Interconnection Term Research Articles

Position and Attitude Tracking Controllers Using Lyapunov Transformations for Quadrotors

In this paper, a novel feedback control strategy for quadrotor trajectory tracking is designed and experimentally tested with proof of exponential stability, using the Lyapunov transformations theory. The controller is derived from an inner-outer loop control structure, namely by considering the position system coupled through an interconnection term with the attitude system. For the design of the position controller, the considered dynamics are worked on the body frame, which is uncommon in the literature, and its synthesis derives from theories such as Pontryagin’s maximum principle, Lyapunov theory, and Linear Quadratic Regulator (LQR), which ensure Input-to-state stability, steady-state optimality, and global exponential stability. The attitude system is based on an error quaternion parameterization via a nonlinear coordinate transformation matrix followed by a state input feedback, rendering the system linear and time-invariant. Under a correct transformation, LQR theory ensures almost exponential stability and steady-state optimality for the overall interconnected closed-loop systems. Experimental and simulation results illustrate the performance of the tracking system onboard a quadrotor.

A COMPARATIVE ANALYSIS WITH THE BLACK BOX MODEL & DSS SYSTEM

This article explores Decision Support Systems (DSS) in emergency management and scrutinizes the mathematical and technological perspectives of DSS. It focuses on how these DSS handle uncertainty, manage resources, and make choices during emergencies. Some features that distinguish them as strong are data analysis as well as coping with ambiguity, while other characteristics include things like real-time monitoring and visualization of data. At the same time, there are certain obstacles to their implementation, such as inadequate data generation or refusal by users. Therefore, instances from real life based on various kinds of disaster-stricken zones are illustrated in this research work. Also, we will find out the interconnection term in Emergency DSS in Uncertainty. It explores the Black Box model and designs the main processes in Emergency DSS in Uncertainty. This work analyzes quantitative adaptation, modeling and optimization, iterative improvement, mathematical formulation, system analysis utilities, and system modeling in dynamic cases.

Design of distributed preview tracking controller for nonlinear interconnected systems with time‐delay

AbstractThe focus of this article is to design a distributed preview tracking controller for a class of nonlinear interconnected systems with time‐delay. By constructing the error systems with the information of previewable reference signal, and defining an performance index, the original preview tracking problem is converted into the control problem of the error system. Based on the relationship between the interconnection matrices and the input matrices, a distributed controller using not only the local state vector information but also the interconnection term information is designed for the error systems. Under this controller, the closed‐loop error system is decoupled. With the help of Lyapunov‐Krasovskii functional, the sufficient conditions, the asymptotic stability of the closed‐loop error system with disturbance attenuation level, are established. The distributed preview tracking controller, which is composed of state feedback, integrator, and preview feedforward, is acquired by integrating the controller of the error system. The proposed preview controller is applied to the chemical reactor recycles system and double‐parallel inverted pendulum system. The simulation verify that this controller is very effective in improving the tracking performance.

Decentralized adaptive tracking control for a class of interconnected nonlinear systems via dynamic high‐gain technique

AbstractIn this article, the problem of decentralized adaptive tracking control for a class of interconnected nonlinear systems is investigated, in which the interconnection term in each subsystem is related to the states of all subsystems. By utilizing the backstepping controller design method and dynamic high‐gain technique, two kinds of decentralized adaptive control schemes are developed. Some dynamic parameters are introduced into the controllers to counteract the effects of interactions among subsystems. Moreover, with the aid of graph theory, it is shown that all signals of the closed‐loop system are bounded. The novelty of the proposed method lies in that the tracking accuracy of each subsystem can be preset without adjusting the controller parameters. Finally, two illustrative examples are presented to demonstrate the efficiency of the proposed schemes.

Task-Space Teleoperation With Time-Delays and Without Velocity Measurements via a Bounded Controller

This letter reports a novel controller for robot teleoperation systems in the task-space. The local and the remote robots are kinematically and dynamically different and they are modeled as Euler-Lagrange agents. We consider the realistic scenario where the robot actuators are not ideal and thus they are prone to saturation. Moreover, velocity measurements are not available and variable time-delays arise in the communications. The human operator and the remote environment are assumed to be passive. The controller is dynamical and it consists of a gravity cancellation plus a plant-controller interconnection term. The controller dynamics is of second-order and damping is injected to ensure convergence. Unit-quaternions are used to obtain a singularity-free representation of the orientation. When the human and the environment forces are zero, then we prove that the pose of both robots converges to a common pose. Experimental results of the proposed scheme are provided to illustrate the controller performance.

