Observer-based Output Feedback Research Articles

Output feedback H∞$$ {H}_{\infty } $$ control of linear systems with infinite distributed input delays

AbstractThis article investigates the output feedback control problem of linear systems with infinite distributed input delays. An observer‐based output feedback (OBOF) controller is proposed via the predictor feedback approach, and a sufficient condition for the existence of the OBOF controller is given in terms of a set of linear matrix inequalities. It is shown that the resulting closed‐loop system is globally exponentially stable with a prescribed performance. The obtained results include some results on the same problem for linear systems with bounded distributed input delays as special cases. Two numerical examples are finally presented to illustrate the effectiveness of the proposed controller.

An adaptive observer based output feedback prescribed‐time control of a class of nonlinear systems with unknown parameters

SummaryIn this paper, an adaptive observer based output feedback prescribed‐time control is designed for a class of nonlinear systems with unknown parameters. According to the characteristics of the nonlinear systems, a novel adaptive observer is first designed. Then by imposing parametric Lyapunov equations, a time‐varying high‐gain observer based output feedback adaptive controller is constructed, by which, it is proven that the states of both the observer and the original system can be driven to zero within any prescribed time. Moreover, the control signal is proven uniformly bounded by a scalar. Two numerical examples are illustrated to verify the effectiveness of the proposed method.

Finite-time semi-global stabilisation of polynomial growth nonlinear systems by linear time-varying feedback

The paper studied the finite-time semi-global stabilisation problems for a class of nonlinear systems with a novel polynomial growth condition. By using some key properties of a class of parametric Lyapunov equations and constructing time-varying Lyapunov-like functions, two time-varying high-gain controllers, where scalar time-varying functions are generated by differential equations, are designed. Both state feedback and observer-based output feedback are considered. It is shown that the proposed methods can achieve finite-time semi-global stabilisation for closed-loop systems and the controls are bound. Two numerical examples verify the effectiveness of the established results.

Optimal Output Consensus of Heterogeneous Linear Multiagent Systems Over Weight-Unbalanced Directed Networks.

This article investigates the distributed optimal output consensus problem of heterogeneous linear multiagent systems over weight-unbalanced directed networks. A novel distributed continuous-time state feedback controller is proposed to steer the outputs of all the agents to converge to the optimal solution of the global cost function. Under the standard condition that the unbalanced digraph is strongly connected and the local cost functions are strongly convex with global Lipschitz gradients, the exponential convergence of the closed-loop multiagent system is established. Then, the proposed state feedback control law is extended to an observer-based output feedback setting. Two examples are finally provided to illustrate the effectiveness of the proposed control schemes.

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.

Observer-based output feedback event-triggered bounded consensus of multi-agent systems under DoS attacks

This paper is concerned with observer-based output feedback event-triggered bounded consensus problem for linear multi-agent systems. The original multi-agent systems are transformed into the switched systems due to DoS attacks, the fast switching is applied to multi-agent systems with DoS attacks, and slow switching is applied to multi-agent systems with no DoS attacks. A novel mode-dependent dynamic event-triggered scheme and a distributed mode-dependent control protocol are proposed by using the relative output, which include some existing results as special cases. It is shown that bounded consensus can be achieved if each agent is both stabilizable and detectable, the appropriate mode-dependent average dwell time and the co-designed feedback matrices are chosen. Two algorithms are also provided to obtain the lower consensus bound. The above results are also extended to undirected topology. Finally, our theoretical results can be verified by two simulation examples.

Cooperative Output Regulation for Linear Multiagent Systems via Distributed Fixed-Time Event-Triggered Control.

In this article, we consider the cooperative output regulation for linear multiagent systems (MASs) via the distributed event-triggered strategy in fixed time. A novel fixed-time event-triggered control protocol is proposed using a dynamic compensator method. It is shown that based on the designed control scheme, the cooperative output regulation problem is addressed in fixed time and the agents in the communication network are subject to intermittent communication with their neighbors. Simultaneously, with the proposed event-triggering mechanism, Zeno behavior can be ruled out by choosing the appropriate parameters. Different from the existing strategies, both the compensator and control law are designed with intermittent communication in fixed time, where the convergence time is independent of any initial conditions. Moreover, for the case that the states are not available, the output regulation problem can further be addressed by the distributed observer-based output feedback controller with the fixed-time event-triggered compensator and event-triggered mechanism. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results.

