Observer-based Output Feedback Control Design Research Articles

Fixed-Time Observer-Based Output Feedback Control for Nonlinear Systems With Full-State Constraints

This brief investigates the problem of fixed-time state observer-based output feedback control design for nonlinear systems with full-state constraints. First, a fixed-time state observer is constructed to estimate the unknown states, which can accurately estimate the system states within a fixed settling time. Then, by combining the integral barrier Lyapunov function with the backstepping method, the full-state constraints are realized after the fixed time. Meanwhile, the proposed control strategy can directly constrain the states rather than impose constraints on errors, which reduces the conservativeness of the constraint satisfaction condition. The proposed control method ensures that all signals in the closed-loop system are bounded and symmetric state constraints are strictly maintained after the fixed settling time. Finally, simulation results prove the effectiveness of the proposed method.

Positivity and separation principle for observer-based output-feedback disturbance attenuation of uncertain discrete-time fuzzy models with immeasurable premise variables

We propose a robust observer-based output-feedback (OBOF) controller design method for the positive stabilization of discrete-time Takagi–Sugeno (T–S) fuzzy models subject to immeasurable premise variables, parametric uncertainties, and l∞ disturbances. The results of this paper are as follows. First, a new fuzzy OBOF controller structure is used to improve the possibility that the uncertain closed-loop system is positive. Second, the separation principle is demonstrated for the l∞–l∞ disturbance attenuation. Finally, the stability, positivity, and disturbance attenuation of T–S fuzzy closed-loop models are analyzed in the presence of the perturbation caused by the imperfect premise matching by the immeasurable premise variable.

Decentralized Resilient Output-Feedback Control Design for Networked Control Systems Under Denial-of-Service

This article deals with the problem of decentralized resilient observer-based output-feedback control design for networked control systems (NCSs). The proposed scheme considers both network imperfections and security issues. It is assumed that the NCS is suffering from time-varying network-induced delays and time-varying transmission intervals. Moreover, data transmission is performed over a nonsecure network that suffers from a denial-of-service (DoS) attack. The DoS jamming attack has affected the network by the occurrence of consecutive packet dropouts, which result in attack-induced packet dropouts. Based on the fact that packet dropouts caused by DoS attacks naturally do not follow a specific statistical pattern, the attack-induced packet dropouts are modeled as an extension of time-varying intervals with no probability distribution. Sufficient conditions are provided to guarantee the uniformly globally exponential stability of the NCS in the form of linear matrix inequalities. Finally, the effectiveness and applicability of the proposed method are demonstrated by simulation results.

Robust observer-based output-feedback control for epidemic models: Positive fuzzy model and separation principle approach

A feedback-type vaccination and treatment policy for a nonlinear susceptible–infected–recovered (SIR) epidemic model involving uncertainties and disturbances is designed by considering only the number of infected individuals. Specifically, an observer-based output-feedback (OBOF) controller design methodology in the Takagi–Sugeno fuzzy model framework is established. The designed controller exhibits L∞–L∞ disturbance attenuation performance, is robust against norm-bounded parametric uncertainties, and can preserve the closed-loop positivity. The primary contributions of the proposed design condition can be characterized as follows: (i) a novel structure of a fuzzy OBOF controller to ensure the closed-loop positivity; (ii) separate disturbance attenuation performances for the independent design of the controller and observer; (iii) The independent design conditions formulated as convex optimization problems in the presence of parametric uncertainties; (iv) the demonstration of the separation principle in the positive L∞–L∞ disturbance attenuation problem. Results of the case study pertaining to the SIR model demonstrate the efficacy of the proposed methodology.

Observer-Based Multiagent Bipartite Consensus With Deterministic Disturbances and Antagonistic Interactions.

This article studies the multiagent bipartite consensus in networks with deterministic disturbances and antagonistic interactions. An observer-based output-feedback controller design is provided to guarantee the bipartite consensus with deterministic disturbances that satisfy the matching condition. Then, by considering that the bandwidths of communication channels are limited in practical systems, the event-triggered scenario of the proposed output controller for the bipartite consensus is further studied; the node-based broadcast updating fashion is utilized and the Zeno behavior is ruled out. Simulations are also offered to support the theoretical results of protocol designs.