Decentralized full-state constrained adaptive tracking control for interconnected time delay systems with input saturation

In this article, the problem of decentralized full-state constrained adaptive tracking control is investigated for interconnected time delay systems with input saturation. The extreme learning machine is applied to approximate the unknown nonlinear function in the design process. By selecting the appropriate Lyapunov–Krasovskii function, the time delay interconnection term could be compensated. A unified barrier function is introduced to ensure that the constraints imposed on all states are not violated. The Nussbaum function is introduced to deal with the problem of input saturation. By applying adaptive backstepping procedures, a novel decentralized full-state constrained adaptive tracking control strategy is proposed for the considered interconnected time delay systems. In terms of Lyapunov stability theory, it is proved that all the signals of the closed-loop systems are semi-global ultimately uniformly bounded and all state variables could be constrained within the time varying asymmetric boundaries. Finally, the effectiveness of the proposed scheme is illustrated by a simulation example of a two-stage chemical reactor.

Optimal model-free fuzzy logic control for autonomous unmanned aerial vehicle

This article deals with the issue of designing a flight tracking controller for an unmanned aerial vehicle type of quadrotor based on an optimal model-free fuzzy logic control approach. The main design objective is to perform an automatic flight trajectory tracking under multiple model uncertainties related to the knowledge of the nonlinear dynamics of the system. The optimal control is also addressed taking into consideration unknown external disturbances. To achieve this goal, we propose a new optimal model-free fuzzy logic–based decentralized control strategy where the influence of the interconnection term between the subsystems is minimized. A model-free controller is firstly designed to achieve the convergence of the tracking error. For this purpose, an adaptive estimator is proposed to ensure the approximation of the nonlinear dynamic functions of the quadrotor. The fuzzy logic compensator is then introduced to deal with the estimation error. Moreover, the optimization problem to select the optimal design parameters of the proposed controller is solved using the bat algorithm. Finally, a numerical validation based on the Parrot drone platform is conducted to demonstrate the effectiveness of the proposed control method with various flying scenarios.

Decentralized Trajectory Tracking Control for Modular and Reconfigurable Robots With Torque Sensor: Adaptive Terminal Sliding Control-Based Approach

The main technical challenge in decentralized control of modular and reconfigurable robots (MRRs) with torque sensor is related to the treatment of interconnection term and friction term. This paper proposed a modified adaptive sliding mode decentralized control strategy for trajectory tracking control of the MRRs. The radial basis function (RBF) neural network is used as an effective learning method to approximate the interconnection term and friction term, eliminating the effect of model uncertainty and reducing the controller gain. In addition, in order to provide faster convergence and higher precision control, the terminal sliding mode algorithm is introduced to the controller design. Based on the Lyapunov method, the stability of the MRRs is proved. Finally, experiments are performed to confirm the effectiveness of the method.

Decentralized reliable guaranteed cost control for large-scale nonlinear systems using actor-critic network

Abstract In this paper, the decentralized reliable guaranteed cost control problem of large-scale nonlinear systems with mismatched interconnection and time-varying actuator fault is investigated. The unknown actuator fault is assumed to be with known upper bounds. Under the case that the interconnection term is unknown and mismatched, the guaranteed cost control problem for a class of large-scale nonlinear systems can be transformed into design an optimal control strategy of the isolated system, which is necessary to solve the HJB (Hamilton–Jacobi–Bellman) equations by using adaptive dynamic programming (ADP) of actor-critic networks. The convergence property of the neural network weights and the stability of the closed-loop system have been strictly proved even if time-varying actuator faults and unknown interconnection coexist. Finally, simulation examples are given to show the effectiveness of the proposed approach.