Observer-Based Output Feedback Tracking Control for Flexible Joint Space Manipulator with Output Constraints

Observer-Based Output Feedback Tracking Control for Flexible Joint Space Manipulator with Output Constraints

Adaptive Observer-Based Output Feedback FTC for Nonlinear Interconnected Vehicle Dynamics with Unknown Actuator Faults

Adaptive Observer-Based Output Feedback FTC for Nonlinear Interconnected Vehicle Dynamics with Unknown Actuator Faults

Robust output regulation for a flexible wing system with unknown output disturbances and references

AbstractFor a flexible wing system, two different exosystems are used to generate unknown references and output disturbances, respectively. The wing system is further perturbed by unknown distributed and boundary disturbances that have the same frequencies to the references and output disturbances. This article proposes two robust control methodologies to address the robust output regulation of the wing. At first, the observer based output feedback controls are designed based on state feedback controls and the following observers: (1) two exosystem observers based on tracking errors; (2) two exosystem observers addressing the uncertainties of output disturbances; (3) the PDE observer estimating the wing states. For the closed‐loop system, the tracking errors are proved to be exponentially convergent toward zero. Let the output disturbances be addressed through two adaption laws, not the observers in the above item (2), which together with other two exosystem observers and the PDE observer, gives observer based adaptive controls. From both cases, we obtain that the exosystem observers based on the tracking errors are necessary for the robust output regulation. By comparison, the former robust controls have a lower dimension and concise structure. Simulation examples have been provided to show the effectiveness of the robust controls.

Output tracking for nonlinear stochastic systems driven by bounded and colored noises

In this paper, we consider practical tracking problem for a class of nonlinear stochastic systems driven by bounded and colored noises by means of active disturbance rejection control approach. The nonlinear extended state observer with homogeneous weighted functions is constructed to estimate in real time the unmeasurable state and the total stochastic disturbance that affects system performance. An observer-based output feedback is designed to guarantee the almost surely practical convergence of the tracking errors. The existence of the global weak solution of the closed-loop system is proved and the tracking convergence accuracy is shown to be higher than that of linear one under the same tuning parameters. Some numerical simulations are carried out to validate the effectiveness of the proposed controller.

Functional and dual observer based prescribed-time control of linear systems by periodic delayed feedback

In this paper the prescribed-time output feedback stabilization of linear systems is addressed using both a functional observer, which includes the reduced-order observer as a special case, and a dual observer. The approach is built upon smooth periodic delayed feedback which is a special case of linear periodic time-varying feedback. In contrast to existing periodic control approaches, the proposed feedback achieves prescribed-time convergence of the state to zero rather than asymptotic convergence. At the same time its synthesis requires solving algebraic equations rather than periodic differential equations. Compared with full-order observer based output feedback, the dimensions of the dynamic equations in the reduced-order observer and dual observer based output feedback are respectively n−p and n−m, where n,m and p are respectively the number of state variables, inputs and outputs, which indicates that the established controllers are less expensive than the full-order observer based controllers in implementations. A numerical example is given to verify the effectiveness of the proposed methods.

Dynamic event-triggered output feedback control for networked Markovian jump systems under hybrid attacks

This paper investigates the dynamic event-triggered control problem for a networked Markovian jump system under hybrid attacks. In the concerned system, both the sensor-controller (S-C) network and the controller-actuator (C-A) network suffer from hybrid attacks, including denial-of-service (DoS) attacks and deception attacks. Two dynamic event-triggers at the controller and the sensor are designed to handle these dual-network hybrid attacks. Moreover, a unified framework is constructed to design an observer-based output feedback controller (OBOFC) which simultaneously considers hybrid attacks and dynamic event-triggering strategies (DETSs). Sufficient conditions to ensure the input-to-state stability (ISS) of the concerned system are derived. Furthermore, a set of linear matrix inequalities (LMIs) are proposed to obtain the desired observer-based feedback control gains and event-triggering parameters. A simulation example is given to further verify the effectiveness of the proposed control and event-triggered schemes.

Attack-free protocols design for leader-following consensus of discrete-time multi-agent systems with multiple input delays

The consensus problem for leader-following multi-agent systems (MASs) characterised by discrete-time multiple input delays linear systems with directed communication topologies is investigated. Under reasonable assumptions, full-order observer-based output feedback protocols are first established by using the relative outputs and inputs of neighbouring agents. In order to overcome the impact of potential network attacks, we truncate the relative inputs of the proposed protocols, namely the exchange of communication information between neighbouring agents is forbidden, so that the closed-loop leader-following MAS is inherently immune to being attacked and achieves consensus. Additionally, the improved attack-free protocols not only allow arbitrarily large yet bounded delays, but also only relative output measurement can be available, which reduces the communication burden and thus are easy to implement in practice. A numerical example is worked out to illustrate the effectiveness of the proposed approach.

On a new method for the state and output feedback exponential stabilization of a cascaded wave PDE-ODE system with nonlinear boundary condition

Abstract This study presents a novel approach for the state and output feedback exponential control of cascaded unstable ODE-wave equations with nonlinear boundary condition. The new approach can be also used to investigate the state and output feedback stabilization of other cascaded ODE-partial differential equation (PDE) systems with nonlinear boundary condition. The interconnection between the ODE and wave PDE with the nonlinear boundary is bi-directional at two points. First, an exponential controller is planned and the well-posed and exponential stability of the closed-loop system is derived. Next, an exponential observer is designed, whereby the exponential stability of the overall error system is shown. Then, an observer-based output feedback control that causes the overall real system to be exponentially stable is built. The existence and exponential stability of the solution to the overall closed-loop system are further deduced. Finally, simulation results are given to verify the effectiveness, feasibility and validity of the proposed technique.

