Stabilization of One‐Dimensional Schrödinger Equation with Variable Coefficient under Delayed Boundary Output Feedback

This article considers stabilization of a one‐dimensional Schrödinger equation with variable coefficient and boundary observation which suffers from an arbitrary given time delay. We design an observer and predictor to stabilize the system. The state is estimated in the time span where the observation is available, and also predicted in the time interval where the observation is not available. It is shown that the estimated state feedback stabilizes the system exponentially. A numerical simulation is presented to illustrate the effect of the stabilizing controller.     

Path‐Tracking Control of a Riderless Bicycle Via Road Preview and Speed Adaptation

In this study, a genetic‐fuzzy control system is used to control a riderless bicycle where control parameters can adapt to the speed change of the bicycle. The equations of motion are developed for a bicycle with constraints of rolling‐without‐slipping contact condition between the wheels and ground. This controller consists of two loops: the inner is a roll‐angle‐tracking controller which generates steering torque to control the roll angle while guaranteeing the stability, and the outer is a path‐tracking controller which generates the reference roll angle for the inner loop. The inner loop is a sliding‐mode controller (SMC) designed on the basis of a linear model obtained from a system identification process. By defining a stable sliding surface of error dynamics and an appropriate Lyapunov function, the bicycle can reach the roll‐angle reference in a finite time and follow that reference without chattering. The outer loop determines the proper reference roll‐angle by using a fuzzy‐logic controller (FLC) in which previewing and tracking errors are taken into consideration. The robustness of the proposed controller against speed change and external disturbances is verified by simulations.     

Continuous Action Generation of Q‐Learning in Multi‐Agent Cooperation

Conventional Q‐learning requires pre‐defined quantized state space and action space. It is not practical for real robot applications since discrete and finite numbers of action sets cannot precisely identify the variances in the different positions on the same state element on which the robot is located. In this paper, a Q‐Learning composed continuous action generator, called the fuzzy cerebellar model articulation controller (FCMAC) method, is presented to solve the problem. The FCMAC displays continuous action generation by linear combination of the weighting distribution of the state space where the optimal policy of each state is derived from Q‐learning. This provides better resolution of the weighting distribution for the state space where the robot is located. The algorithm not only solves the single‐agent problem but also solves the multi‐agent problem by extension. An experiment is implemented in a task where two robots are taking action independently and both are connected with a straight bar. Their goal is to cooperate with each other to pass through a gate in the middle of a grid environment.     

Sliding Mode Control for Swing‐Up and Stabilization of the Cart‐Pole Underactuated System

This paper uses sliding mode control to accomplish the objectives of swing‐up and stabilization of the cart‐pole underactuated system. The features of underactuated systems prohibit direct application of conventional sliding mode control for fully‐actuated systems. In this paper, we design a novel sliding mode control for the cart‐pole underactuated system so that the control goals can be achieved. In addition, by simply changing the parameters of the sliding surface, we use only one sliding mode control scheme to swing up and to stabilize the cart‐pole system. Using the sliding mode dynamics and the internal dynamics, we show that the proposed sliding mode control can swing up the cart‐pole system from the stable equilibrium and can stabilize the system to the unstable equilibrium. Our simulation results on a cart‐pole system demonstrate the feasibility of the proposed sliding mode control. The proposed control schemes, the stability analysis, and the numerical simulation provide a useful guideline for designing the sliding mode control for the cart‐pole underactuated system.     

Variable Structure Control with Chattering Reduction of a Generalized T‐S Model

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) is presented. The main objective is to obtain an improved performance of highly non‐linear unstable systems. New functions for chattering reduction and error convergence without sacrificing invariant properties are proposed. The main feature of the proposed method is that the switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules; together with the state variables. In this work, a tuning of the well known weighting parameters approach is proposed to optimize local and global approximation and modelling capability of the Takagi‐Sugeno (T‐S) fuzzy model to improve the choice of the performance index and minimize it. The main problem encountered is that the T‐S identification method can not be applied when the membership functions are overlapped by pairs. This in turn restricts the application of the T‐S method because this type of membership function has been widely used in control applications. The approach developed here can be considered as a generalized version of the T‐S method. An inverted pendulum mounted on a cart is chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of the proposed estimation approach in comparison with the original T‐S model. Simulation results indicate the potential, simplicity and generality of the estimation method and the robustness of the chattering reduction algorithm. In this paper, we prove that the proposed estimation algorithm converge the very fast, thereby making it very practical to use. The application of the proposed FLC‐VSC shows that both alleviation of chattering and robust performance are achieved.     