Distributed Kalman filters with adaptive strategy for linear time‐varying interconnected systems

SummaryWe consider the problem of distributed state estimation over a sensor network in which a set of nodes collaboratively estimates the state of a continuous‐time linear time‐varying system. In particular, our work focuses on the benefits of weight adaptation of the interconnection gains in distributed Kalman filters. To this end, an adaptation strategy is proposed with the adaptive laws derived via a Lyapunov‐redesign approach. The justification for the gain adaptation stems from a desire to adapt the pairwise difference of state estimates as a function of their agreement, thereby enforcing an interconnection‐dependent gain. In the proposed scheme, an adaptive gain for each pairwise difference of the interconnection terms is used in order to address edge‐dependent differences in the state estimates. Accounting for node‐specific differences, a special case of the scheme is also presented, where it uses a single adaptive gain in each node estimate and which uniformly penalizes all pairwise differences of state estimates in the interconnection term. The filter gains can be designed either by standard Kalman filter or Luenberger observer to construct the adaptive distributed Kalman filter or adaptive distributed Luenberger observer. Stability of the schemes has been shown, and it is not restricted by the graph topology and therefore the schemes are applicable to both directed and undirected graphs. The proposed algorithms offer a significant reduction in communication costs associated with information flow by the nodes. Finally, numerical studies are presented to illustrate the performance and effectiveness of the proposed adaptive distributed Kalman filters. Copyright © 2015 John Wiley & Sons, Ltd.

Decentralised control for large-scale sampled-data systems: digital redesign approach

In this paper, digital redesign (DR) techniques are presented for a decentralised controller of large-scale sampled-data systems. To improve the performance of the previous DR technique, the state-matching error is defined and directly minimised by using the state-matching error cost function. Also, the discretisation error of the interconnection term is eliminated through an exact discrete-time design approach. Sufficient conditions of the proposed DR techniques are obtained in the Lyapunov sense and are converted into optimal problems with linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the performance improvement of the proposed techniques.

Adaptive neural network control for a two continuously stirred tank reactor with output constraints

An adaptive control scheme is studied for a class of continuous stirred tank reactors (CSTR). The considered reactors can be viewed as a class of MIMO systems with unknown functions and interconnections as well as the output constraints. These properties of the reactors will lead to a completed task for designing a stable control algorithm. To this end, several unknown functions are approximated based on the neural approximation, a novel recursive design method is used to remove the interconnection term, and Barrier Lyapunov function is introduced to avoid the violation of the output constraints. The stability of the proposed scheme is proved based on the Lyapunov analysis method. A simulation example for continuous stirred tank reactor is illustrated to verify the validity of the algorithm.

Adaptive fuzzy control for a class of unknown nonlinear dynamical systems

In this study, we investigate an adaptive fuzzy controller design for a class of nonlinear multi-input multi-output (MIMO) systems in interconnected form. The systems considered comprise n subsystems and an unknown interconnection term is included in every equation for each subsystem. The interconnection term is a function of all the states from the first to the (n−1)th subsystems. Moreover, the effects of dead-zone models are considered in each subsystem of the systems. These properties of the systems cause the difficulties and add further complexity to the design. In order to overcome these difficulties, we use the following methods: (1) the fuzzy logic systems are employed to approximate the appropriate unknown functions of the systems, (2) a novel backstepping design procedure is constructively designed, and (3) compensative adaptation laws are provided to compensate for the effects of the dead-zone inputs. We show that all the signals in the closed-loop system are bounded and that the outputs converge to a compact set by using the Lyapunov analysis theorem. Simulated examples are presented that validate the effectiveness of the approach.

Neural network control for a class of continuous stirred tank reactor process with dead-zone input

An adaptive control scheme is studied for a class of continuous stirred tank reactors (CSTR) with unknown functions. Because the nonlinear property and the unknown functions are included in the considered reactor, it leads to a completed task for designing the controller. Based on the approximation property of the neural networks, several unknown functions are approximated. The main contribution of this paper is that a more general class of CSTR is controlled. A novel recursive design method is used to remove the interconnection term. It is proven that the proposed algorithm can guarantee that all the signals in the closed-loop system are bounded and the system output can converge to a neighborhood of zero based on the Lyapunov analysis method. A simulation example for continuous stirred tank reactor is illustrated to verify the validity of the algorithm.

Controller design for nonlinear affine systems by control Lyapunov functions

This paper addresses the stabilization problems for nonlinear affine systems. First of all, the explicit feedback controller is developed for a nonlinear multiple-input affine system by assuming that there exists a control Lyapunov function. Next, based upon the homogeneous property, sufficient conditions for the continuity of the derived controller are developed. And then the developed control design methodology is applied to stabilize a class of nonlinear affine cascaded systems. It is shown that under some homogeneous assumptions on control Lyapunov functions and the interconnection term, the cascaded system can be globally stabilized. Finally, some interesting results of finite-time stabilization for nonlinear affine systems are also obtained.