New Results on Nonsynchronous-Observer-Based Output-Feedback Control of Fuzzy-Affine-Model-Based Discrete-Time Nonlinear Systems

This work investigates the non-synchronous observer-based output feedback control of nonlinear systems by T-S fuzzy affine models. In order to estimate the unmeasurable system states and handle the non-synchronization issue of premise variables between the observer/controller and the original system, a new non-synchronous piecewise fuzzy affine observer is firstly synthesized to estimate the unmeasurable system state variables. Via utilizing some elegant matrix inequalities with convexification techniques, new observer-based piecewise output feedback controller design results are proposed within the framework of piecewise quadratic Lyapunov functions. Simulation studies are given to illustrate the validity of the developed approach.

Prescribed-time control of perturbed nonholonomic systems by time-varying feedback

This paper studies the prescribed-time control problem of nonholonomic systems. By using some properties of a class of parametric Lyapunov equations and constructing time-varying Lyapunov-like functions, a time-varying high-gain feedback controller is firstly proposed for the chained nonholonomic system such that the state of the closed-loop system converges to zero at any prescribed time. The advantage of time-varying feedback is revealed by comparison with time-invariant feedback. Then time-varying high-gain feedback controllers for a class of perturbed nonholonomic systems are designed to achieve prescribed time convergence of the states. Both state feedback and observer-based output feedback are considered and the controls are proved to be bounded in all the cases. The effectiveness of the proposed methods are verified by numerical examples.

Reduced-order observer based output feedback control for a Timoshenko beam

This paper proposes observer based controls for a MIMO Timoshenko beam system with disturbances and references from an exosystem, and by further limiting the references and disturbances, also gives reduced-order controls. At first, we propose state feedback controls to guarantee the output regulation problem of a nominal Timoshenko beam system, which is obtained by specially choosing known disturbances and references. This also makes the PDE observer easily designed based on tracking errors only. Then, exosystem observers and their reduced-order forms are proposed in case of different geometric multiplicities and limited conditions of disturbances, references and system uncertainties. This gives observer based robust controls and reduced-order observer based controls. Robust output regulation is proved for the Timoshenko beam under observer based controls. Simulation examples are provided for a Timoshenko beam system with different references and system uncertainties.

Boundary Fuzzy Output Tracking Control of Nonlinear Parabolic Infinite-Dimensional Dynamic Systems: Application to Cooling Process in Hot Strip Mills

This paper utilizes a combination of integral control, fuzzy control, and observer-based output feedback control to deal with the issue of nonlinear output tracking control (OTC) design for nonlinear infinite-dimensional dynamic systems. The system dynamics model is represented by a semi-linear parabolic partial differential equation (PDE) with boundary control and non-collocated boundary measurement. Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is constructed to surmount the OTC design difficulty from the infinite-dimensional nonlinear system dynamics. Subsequently, a fuzzy-observer-based OTC law is proposed via the T-S fuzzy PDE model and the integral control approach. Here, the integral control ensures asymptotic output regulation, and the observer-based output feedback control is employed to conquer the stabilizing control design difficulty caused by the non-collocation between control actuation and measurement. It is shown via the Lyapunov technique with variants of vector-valued Poincaré-Wirtinger's inequality that the suggested fuzzy OTC law drives the measurement output to asymptotically track the desired reference signal and ensures the boundedness of the resulting closed-loop system, provided that a sufficient condition given in the form of linear matrix inequalities is fulfilled. Moreover, the proposed fuzzy-model-based OTC design is also revised for the exponential stabilization case. Finally, extensive simulation results for a numerical example and a cooling process in hot strip mills are provided to examine the effectiveness and merit of the proposed fuzzy OTC scheme.

A New Design of Fuzzy Affine Model-Based Output Feedback Control for Discrete-Time Nonlinear Systems

The observer-based output feedback control problem for nonlinear systems is studied through Takagi-Sugeno fuzzy affine models. A novel piecewise fuzzy affine observer is designed to estimate the unmeasurable state variables. To remove the assumptions in the existing works that the system input matrices and/or output matrices should be common, full rank and uncertainties-free, a new approach is developed for the observer-based piecewise output feedback controller synthesis by making sufficient use of Young's inequality with its variance. Through fuzzy piecewise quadratic Lyapunov functions, improved and less conservative results on the output feedback controller design are obtained in terms of linear matrix inequalities, and the restrictions imposed in the existing results can be relaxed. Simulation studies are provided to confirm the effectiveness and conservatism reduction of the developed method.