Linear Constant Systems Research Articles

Robust Cooperative Control for Heterogeneous Uncertain Nonlinear High-Order Fully Actuated Multiagent Systems.

This research is intended to address a robust cooperative control problem of heterogeneous uncertain nonlinear high-order fully actuated multiagent systems (HUN-HOFAMASs). A nonlinear HOFA system model is used to describe the multiagent systems (MASs) with heterogeneous uncertain nonlinear dynamics, which is called the HUN-HOFAMASs. A predictive terminal sliding-mode control-based robust cooperative control scheme is presented to address this problem. In this scheme, heterogeneous nonlinear dynamics of original system are offset to establish a linear constant HOFA system with the help of full actuation feature. Then, a terminal sliding-mode variable for enhancing the system robustness is introduced to handle the uncertainties. Furthermore, a linear incremental prediction model is developed in a HOFA form by means of a Diophantine equation. According to this model, the multistep terminal sliding-mode predictions are yielded to optimize the robust cooperative control performance and compensate for the network-induced communication constraints in the feedback and forward channels. Based on a linear matrix inequality (LMI) method, a necessary and sufficient criterion is derived to discuss the simultaneous consensus and stability of closed-loop HUN-HOFAMASs. The simulation and comparison results of cooperative flying around of multiple spacecraft system are shown to illustrate the capability and advantage of the presented predictive terminal sliding-mode control for robust cooperative control.

Fully actuated system approach for spacecraft rendezvous system with actuator saturation

This paper explores the application of a fully actuated system (FAS) approach to a spacecraft rendezvous system with actuator saturation. A FAS model for the spacecraft rendezvous system is developed, followed by the design of an extended state observer (ESO) to estimate unmeasurable states and the system's nonlinear terms. The saturation issue is addressed using the convex hull method. By the designed ESO, a state feedback controller for the system is designed using the FAS approach, resulting in a constant linear closed-loop system whose eigenvalues can be arbitrarily assigned. This method simplifies the controller design process and provides a more accurate system model without the linearisation of nonlinear terms, thereby improving control accuracy. Simulation results show the effectiveness and usefulness of the proposed method.

Controllability and control for discrete periodic systems based on fully-actuated system approach

The problem of controllability and control of linear discrete-periodic systems is investigated in this paper. The high-order fully-actuated models for linear discrete periodic time-varying systems are constructed, and a controllability criterion based on fully-actuated system models is proposed. On this basis, stabilization as the fundamental issue is studied and periodic state-feedback control laws are designed via fully-actuated systems approach and parametric design, which converted the original problem into the pole assignment problem for linear constant systems. Finally, a numerical example is given to verify the validity and feasibility of the proposed method.

Tracking control for nonlinear high-order fully actuated system with state constraints: an explicit reference governor approach

This paper studies the tracking control problem of nonlinear high-order fully actuated system subject to state constraints. In order to guarantee the stability of the closed-loop system, a generalised nonlinear proportional differential controller is designed to configure the system into a desired linear constant system. Then, an explicit reference governor for high-order system is introduced to modify the reference signal such that the system state and the state derivatives of certain orders always remain within a prescribed constraint set. Furthermore, we prove that the modified reference will converge to the original reference as much as possible. Therefore, the system state can finally track to the original reference by tracking the modified reference. Two numerical examples demonstrate the validity of the proposed method in this paper.

Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles

This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glide-guided projectile (SGGP), addressing model uncertainties and external disturbances. Based on fixed-time stable theory, a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects, irrespective of initial conditions. By introducing an error integral signal, the dynamics of the SGGP are transformed into two separate second-order fully actuated systems. Subsequently, employing the high-order fully actuated approach and a parametric approach, the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system, ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure. Under the proposed composite control framework, the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method. Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.

A new design of positive functional filters for positive linear time-delay systems

This paper solves the problem of designing positive functional filters for positive linear time-delay systems. In fact, we propose a new positive reduced order filter for positive linear constant state time-delay systems for which the states remain in the nonnegative orthant of the state space, subject to disturbances and unknown inputs. This paper is a first attempt to design positive unknown inputs functional filter for such positive linear delayed systems. The proposed approach is based on the positivity of an augmented system composed of dynamics of both considered system and proposed filter, on the unbiasedness of the estimation error by the resolution of Sylvester equation and also on Lyapunov-Krasovskii stability theory; then conditions for the establishment of such filters are formulated in terms of an optimization problem. An algorithm that summarizes the different steps of the proposed positive functional filter design is given. Finally, numerical example and simulation results are given to illustrate the effectiveness of the proposed design method.

