The semi-global stabilization problem of discrete-time systems subject to infinite distributed input delays and actuator saturations is investigated in this article. This article develops two low-gain feedback control laws for two types of systems, respectively. It is shown that the resulting system is semi-globally exponentially stabilized. Our results include those existing results on systems subject to only input saturations and systems subject to bounded delays and input saturations as special cases. Compared with existing results on infinite delays and actuator saturations, this article develops a more accurate scaling utilizing a more general framework. Furthermore, a novel converse Lyapunov theorem for discrete-time linear infinite-delayed systems and a novel stability analysis theorem for perturbed discrete-time linear infinite-delayed systems are developed to handle the nonlinearity induced by saturations. Finally, this article provides two numerical examples to illustrate the effectiveness of the developed theorems.

Navigation control of microrobots in vivo has great potential in precision medicine and has attracted considerable attention in recent years. The control performance of the existing methods is considerably affected by hysteresis nonlinearity. This article presents a robust control method that can overcome hysteresis influence in navigating a microrobot actuated by an electromagnetic coil system. A motion planner that combines the breadth-first search (BFS) method and genetic algorithm (GA) is used to plan a reliable and flexible trajectory for the microrobot navigation. To compensate for hysteresis nonlinearity existing in the system, the Prandtl–Ishlinskii (PI) model is introduced. A robust controller that integrates adaptive sliding mode control (ASMC) and nonlinear disturbance observer is designed to guarantee the stability and accuracy of the microrobot in motion. Experiments have been performed to demonstrate the effectiveness of the proposed approach. The success of this research will advance the microrobot navigation for in vivo applications. Note to Practitioners—The motivation of this article is to eliminate the effect of hysteresis caused by the electromagnetic system on microrobot motion. Existing research on hysteresis compensation mostly uses inverse model or online model identification, which is not suitable for real-time control of the microrobot. In addition, the disturbance and uncertainty caused by the microfluidic environment at different flow rates will also affect the control performance of the microrobot. To solve the above problems, an adaptive robust control method is developed in this article. Experimental results have shown that the proposed method can successfully control the microrobot in the in vitro and in vivo environment.

The well-known generalized Kalman–Yakubovich–Popov lemma is widely used in system analysis and synthesis. However, the corresponding theory for singular systems, especially singular fractional-order systems (SFOSs), is lacking. Therefore, many control problems for this type of systems cannot be optimized in limited frequency ranges. In this article, a universal framework of the finite frequency band generalized Kalman–Yakubovich–Popov lemma for SFOSs is established, the bounded real lemma in the sense of the${L_{\infty }}$-norm is derived for different frequency ranges, and the corresponding controller is designed to improve the${L_{\infty } }$performance index of SFOSs. Three illustrative examples are given to demonstrate the correctness and effectiveness of the theoretical results.

Microrobots show great targeted-delivery potential in precision medicine. This article presents the use of a model-free approach to the navigation control of a microrobot in the cardiovascular environment. With the proposed approach, the microrobot can adapt to the non-Newton behavior of blood and environmental disturbances when it moves in blood vessels without knowledge of blood-velocity distribution. The referred trajectory of the navigated microrobot is generated by using a breadth-first search and genetic algorithm, aiming to minimize the energy consumption. The proposed navigation controller combines sliding mode control, backstepping control, and disturbance compensation. A high-gain extended state observer is designed to estimate and reject the uncertainties of model parameters and environmental disturbances. Simulations are performed to demonstrate the effectiveness of the proposed approach in a small artery compared with other control methods.