Pole assignment and distributed output feedback control via graph-based decomposition

ABSTRACT A new distributed observer-based output feedback control design with an arbitrary control structure is proposed. Assuming that the linear time-invariant (LTI) system does not have any fixed-modes with respect to the control structure, the pole placement at the desired locations becomes theoretically feasible. In this paper, the structural output feedback controller design is transformed into equivalent problems based on a graph-theoretic approach. Two augmented structures are established and formulated as the solution of a set of binary linear programs (BLP). The first one facilitates the incorporation of the maximum number of edges in the principal bipartite graph and the second one results in the least order of dynamic control for the principal block. Next, the distributed design problem is segmented into two stages: (i) design of a set of static control loops based on convex optimisation, to maximise the controllability/observability radius and (ii) design of the control loops corresponding to the principal bipartite graph based on the reduced-order observer-based control. The performance of the proposed approach is investigated in terms of the pole-placement accuracy, control effort, robustness to perturbations in system dynamics, and effect of controller order reduction.

Observer-based output feedback control design for a fractional ODE and a fractional PDE cascaded system

This paper considers a new bi-directional cascaded system of a fractional ordinary differential equation (FODE) and a fractional partial differential equation (FPDE) which interacts at an intermediate point. The space-dependent coefficients, interaction between the FODE and FPDE at an intermediate point and the presence of fractional calculus makes the FODE–FPDE cascaded system, representative. In this note, we first apply an invertible integral transformation to convert the system into a FODE–FPDE coupled system, as the target system, which is Mittag–Leffler stable. Using the backstepping method and under some assumptions of the space-dependent coefficients, we work out the kernel functions in the transformation and we design a boundary controller. Also, by the invertibility of the transformation, we show the Mittag–Leffler stability of the closed-loop system via the Lyapunov approach. Second, we propose an observer for which we prove that it can well estimate the original cascaded system. Then, we design an output feedback boundary control law and show that the closed-loop system is Mittag–Leffler stable under the designed output feedback control law. Finally, we present some numerical illustrations to show the correctness of the theoretical results.

Observer-based Adaptive Neural Network Output-feedback Control for Nonlinear Strict-feedback Discrete-time Systems

This paper focuses on an observer-based output-feedback controller design for a nonlinear discrete-time system. The major characteristics of this system is that all of the subsystems are in strict-feedback form and all the states of the system are not measurable. An output tracking control problem is firstly considered in this paper. NNs are utilized to approximate unknown functions, while a state observer is designed to approximatethe unvailable states. An adaptive controller is designed on the basis of the backstepping technique. On the basis of the Lyapunov analysis approach, the boundedness of all the signals is provided. The feasibility of the proposed scheme is verified through a simulation example.

Vibration Suppression for Coupled Wave PDEs in Deep-Sea Construction

A deep-sea construction vessel (DCV) is used to install underwater parts of an offshore oil drilling platform at the designated locations on the seafloor. By using extended Hamilton's principle, a nonlinear partial differential equation (PDE) system governing the lateral-longitudinal coupled vibration dynamics of the DCV consisting of a time-varying-length cable with an attached item is derived, and it is linearized at the steady state generating a linear PDE model, which is extended to a more general system including two coupled wave PDEs connected with two interacting ordinary differential equations (ODEs) at the uncontrolled boundaries. Through a preliminary transformation, an equivalent reformulated plant is generated as a 4×4 coupled heterodirectional hyperbolic PDE-ODE system characterized by spatially varying coefficients on a time-varying domain. To stabilize such a system, an observer-based output-feedback control design is proposed, where the measurements are only placed at the actuated boundary of the PDE, namely, at the platform at the sea surface. The exponential stability of the closed-loop system, boundedness and exponential convergence of the control inputs, are proved via Lyapunov analysis. The obtained theoretical result is tested on a nonlinear model with ocean disturbances, even though the design is developed in the absence of such real-world effects.