Parametric control for flexible spacecraft attitude maneuver based on disturbance observer

This paper considers the problems of control performance degradation caused by the vibration of flexible accessories and external disturbance during the attitude maneuvering process of flexible spacecraft. A parametric design method for attitude maneuver control (AMC) of flexible spacecraft based on disturbance observer is proposed to improve the anti-interference ability and control accuracy of the control system. Firstly, considering the spacecraft kinematics model for quasi-linear system modeling then design a disturbance observer to solve the external disturbance and vibration generated by the flexible attachment during maneuvering. Further, a controller designed using direct parametric method is proposed that can transform the nonlinear closed-loop system into a second-order linear constant system with the desired characteristic structure and provide all degrees of freedom in the control system design. Finally, numerical examples are given to evaluate the efficacy of the proposed approach.

Analysis of wireless English multimedia communication based on spatial state model equation

Abstract In order to improve the quality of wireless English multimedia communication, according to the characteristics of space multimedia communication environment and communication equipment, this paper proposes a wireless English synchronous QoS control algorithm with low complexity and easy implementation. Using RTCPSRRTP timestamp and NTP absolute timestamp, the wireless English RTP timestamp is mapped to the same absolute reference clock (sender system time) respectively, and the wireless English synchronization detection decision rule is established according to the synchronization QoS performance requirements between wireless English media. Wireless English synchronization control system model at the receiver. At the receiving end, the wireless English stream is the main media stream and the video stream is the slave media stream. The synchronization detection and judgment is implemented in real time before the video frame is played. The synchronization between audio and video media is realized by corresponding synchronization control of wireless English playback. State space model reflects all the information of system dynamic behavior and is a complete description of system behavior. The state space model has a wide range of applications. It is not only suitable for SISO linear constant systems, but also suitable for nonlinear systems, time-varying systems, MIMO systems and stochastic systems. The more outstanding advantage is that the state space model adopts local calculation and uses the state variables inside the system to describe its dynamic characteristics. This property of local calculation not only greatly simplifies the mathematical expression of multi-dimensional system, but also facilitates the analysis and research of the system. The air link rate of the wireless transceiver is set to 512Kbps. The video is encoded based on H.264 and the audio is encoded based on G.729 Speech coding standard. Compared with the wireless English media synchronization control algorithm based on RTP / RTCP, the results show that the RMSE value after adopting the synchronization algorithm in this paper is reduced by 60.09% and 77.69% at most; Compared with the wireless English media synchronization control algorithm based on RTP / RTCP, the synchronization performance of this algorithm is better than the wireless English media synchronization control algorithm. The RMSE value is reduced by 2% on average and 5.2% at most. In addition, the synchronization control algorithm between wireless English media performs synchronization control by losing frames or pausing decoding before video decoding at the receiver, which affects the quality of wireless English video decoding and reconstruction.

Modeling and Calibration for Dithering of MDRLG and Time-Delay of Accelerometer in SINS.

At present, the design and manufacturing technology of mechanically dithered ring laser gyroscope (MDRLG) have matured, the strapdown inertial navigation systems (SINS) with MDRLG have been widely used in military and business scope. When the MDRLG is working, high-frequency dithering is introduced, which will cause the size effect error of the accelerometer. The accelerometer signal has a time delay relative to the system, which will cause the accelerometer time delay error. In this article, in order to solve the above-mentioned problem: (1) we model the size effect error of the mechanically dithering of the MDRLG and perform an error analysis for the size effect error of the mechanically dithering of the MDRLG; (2) we model the time delay error of accelerometer and perform an error analysis for the time delay error of accelerometer; (3) we derive a continuous linear 43-D SINS error model considering the above-mentioned two error parameters and expand the temperature coefficients of accelerometers, inner lever arm error, outer lever arm error parameters to achieve high-precision calibration of SINS. We use the piecewise linear constant system (PWCS) method during the calibration process to prove that all calibration parameters are observable. Finally, the SINS with MDRLG is used in laboratory conditions to test the validity of the calibration method.