Adaptive neural network control for continuous stirred tank reactor process

In this paper, an adaptive control algorithm is proposed for a two continuous stirred tank reactor (CSTR) with unknown functions based on the approximation property of the neural networks. Because the considered reactor contains the nonlinear property and the unknown functions are included in the subsystem, it is a completed system and is very difficult to be controlled. In order to avoid the difficulties, novel recursive design method is used to remove the interconnection term and special approximated functions are defined to be approximated by using the neural networks. Using the Lyapunov stability analysis method, the proposed algorithm ensures that all the signals in the closed-loop system are bounded and the system output can converge to a neighborhood of zero.

Author's reply to comments on "Decentralized stabilization of interconnected systems with time-varying delays"

This paper is a response to the comments on the paper titled "Decentralized Stabilization of Interconnected Systems With Time-Varying Delays". This response states that it was clearly mentioned that the paper deals with a class of interconnected systems where time-varying delay factors are within the local subsystems and across subsystems as well. As per the standard formulations of large-scale systems, the interconnection term should have been expressed as Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k≠3</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ns</sup> E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">jk</sub> x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> (t - η <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> k) and this silly oversight seemed to create a sort of an overall misunderstanding.

Decentralized adaptive fuzzy sliding mode control for reconfigurable modular manipulators

AbstractA stable decentralized adaptive fuzzy sliding mode control scheme is proposed for reconfigurable modular manipulators to satisfy the concept of modular software. For the development of the decentralized control, the dynamics of reconfigurable modular manipulators is represented as a set of interconnected subsystems. A first‐order Takagi–Sugeno fuzzy logic system is introduced to approximate the unknown dynamics of subsystem by using adaptive algorithm. The effect of interconnection term and fuzzy approximation error is removed by employing an adaptive sliding mode controller. All adaptive algorithms in the subsystem controller are derived from the sense of Lyapunov stability analysis, so that resulting closed‐loop system is stable and the trajectory tracking performance is guaranteed. The simulation results are presented to show the effectiveness of the proposed decentralized control scheme. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Decentralized adaptive fuzzy control of time-delayed interconnected systems with unknown backlash-like hysteresis

The problem of decentralized adaptive fuzzy control for a class of time-delayed interconnected non-linear systems with unknown backlash-like hystersis is discussed. On the basis of the principle of variable structure control (VSC) and by using the fuzzy systems with linear adjustable parameters that are used to approximate plant unknown functions, a novel decentralized adaptive fuzzy control strategy with a supervisory controller is developed. A general method, which is modeled the backlash-like hysteresis, is proposed and removes the assumption that the boundedness of disturbance, and the slope of the backlash-like hystersis are known constants. Furthermore, the interconnection term is supposed to be pth-order polynomial in time-delayed states. In addition, the plant dynamic uncertainty and modeling errors are adaptively compensated by adjusting the parameters and gains on-line for each subsystems. By theoretical analysis, it is shown that the closed-loop fuzzy control systems are globally stable, with tracking error converging to zero. Simulation results demonstrate the effectiveness of the approach.

Control of a cylindrical PVTOL vehicle: global non-linear velocity tracking control considering aerodynamics

In the following paper, a non-linear control law is designed for a three degree-of-freedom “hovering rocket”. The proposed control problem is similar to the classic planar vertical take-off and landing (PVTOL) control problem introduced by Hauser et al. (1992). However, the dynamic model of the “hovering rocket” used for controller design includes a description of vehicle aerodynamics such that the designed controller will enable tracking at velocities where aerodynamics effects are significant. The controller design is based on an innovative extension to the published idea of using feedback to cast the system's closed-loop dynamics into a stable cascade structure; see Sepulchre et al. (1997) and Olfati-Saber (2002). Approximations to the system's aerodynamics are made to enable control design. An innovative control law is proposed that minimizes the norm of the interconnection term between closed-loop subsystems and enables trade-off between horizontal and vertical tracking performance. Global stability of this control law is proven. Simulation results demonstrate aggressive tracking performance, superiority of the improved cascade control design, and robustness of the controller to approximations necessary for controller design.