Cell migration plays an essential role in cancer cell study. Investigation of a novel method for controlling cell migration movement can help develop new therapeutic strategies. In this paper, a chemoattractant-loaded microbead, which is controlled by optical tweezers, is used to stimulate a target cell to accomplish automated migration along a desired path while avoiding obstacles. Models of both tweezers-bead and bead-cell interactions are investigated. A dual closed-loop control strategy is proposed, which includes an inner tweezers-bead control loop and an outer bead-cell control loop. A proportional-integral feedback plus feedforward controller is used to control the inner loop, and an active disturbance rejection controller is used for the outer loop, which can address the cell migration modeling errors and unknown external disturbances. A traffic rule based on interference-clearing mechanism is also proposed to reduce external disturbances on the system by preventing other particles from interfering with the migration process. The effectiveness of the proposed control approach is verified by simulations and experiments on migrating leukemia cancer cells.

As the rapid development of precision medicine, in-vivo manipulation of micro/nano-scaled particles has attracted increasing attention in recent years. The collision is one of the main reasons that falls the in-vivo particle transportation fail. In this paper, we develop an in-vivo cell transportation control approach using a robotically controlled optical tweezers manipulation system, where a so-called wide-area image gradient algorithm is used to avoid collision of the transported cell with other obstacles. The controller exhibits advantages of the reduced online calculation for collision avoidance, fast response, high accuracy, as well as an ability to compensate the environmental disturbance caused by blood flow. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed controller.

In vivo manipulation of biological cells has attracted considerable attention in recent years. This process is particularly useful for precision medicine, such as cancer target therapy. Robotics technology is becoming necessary to stably and effectively manipulate and control single target cells in a complex in vivo environment. This paper presents a robot-aided optical tweezers-based manipulation technology that serves a function in the transport of single biological cells in vivo. An enhanced disturbance compensation controller is developed to minimize the effect of fluids (e.g., blood flow) on the cell. The method has exhibited advantages of flexibility in adjusting cell tracking trajectory online and the capability to minimize steady-state error and eliminate overshoot. Simulations and experiments of tracking single target cells in living zebrafish embryos have demonstrated the effectiveness of the proposed approach in a dynamic in vivo environment.

As rapid development of precision medicine, in vivo manipulation of micro/nano-scaled particles have attracted increasing attention in recent years. To accommodate complex in-vivo environment, robot-aided automated manipulation technology is highly demanded in trapping and controlling micro/nano-particles stably and effectively. This paper presents an in-vivo cell manipulation system, where a disturbance compensation controller is utilized to minimize the effect of fluid (e.g., blood flow) on the cell. The controller has exhibited advantages in adjusting cell tracking trajectory online, minimizing the steady-state error, and eliminating overshoot. Simulation and experimental results verify the performance of the controller.

Research and biomedical applications in cell surgery require transportation and rotation of biological cells. In these cell manipulation tasks, the cell of interest must be translated and oriented properly such that the desired component, such as the polar body or other organelles, can be imaged with optical microscopy. This paper presents a holographic optical tweezers (HOT) based system to carry out automated translational control in the plane, and rotational control about one rotational axes of a suspended cell. Based on the proposed general equations of motion of the cell, held in an optical trap, two controllers, one for cell translational and one for rotational control, are developed to translate and orient the cells to the desired position and orientation in a sequential manner. Experiments are performed to demonstrate the effectiveness of the proposed approach.

Optical tweezers has become a powerful tool in automated cell transportation control and has been used in a variety of biological applications. The use of optical tweezers for cell surgery has great potential for various biomedical applications such as microinjection, organelle extraction and modification, and preimplantation genetic diagnosis (PGD). In these cell surgical manipulation tasks, the cell of interest must be oriented properly such that the desired component, e.g., the polar-body or organelles, can be visualized by optical microscopy; thus cell rotation becomes a necessary procedure. Currently, cell rotational control can be carried out by laser tools that are usually handled by skilled people. The open-loop manual operation cannot be readily used for applications requiring precise and high throughput cell rotational control. This highlights the need of developing an automated controlled robot manipulator to rotate biological cells more accurately and efficiently. In this paper, we propose a cell surgery system that utilizes two optical traps, generated by robotically controlled holographic optical tweezers (HOT), to manipulate the cell for rotation, where the optical tweezers functions as special robot manipulators. Through dynamic modeling using T-matrix approach, the relationship between the applied torques and the spherical coordinates of the optical tweezers is characterized. A rotational controller is further developed to rotate the cell to the pre-desired orientation accurately. Experiments are performed to demonstrate the effectiveness of the proposed approach.