High-order fully actuated system approaches: Part X. Basics of discrete-time systems

A basic introduction to high-order fully actuated (HOFA) approaches for discrete-time systems is given. Firstly, it is shown that, different from the continuous-time systems, general dynamical discrete-time systems can be represented by two types of discrete-time HOFA models, namely, the step forward HOFA models and the step backward HOFA models. Secondly, controllers for the step backward HOFA models are designed, which result in constant linear closed-loop systems with arbitrarily assignable eigenstructures. The related problem of feasibility is also discussed. The well-known discrete-time feedback linearisable systems and strict-feedback systems are shown to be equivalent to both the step forward and step backward HOFA models. Finally, a generalised step backward HOFA model containing control vectors of different time instants is proposed and investigated and demonstrated with a type of proposed pseudo feed-forward systems. The contribution in this paper has laid a fundamental basis for discrete-time HOFA approaches. Further analysis and design problems can be naturally established parallel to the continuous-time system case.

Gauss Stylization: Interactive Artistic Mesh Modeling based on Preferred Surface Normals

AbstractExtending the ARAP energy with a term that depends on the face normal, energy minimization becomes an effective stylization tool for shapes represented as meshes. Our approach generalizes the possibilities of Cubic Stylization: the set of preferred normals can be chosen arbitrarily from the Gauss sphere, including semi‐discrete sets to model preference for cylinder‐ or cone‐like shapes. The optimization is designed to retain, similar to ARAP, the constant linear system in the global optimization. This leads to convergence behavior that enables interactive control over the parameters of the optimization. We provide various examples demonstrating the simplicity and versatility of the approach.

High-order fully-actuated system approaches: Part VI. Disturbance attenuation and decoupling

Two types of high-order fully actuated (HOFA) system models subject to external disturbances are firstly introduced. For the type of HOFA systems with deterministic disturbances, the problem of disturbance attenuation via state feedback is treated. While for the type of HOFA systems with dynamical disturbances, the problem of asymptotic disturbance decoupling via output feedback is considered. Utilising the full-actuation feature of the HOFA systems, disturbance attenuation and decoupling controllers for the corresponding systems are conveniently designed such that constant linear closed-loop systems with designed disturbance rejection properties are resulted in. Parametric designs for both controllers are provided, and disturbance attenuation is achieved by establishing a parametric form of the closed-loop transfer function from the disturbance to the output, while the parametric form of the disturbance decoupling controller is derived based on a complete parametric solution to a type of generalised Sylvester equations (GSEs). As a consequence of the parameter approaches, additional performance requirements on the closed-loop systems can be also easily handled. An illustrative example demonstrates the effect of the proposed approach.

Analysis of a model of a natural gas pipeline—a transfer function approach

Abstract A framework for natural gas pipelines is developed in a context similar to the theory of electric transmission lines. The system of semi-linear partial differential equations describing the time-dependent flow of natural gas is linearized around the steady-state flow. Additional approximations lead to a constant coefficient linear system that is equivalent to an electrical circuit that is analytically solvable and admits an ABCD matrix representation of input and output. The sinusoidal steady-state operation of natural gas pipelines is analysed including the distortion of waves. It is shown that the timing of the propagation of phases and other events is accurately represented in the approximation. The quantitative accuracy for flux and gas density of the approximation depending on different operating scenarios and depending on the frequency of the disturbances is documented.

High-order fully actuated system approaches: Part II. Generalized strict-feedback systems

An advantage of a high-order fully-actuated (HOFA) system is that there exists a controller such that a constant linear closed-loop system with an arbitrarily assignable eigenstructure can be obtained. In this paper, a generalised form of the conventional first-order strict-feedback systems (SFSs) is firstly proposed, and a recursive solution is proposed to convert equivalently the generalised SFS into a HOFA model. Then the second- and high-order SFSs are defined and their equivalent HOFA models are also derived. It is further shown that, under certain common conditions, the recursive solutions for converting the generalised SFSs into HOFA models can be rearranged into direct analytical explicit solutions. Such a high-order system approach is more direct and simpler than the first-order system approach since it avoids the process of converting firstly these second- and high-order SFSs into first-order ones for control, and can finally produce a constant linear closed-loop system. Particularly, it is more effective than the well-known method of backstepping since, for the generalised complicated SFSs with more subsystems, the method of backstepping may simply be not applicable due to more serious ‘differential explosion’ problem. Two examples are worked out to demonstrate the effect of the approach.