Anti-collocated observer-based output feedback control of wave equation with cubic velocity nonlinear boundary and Dirichlet control

This study focuses on the observer and observer-based output feedback control design for a one-dimensional wave equation with van der Pol type nonlinear boundary condition and Dirichlet boundary control. The contribution of this work is divided into two parts. Firstly, the anti-collocated backstepping observer design for the nonlinear wave system is investigated, and the well-posedness and the asymptotical stability analysis of the observer error are studied. Secondly, an output feedback observer-based controller is set up by using boundary displacement measurement only to stabilise the nonlinear wave system; also the asymptotical stability of the closed-loop system is shown. The validity of the theoretical results is demonstrated by numerical simulations.

Observer-based output feedback control design for a coupled system of fractional ordinary and reaction–diffusion equations

Abstract In this paper, we investigate the stabilization problem of a cascade of a fractional ordinary differential equation (FODE) and a fractional reaction–diffusion (FRD) equation where the interconnections are of Neumann type. We exploit the partial differential equation backstepping method for designing a controller, which guarantees the Mittag–Leffler stability of the FODE-FRD cascade. Moreover, we propose an observer that is Mittag–Leffler convergent. Also, we propose an output feedback boundary controller, and we prove that the closed-loop FODE-FRD system is Mittag–Leffler stable in the sense of the corresponding norm. Finally, numerical simulations are presented to verify the results.

Adaptive Fuzzy Tracking Control Design for a Class of Uncertain Nonstrict-Feedback Fractional-Order Nonlinear SISO Systems.

In this article, a class of uncertain nonstrict-feedback fractional-order nonlinear single-input-single-output (SISO) systems is investigated. Fuzzy-logic systems (FLSs) are employed to approximate the unknown nonlinear functions and model the uncertain fractional-order nonlinear systems. For the states measurable case, an adaptive fuzzy state-feedback control scheme is developed under the framework of the backstepping technique. For the states unmeasurable case, an observer-based output-feedback control design is proposed by introducing a serial-parallel estimation model and using the dynamic surface control (DSC) technique. Under the drive of the reference signals, the semiglobally uniformly ultimate boundedness for all signals and the tracking errors converging to a small neighborhood of the origin are proved based on the Lyapunov function theory by choosing appropriate design parameters. Two examples with numerical simulations are presented to illustrate the availability of the proposed control approaches.

A New Design of Membership-Function-Dependent Controller for T-S Fuzzy Systems Under Imperfect Premise Matching

This paper examines the problem of membership-function-dependent controller design for a class of discrete-time T-S fuzzy systems. Based on the partition method of premise variable space, the original T-S fuzzy model is equivalently converted into a piecewise-fuzzy system. Then, by employing some staircase functions, the continuous membership functions are approximated by a series of discrete values via which the information of membership functions is brought into the stability analysis to reduce the design conservatism. With piecewise-Lyapunov functions, the approaches to the piecewise-fuzzy state feedback and observer-based output feedback controller design are proposed, respectively, in terms of linear matrix inequalities such that the closed-loop system is asymptotically stable with a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance level. It is shown that the membership functions of the fuzzy model and fuzzy controllers are not necessarily the same, which allows more design flexibility. Finally, two illustrative examples are provided to show the effectiveness of the developed methods.

Observer-based output feedback control of networked control systems with non-uniform sampling and time-varying delay

ABSTRACTThis paper investigates the problem of observer-based output feedback control for networked control systems with non-uniform sampling and time-varying transmission delay. The sampling intervals are assumed to vary within a given interval. The transmission delay belongs to a known interval. A discrete-time model is first established, which contains time-varying delay and norm-bounded uncertainties coming from non-uniform sampling intervals. It is then converted to an interconnection of two subsystems in which the forward channel is delay-free. The scaled small gain theorem is used to derive the stability condition for the closed-loop system. Moreover, the observer-based output feedback controller design method is proposed by utilising a modified cone complementary linearisation algorithm. Finally, numerical examples illustrate the validity and superiority of the proposed method.