In this paper, a novel approach is presented to approximate the general fractional order nonlinear dynamic systems. Firstly, a generalized T-S fuzzy method is used to approximate the original models. Then a new method to approximate the fractional order T-S models is utilized, and obtain a series of integer order linear model. It is revealed for the first time that a general fractional order nonlinear system (FONS) can be approximated by a series of integer order linear models to any degree of accuracy on any compact set. Finally, numerical simulation results are provided to illustrate the effectiveness of the proposed approach.

In this paper, a novel dynamic sliding mode control scheme is proposed for a class of uncertain stochastic nonlinear time-delay systems represented by Takagi-Sugeno fuzzy models. The key advantage of the proposed scheme is that two very restrictive assumptions in most existing sliding mode control approaches for stochastic fuzzy systems have been removed. It is shown that the closed-loop control system trajectories can be driven onto the sliding surface in finite time almost certainly. It is also shown that the stochastic stability of the resulting sliding motion can be guaranteed in terms of linear matrix inequalities; moreover, the sliding-mode controller can be obtained simultaneously. Simulation results illustrating the advantages and effectiveness of the proposed approaches are also provided.

In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.

In this paper, a novel dynamic integral sliding-mode control (ISMC) scheme is proposed for a class of uncertain stochastic nonlinear time-delay systems represented by Takagi-Sugeno fuzzy models. The key advantage of the proposed scheme is that two very restrictive assumptions in most existing ISMC approaches for stochastic fuzzy systems have been removed. It is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time. It is also shown that the stochastic stability of the resulting sliding motion can be guaranteed in terms of linear matrix inequalities, and moreover, the sliding-mode controller can be obtained simultaneously. Simulation results from an inverted pendulum example illustrating the advantages and effectiveness of the proposed approaches are provided in the end.

This paper addresses the sliding-mode control (SMC) design problem for a class of uncertain nonlinear systems that can be represented by Takagi-Sugeno (T-S) fuzzy models. We propose a novel dynamic sliding-mode control scheme for T-S fuzzy models, aiming to eliminate the restrictive assumption that all subsystems share a common input matrix, which is required in most existing fuzzy SMC approaches. Sufficient conditions for the reachability of the sliding surface and asymptotic stability of the sliding motion are formulated in the form of linear matrix inequalities. Finally, simulation results that illustrate the advantages and effectiveness of the proposed approaches are provided.

This paper addresses the universal fuzzy integral sliding-mode controllers' problem for continuous-time multi-input multi-output nonlinear systems based on Takagi-Sugeno (T-S) fuzzy models. By using the approximation capability of T-S fuzzy models, the nonlinear systems are expressed by uncertain T-S fuzzy models with norm-bounded approximation errors. A novel fuzzy dynamic integral sliding-mode control (DISMC) scheme is then developed for the nonlinear systems based on their T-S fuzzy approximation models. One of the key features of the new DISMC scheme is that the restrictive assumption that all local linear systems share a common input matrix, which is required in most existing fuzzy integral sliding-mode control (ISMC) approaches, is removed. Furthermore, the results of universal fuzzy ISMCs for two classes of nonlinear systems, along with constructive procedures to obtain the universal fuzzy ISMCs, are provided, respectively. Finally, the advantages and effectiveness of the proposed approaches are illustrated via a numerical example.