Parametric control to a type of descriptor quasi-linear high-order systems via output feedback

This study presents a parametric approach to design output feedback for descriptor quasi-linear high-order systems. Utilizing the solution to the high-order generalized Sylvester equations (HGSEs), the more unified parametric form of output feedback is developed. With the proposed approach, the closed-loop is transformed into a linear constant system with an expected eigenstructure. Meanwhile, the regularity of the closed-loop system is maintained easily and effectively. Finally, a synchronization problem of Genesio-Tesi and Coullet systems is proposed to illustrate the effectiveness of the parametric approach.

Application of a novel linearization method to compare the on–off control strategies modeled by piecewise linear systems

In this study, a novel approach for linearization of piecewise linear systems is applied to approximate the root mean square output of a quarter car model with semiactive control. The on–off control strategies, balance logic, skyhook, groundhook, and hybrid are modeled by piecewise linear systems with variable friction. By the proposed method, one can attach, for each output of practical interest, a linear system with the same transmissibility factor. The obtained transmissibility factors are used to approximate the root mean square output of considered semiactive systems using the power spectral density input–output relationships for constant parameter linear systems with stationary random inputs. The method is applied for optimization of hybrid control strategy with respect to a performance index defined in terms of sprung mass acceleration, suspension travel, and dynamic contact force.

Square-Root Approach for Chandrasekhar-Based Maximum Correntropy Kalman Filtering

The first two Chandrasekhar recursions for the maximum correntropy criterion (MCC) Kalman filter (KF) have been recently derived for constant discrete-time linear systems. Their key feature is a mathematical re-formulation of the underlying MCC-based Riccati-type difference equation in terms of the involved error covariance matrix increment. Thus, the Chandrasekhar recursion-based solution is proved to yield a significant reduction of the computational complexity. This letter discusses the existence of a stable square-root solution for Chandrasekhar-type MCC-KF estimators, i.e. their computational reliability issue in a finite precision arithmetic. Two square-root solutions are proposed in terms of covariance quantities, namely within the Cholesky factorization and singular value decomposition.

H∞ control of periodic piecewise polynomial time-varying systems with polynomial Lyapunov function

In this paper, the H∞ control problem of periodic piecewise systems with polynomial time-varying subsystems is addressed. Based on a periodic Lyapunov function with a continuous time-dependent Lyapunov matrix polynomial, the H∞ performance is studied. The result can be easily reduced to the conditions for periodic piecewise systems with constant subsystems or linear time-varying systems based on a common Lyapunov function or a linear time-varying Lyapunov matrix. Moreover, an H∞ controller with time-varying polynomial controller gain is proposed as well, which could be directly solved with the linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the proposed method.

Direct parametric attitude tracking control for generic hypersonic vehicle

ABSTRACTThis paper considers the attitude tracking problem for the generic hypersonic vehicle (GHV). First, the second-order nonlinear GHV attitude model is introduced. Second, by utilising the direct parametric approach, a modified parametric controller composed of the parametric state proportional plus derivative feedback controller and the feedforward controller is proposed. With application of the first part, the closed-loop system is a constant linear system with desired eigenstructures, and the second part is used to ensure the asymptotic tracking property of the outputs of the GHV attitude system. Since the control input of the established GHV attitude model is moment command, an algorithm that transforms the moment commands into the fins deflection command is proposed. Finally, the effectiveness of the proposed parametric controller and transform algorithm is illustrated by the numerical simulation results.

Parametric control to a type of quasi-linear second-order systems via output feedback

ABSTRACTThis paper considers the design of output feedback control for a type of quasi-linear second-order systems with the time-varying coefficient matrices containing the state variables and a time-varying parameter vector. Based on the solution to a type of second-order generalised Sylvester matrix equations, general complete parameterisation of a quasi-linear output feedback controller is established with respect to the state variables, the time-varying parameter vector, the constant closed-loop system and another two groups of arbitrary parameters, and also for the left and right closed-loop eigenvectors matrices. With the proposed parametric output feedback control, the closed-loop system can be transformed into a constant linear system with desired eigenstructure. Finally, simulation results are provided to illustrate the convenience and effectiveness of application in the general spacecraft rendezvous problem.