Robust Fault‐Tolerant Control of Launch Vehicle Via GPI Observer and Integral Sliding Mode Control

A robust fault‐tolerant attitude control scheme is proposed for a launch vehicle (LV) in the presence of unknown external disturbances, mismodeling dynamics, actuator faults, and actuator's constraints. The input‐output representation is employed to describe the rotational dynamics of LV rendering three independently decoupled second order single‐input‐single‐output (SISO) systems. In the differential algebraic framework, general proportional integral (GPI) observers are used for the estimations of the states and of the generalized disturbances, which include internal perturbations, external disturbances, and unknown actuator failures. In order to avoid the defects of the conventional sliding surface, a new nonlinear integral sliding manifold is introduced for the robust fault‐tolerant sliding mode controller design. The stability of the GPI observer and that of the closed‐loop system are guaranteed by Lyapunov's indirect and direct methods, respectively. The convincing numerical simulation results demonstrate the proposed control scheme is with high attitude tracking performance in the presence of various disturbances, actuator faults, and actuator constraints.     

A Lyapunov functional approach to robust stability analysis of continuous-time uncertain linear systems in polytopic domains

In this paper, a sufficient linear matrix inequality (LMI) condition is presented for robust stability analysis of continuous-time linear time-invariant (LTI) systems in polytopic domains. The underlying idea behind the proposed approach is to introduce a family of complex functions which map the closed right-hand side of the complex plane into the inside of the closed unit circle centered at the origin. Then, the mapping properties are used to assure that all the eigenvalues of a system are located in the open left-hand side of the complex plane. Examples show the validity of the proposed condition.     

Forward kinematic singularity avoiding design of a Schönflies motion generator by asymmetric attachment of subchains

In most of the previous studies on parallel mechanisms (PMs), architectural design mainly relying on symmetric geometry was investigated without in-depth analysis of its performance. This work demonstrates that such a symmetric geometry of multiple subchains sometimes induces a forward kinematic singularity which degrades the overall kinematic performance of PMs within the desired workspace and claims that an asymmetric attachment of those subchains on a moving platform can effectively resolve such a singularity problem. A 4-Degree-of-Freedom (DOF) PM exhibiting Schönflies motions is examined as an example device. First, its mobility analysis and kinematic modeling via screw theory are conducted. Then a singularity analysis based on Grassmann line geometric conditions is carried out, and the forward kinematic singularities of the mechanism are identified and verified by simulations. Based on these analysis and simulations, a forward kinematic singularity-free design is suggested. To show the high potential of the device in practical applications, its output stiffness and dynamic motion capability are examined. Then a prototype is built and its motions capability is verified through experiments.     

Intelligent digital redesign for nonlinear systems using a guaranteed cost control method

In this paper, a novel intelligent digital redesign (IDR) technique using the guaranteed cost control method is proposed for nonlinear systems which can be represented by a Takagi-Sugeno (T-S) fuzzy model. The IDR technique, which is one of the sampled-data fuzzy controller design methods, guarantees not only the stability condition of the sampled-data closed-loop system with the sampleddata fuzzy controller and the state-matching error is presented. By using the concept of the guaranteed cost control method, sufficient conditions are obtained for both minimization of the state-matching error and stabilization of the sampled-data closed-loop system and derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to verify the effectiveness of the proposed technique.     

Development of a nanofluidic preconcentrator with precise sample positioning and multi-channel preconcentration

A nanofluidic preconcentrator with the capability of rapidly preconcentrating and precisely positioning protein bands in multiple microchannels has been developed for highly sensitive detection of biomolecules. A novel electrical resistive network model is developed to guide the design of the nanofluidic preconcentrator which consists of a PDMS slab bonded with a glass slide. In the prototype design, two microchannels (23 mm long, 25–50 μm wide, and 5–15 μm deep), one preconcentration microchannel and one ground microchannel are connected in the middle via 16 nanochannels (25–50 μm long, 25 μm wide, and 50–80 nm deep). With two sets of optimal voltage settings applied on the opposite ends of the nanofluidic chip, the ion depletion region and electrokinetic trapping were generated to carry out the preconcentration. With the optimal voltage settings (30–30 V) predicted by the model, the ionic current of the nanochannel in our optimized preconcentrator was adjusted to be greater than the threshold value (3.9 nA) needed for the occurrence of the preconcentration, and a preconcentration factor >10⁵ was achieved in 5 min. The sample positioning capability of the preconcentrator was demonstrated by adjusting the applied voltages and moving the preconcentrated protein bands to multiple sites by a distance from several micrometers to several millimeters in the preconcentration channel. The multi-channel preconcentration capability was also demonstrated by preconcentrating two protein bands in two separate microchannels. In this work, the resistive network model was developed and validated to optimize nanofluidic preconcentrators for rapid, high throughput and highly sensitive sensing of low abundance analytes.