In this paper, the sliding mode control (SMC) design problem for uncertain T-S fuzzy systems is investigated. It is noted that most existing fuzzy SMC approaches rely on a very restrictive assumption that all subsystems of the T-S fuzzy systems have the same input matrix. Aiming to remove this assumption, we propose a novel dynamic sliding mode control (DSMC) scheme for a class of uncertain T-S fuzzy systems. It is shown that the sliding surface can be reached in finite time and the asymptotic stability of the sliding motion can be guaranteed if a set of linear matrix inequalities are feasible. Simulation results from two numerical examples illustrating the effectiveness and advantages of the proposed approaches are also provided.

Chemotaxis is an event in which cells spatially sense their extro-environment and move along a chemokine gradient. Rapid advances in various cell- and molecule-based biomedical applications have led to increasing demands for the precise and proactive control of cell chemotaxis movement. This paper presents the development of a robot-aided optical manipulation tool for dynamics analysis and automated control of cell chemotaxis movement. Cell locomotion model is developed to characterize the relationship between the chemoattractant and the forces that govern the cell migration. The microparticles, releasing a chemokine while in motion, are optically trapped and robotically controlled to induce cell polarization and migration. Experiments performed on migrating leukemia cancer cells demonstrate the effectiveness of the proposed approach. The arising research income of this paper will benefit the development of an automated control strategy for cell migration, targeting at the novel therapies in the future medicine.

This paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems. The underlying mechanism of stochastic fuzzy logic is first discussed, and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given. Based on their function approximation capability, these kinds of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic nonaffine nonlinear systems under some sufficient conditions. An approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized Takagi-Sugeno (T-S) fuzzy approximation models. Then, the results of universal fuzzy controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy controllers, are also provided, respectively. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.

This paper investigates the universal fuzzy models problem and universal fuzzy controllers problem for discrete-time general nonlinear systems based on a class of generalized T-S fuzzy models. The generalized T-S fuzzy models, which are shown to be universal function approximators, are also proved to be universal fuzzy models for non-affine nonlinear systems under some sufficient conditions. The results of static and dynamic universal fuzzy controllers for two classes of nonlinear systems are then given, respectively, and constructive procedures to obtain the universal fuzzy controllers are also provided.

This paper presents a novel approach to control general nonlinear systems based on Takagi-Sugeno (T-S) fuzzy dynamic models. It is first shown that a general nonlinear system can be approximated by a generalized T-S fuzzy model to any degree of accuracy on any compact set. It is then shown that the stabilization problem of the general nonlinear system can be solved as a robust stabilization problem of the developed T-S fuzzy system with the approximation errors as the uncertainty term. Based on a piecewise quadratic Lyapunov function, the robust semiglobal stabilization and H∞ control of the general nonlinear system are formulated in the form of linear matrix inequalities. Simulation results are provided to illustrate the effectiveness of the proposed approaches.

A novel approach to control of general nonlinear system based on T-S fuzzy model is presented in this paper. Firstly, it is shown that a general nonlinear system can be approximated by a generalized T-S fuzzy model to arbitrary degree of accuracy on any compact set. And the basic idea of the proposed approach is to stabilize the general nonlinear system by solving a robust stabilization problem of the developed T-S fuzzy system with the approximation errors as the uncertainty term. Then using a piecewise Lyapunov function, robust semi-global stabilization and generalized H2control of the general nonlinear system are formulated in the form of linear matrix inequalities. Finally, an example is provided to demonstrate the effectiveness of the proposed approaches.

Consensus strategies find extensive applications in coordination of robot groups and decision making of agents. Since balanced graph plays an important role in the average consensus problem for directed communication networks, this work explores the conditions and algorithms for the digraph balancing problem. It has been proved that a directed graph can be balanced if and only if the null space of its incidence matrix contains positive vectors. Then two weight balance algorithms have been proposed, and the conditions for obtaining a unique balanced solution have been investigated. This work has also pointed out the relationship between the weight balance problem and the features of the corresponding underlying Markov chain. Finally, two numerical examples are presented to verify the proposed algorithms.