Observer-Based Output-Feedback Control Design for a Class of Nonlinear Switched T–S Fuzzy Systems with Actuator Saturation and Time Delay

A state observer-based output-feedback controller is proposed for a class of nonlinear switched T–S fuzzy systems with actuator saturation and time delay in this paper. The proposed control scheme is developed by applying the parallel distributed compensation technique. The nonlinear switched fuzzy systems consist of several switched modes, and each switched mode is linear system. Therefore, by using Lyapunov function theory and average dwell time approach, the sufficient stability conditions are given. The effectiveness and feasibility of the proposed scheme are verified through numerical and practical examples.

Command-Filtered-Based Fuzzy Adaptive Control Design for MIMO-Switched Nonstrict-Feedback Nonlinear Systems

The adaptive fuzzy tracking control design problem for multi-input and multi-output uncertain switched nonstrict-feedback nonlinear systems with arbitrary switchings is investigated in this paper. Fuzzy logic systems are introduced to identify the unknown nonlinear functions (for state measurable case) and model the uncertain nonlinear systems (for state immeasurable case). Both state feedback and observer-based output feedback control design schemes are developed based on combined command filter and adaptive fuzzy control technique. The proposed adaptive fuzzy controllers not only solve the “explosion of complexity” problem existing in conventional backstepping control schemes, but as well as avoid the calculation of partial derivatives. Furthermore, the stability of the fuzzy control systems under arbitrary switchings is proven based on the common Lyapunov function method. Two simulation examples are presented to further demonstrate the effectiveness of the proposed control strategies.

Adaptive Fuzzy Tracking Control Design for SISO Uncertain Nonstrict Feedback Nonlinear Systems

This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems. For the cases of the states measurable and the states immeasurable, fuzzy logic systems are separately adopted to approximate the unknown nonlinear functions or model the uncertain nonlinear systems. In the unified framework of adaptive backstepping control design, both adaptive fuzzy state feedback and observer-based output feedback control design schemes are proposed. The stability of the closed-loop systems is proved by using Lyapunov function theory. The simulation examples are provided to confirm the effectiveness of the proposed control methods.

특이섭동 타카기 수게노 퍼지모델의 관측기기반 - 출력궤환 샘플치제어

This paper addresses an observer-based output-feedback sampled-data controller design problem for nonlinear systems in Takagi-Sugeno (T-S) form including singular perturbations. The design condition is represented in terms of linear matrix inequalities. The separation principle is also investigated.

Adaptive fuzzy backstepping output constraint control of flexible manipulator with actuator saturation

This paper deals with the problem of adaptive fuzzy tracking control for a single-link robotic manipulator coupled to a brushed direct current motor with actuator saturation. Fuzzy logic systems are used to approximate the unknown nonlinear systems. The filtered signals are introduced to eliminate the interference of high-frequency signals. The virtual/actual control inputs are derived from the solutions of a series of dynamical equations. Under the framework of the backstepping control design, an observer-based output feedback control design scheme is proposed. It is proved that the control approach can guarantee that all the signals in the closed-loop system are bounded.

Command filter-based adaptive fuzzy backstepping control for a class of switched nonlinear systems

This paper considers the adaptive fuzzy output feedback control design problem for a class of switched nonlinear systems. The considered switched nonlinear systems contain unknown nonlinearities, the switching signals with average dwell time, and without requiring that state variables are available for measurement. Fuzzy logic systems are used to approximate the unknown nonlinearities, and a fuzzy switched state observer is designed to estimate the immeasurable states. In the framework of observer-based output feedback control design technique, and by introducing a command filter into the backstepping design algorithm, a command filter-based adaptive fuzzy backstepping output feedback control scheme is developed. The stability of the closed-loop system and the convergence of the tracking error are proved via average dwell time and multiple Lyapunov function. A numerical example is provided to illustrate the effectiveness of the proposed approach.