system device where the proposed controller is evaluated. This evaluation considers a comparison of the control effectiveness (using the root mean square value of the tracking error) with a traditional non-adaptive state feedback and a first-order sliding mode control. This comparison shows that the proposed adaptive controller induces the smallest root mean square among the tested control forms while reducing the magnitude of the overshoot for each actuator.

Harmonic Suppression and Stability Enhancement of a Voltage Sensorless Current Controller for a Grid-Connected Inverter Under Weak Grid

This paper presents the harmonic suppression and stability enhancement of a grid voltage sensorless current controller for a grid-connected inverter under weak grid conditions. Given that inductive-capacitive-inductive (LCL) filters represented as higher-order dynamics cause resonance problems, a considerate resonance frequency damping process is required. In particular, the resonance phenomenon of the LCL filter crucially influences the current quality when the grid-connected inverter is connected to a weak grid with uncertain grid impedance and distorted harmonics. Additionally, there is a possibility that the control system will become unstable due to changes in system parameters, even after considerate resonance frequency damping. In order to solve these problems, this paper presents an active damping (AD) method by using integral variables in an integral state feedback current controller for a grid voltage sensorless inverter system, which significantly improves the current harmonics and stability of the grid-connected inverter under weak grid condition. The presented closed-loop current control scheme only requires the measurement of the injected grid currents and DC-link voltage. Compared to the traditional state feedback control methods, the reliability and robustness of the proposed control scheme are much improved even with reduced system cost. The stability and current control performance of the closed-loop system are investigated in the presence of uncertainty in the grid impedance and filter capacitor parameter under distorted grids. In order to support the theoretical analyses, the comprehensive simulation results are presented in terms of the grid current quality and control stability in an environment with both uncertain grid impedance and a distorted grid. Experimental results are also presented by using a 32-bit digital signal processor (DSP) TMS320F28335 controller for a 2 kVA grid-connected inverter to validate the feasibility of the proposed scheme practically.

Tridimensional autonomous motion robust control of submersible ship based on averaged sub-gradient integral sliding mode approach

The design of a state feedback and robust controller for regulating the tridimensional (3D) movement of autonomous underwater mobile crafts (AUMCs). The controller design is based on the application of Averaged Sub-Gradient Integral Sliding Mode Realisation (ASGISMR). The application of the ASGISMR yields the solution of the closed-loop extreme seeking control for a non-strictly convex functional depending on the tracking error between reference and 3D position of the AUMC. The design of reference trajectories was proposed to enforce the AUMC to follow a continued submersion and ellipsoidal detouring. The mechanical dynamical form of AUMC is well posed for applying the extended version of ASGISMR, considering that integral term represents an ASG associated to the euclidean norm of the tracking error. The time evolution of the functional over the controlled trajectories of the AUMC is compared with the corresponding functional enforced by a traditional state feedback controller with gravity effect compensation. The proposed controller exhibits better tracking and similar control magnitude than the considered reference state feedback realisation. These outcomes justify the potential contributions of the suggested ASGISMR to obtain the local minimisation of the evaluated functional, considering such controller as an extreme seeking realisation for the proposed AUMC.

Robust 3-D autonomous navigation of submersible ship using averaged sub-gradient version of integral sliding mode

This study presents the design of a state feedback controller for an Unmanned Underwater Mobile Vehicle (UUMV) considering the implementation of an Averaged Sub-Gradient (ASG) version of the Integral Sliding Modes (ISM) method. The control problem is formulated here as an extreme seeking problem for the UUMV dynamics, which must track attainable reference trajectories in three-dimensional space. The dynamic nature of the UUMV induces the application of the extended version of ISM, where the integral term represents an ASG of the tracking error norm. The realized trajectory tracking is compared with the trajectories enforced by a traditional state feedback controller with gravity effect compensation. The proposed controller exhibits better tracking and similar control magnitude than the considered classical state feedback realization. These two results confirm the benefits of introducing the mixed extended strategy, including ISM and ASG as an extreme seeking controller for the considered UUMV.

State and mode feedback control strategy for discrete‐time Markovian jump linear systems with time‐varying controllable mode transition probability matrix

SummaryIn this article, the state and mode feedback control strategy is investigated for the discrete‐time Markovian jump linear system (MJLS) with time‐varying controllable mode transition probability matrix (MTPM). This strategy, consisting of a state feedback controller and a mode feedback controller, is proposed to ensure MJLS's stability and meanwhile improve system performance. First, a mode‐dependent state feedback controller is designed to stabilize the MJLS based on the time‐invariant part of the MTPM such that it can still keep valid even if the MTPM is adjusted by the mode feedback control. Second, a generalized quadratic stabilization cost is put forward for evaluating MJLS's performance, which contains system state, state feedback controller, and mode feedback controller. To reduce the stabilization cost, a mode feedback controller is introduced to adjust each mode's occurrence probability by changing the time‐varying controllable part of MTPM. The calculation of such mode feedback controller is given based on a value‐iteration algorithm with its convergence proof. Compared with traditional state feedback control strategy, this state and mode feedback control strategy offers a new perspective for the control problem of general nonhomogeneous MJLSs. Numerical examples are provided to illustrate the validity of the proposed strategy.

Stabilization of logical control networks: an event-triggered control approach

This paper investigates the global stabilization problem of k-valued logical control networks (KVLCNs) via event-triggered control (ETC), where the control inputs only work at several certain individual states. Compared with traditional state feedback control, the designed ETC approach not only shortens the transient period of logical networks but also decreases the number of controller executions. The content of this paper is divided into two parts. In the first part, a necessary and sufficient criterion is derived for the event-triggered stabilization of KVLCNs, and a construction procedure is developed to design all time-optimal event-triggered stabilizers. In the second part, the switching-cost-optimal event-triggered stabilizer is designed to minimize the number of controller executions. A labeled digraph is obtained based on the dynamic of the overall system. Utilizing this digraph, we formulate a universal and unified procedure called the minimal spanning in-tree algorithm to minimize the triggering event set. Furthermore, we illustrate the effectiveness of obtained results through several numerical examples.

Dynamic output‐feedback fuzzy MPC for Takagi‐Sugeno fuzzy systems under event‐triggering–based try‐once‐discard protocol

SummaryThe fuzzy model predictive control (FMPC) problem is studied for a class of discrete‐time Takagi‐Sugeno (T‐S) fuzzy systems with hard constraints. In order to improve the network utilization as well as reduce the transmission burden and avoid data collisions, a novel event‐triggering–based try‐once‐discard (TOD) protocol is developed for networks between sensors and the controller. Moreover, due to practical difficulties in obtaining measurements, the dynamic output‐feedback method is introduced to replace the traditional state feedback method for addressing the FMPC problem. Our aim is to design a series of controllers in the framework of dynamic output‐feedback FMPC for T‐S fuzzy systems so as to find a good balance between the system performance and the time efficiency. Considering nonlinearities in the context of the T‐S fuzzy model, a “min‐max” strategy is put forward to formulate an online optimization problem over the infinite‐time horizon. Then, in light of the Lyapunov‐like function approach that fully involves the properties of the T‐S fuzzy model and the proposed protocol, sufficient conditions are derived to guarantee the input‐to‐state stability of the underlying system. In order to handle the side effects of the proposed event‐triggering–based TOD protocol, its impacts are fully taken into consideration by virtue of the S‐procedure technique and the quadratic boundedness methodology. Furthermore, a certain upper bound of the objective is provided to construct an auxiliary online problem for the solvability, and the corresponding algorithm is given to find the desired controllers. Finally, two numerical examples are used to demonstrate the validity of proposed methods.

Robust finite-horizon stability and stabilization for positive switched FM-II model with actuator saturation

In this paper, robust finite-horizon stability and stabilization problems are investigated for a class of Fornasini–Marchesini second (FM-II) type positive switched systems with actuator saturation. Firstly, finite-horizon stability is analyzed for the addressed 2-D model by utilizing the mode-dependent average dwell time method. Secondly, the traditional state feedback control idea is introduced in the system, and sufficient criteria are derived to guarantee the resulting closed-loop system to be positive and finite-horizon stable. Then, an observer-based control scheme is implemented, where the observer is presented to make the system finite-horizon stabilizable. Explicit controller design schemes are also presented for both of these two types of controllers. Finally, two illustrative examples are provided to show effectiveness of the theoretical criteria.

New results on regional observer-based stabilization for locally Lipchitz nonlinear systems

Abstract This paper describes the design of a regional observer-based controller for the locally Lipchitz nonlinear systems, which can be employed successfully to attain both monitoring and control of a wide range of systems. An observer-based control approach has been employed to attain advantages of the traditional state feedback along with the state estimation through an observer. A lot of work has been accomplished for the globally Lipchitz nonlinear systems. However, a less conservative continuity, called the generalized ellipsoidal Lipchitz condition, has been applied in this paper to consider the locally Lipchitz systems. This condition is then incorporated to attain convex routines for computing the local controller and observer gains. The focus of the present study is to investigate conditions for simultaneous design of observer and controller under locally Lipchitz nonlinearities for systems with norm-bounded disturbances that not only guarantees the stabilization and true state estimation but also robustness against external perturbations. Furthermore, the decoupling of the observer and controller design conditions has been worked out for obtainment of a simple design method. Since the resultant control approach applies to a general class of systems, it can be straightforwardly employed to the globally Lipschitz nonlinear systems as a specific case. The approach is tested via a chaotic system and simulation results are provided to validate the effectiveness of resultant control schemes for the locally Lipschitz systems.