Observer-based Output Feedback Control Research Articles

Observer-based parametric decoupling controller design for a class of multi-variable non-linear uncertain systems

ABSTRACTThis paper presents a novel decoupling control strategy for Lipschitz multi-variable non-linear uncertain systems. Using the explicit parametric design, an observer-based output feedback controller has been developed with free parameters while the closed-loop system can be further described by transfer function matrix with these free parameters. The coupling effects of the systems would be attenuated if the free parameters are optimised where the performance criterion is given based on the norm of the transfer functions. Moreover, the sufficient conditions of stabilization have been obtained for observer, controller and closed-loop system, respectively. Following the procedure of the presented control strategy, an illustrative numerical example is given to demonstrate the effectiveness of the presented control strategy. In addition, the similar design approach has been discussed for filtering problem which is a potential extension of the presented control strategy.

A Novel Fuzzy Observer-Based Steering Control Approach for Path Tracking in Autonomous Vehicles

In this paper, the problem of steering control is investigated for vehicle path tracking in the presence of parametric uncertainties and nonlinearities. In practice, the vehicle mass varies due to the number of passengers or amount of payload, while the vehicle velocity also changes during normal cruising, which significantly influences vehicle dynamics. Moreover, the vehicle dynamics are strongly nonlinear caused by the tire/road forces under different road surface conditions. With fuzzy modeling method, the original nonlinear path tracking system with parameter variations is first formulated as a T–S fuzzy model with additive norm-bounded uncertainties, and then an approach to the fuzzy observer-based output feedback steering control for vehicle dynamics is proposed under a fuzzy Lyapunov function framework. By employing matrix inequality convexifying techniques, a sufficient condition is developed in the form of linear matrix inequalities such that the closed-loop path tracking error system is asymptotically stable with a guaranteed $\mathcal {H}_{\infty }$ level. Finally, the effectiveness of the proposed fuzzy observer-based output feedback controller is demonstrated in Carsim/Matlab joint simulation environment, via which the advantage of a T–S fuzzy observer-based output controller over the closed-loop driver model embedded in Carsim is also shown with parametric uncertainties and nonlinearities.

Resilient observer-based control for networked nonlinear T–S fuzzy systems with hybrid-triggered scheme

In this paper, the resilient observer-based output feedback controller is designed for a class of networked T–S fuzzy systems under a hybrid-triggered scheme and mismatched membership functions. In order to improve network bandwidth utilization, a hybrid-triggered scheme is introduced between the state observer and the controller, which is based on a switching between periodic sampling and an event-triggered scheme. Considering the inaccurate implementation of the parameters of the observer-based controller, a novel hybrid-triggered T–S fuzzy model is constructed. Sufficient conditions are established for the augmented fuzzy systems by using Lyapunov theory and the linear matrix inequality techniques. Furthermore, the observer-based controller gains are designed in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the usefulness of the proposed method.

Output-Feedback Adaptive Neural Control of a Compliant Differential SMA Actuator

This brief focuses on modeling and neural-network-based control of a novel compliant differential shape memory alloy (SMA) actuator characterized by reduced total stiffness and increased compliance. A fourth-order strict-feedback nonlinear model with an internal dynamics is derived to fully describe the SMA actuator. Due to nonlinearity, parametric uncertainty, and state-measurement difficulty of the SMA actuator, an adaptive observer-based output-feedback adaptive neural control method is developed to rigorously guarantee closed-loop stability. An experimental device is constructed to test the performance of the SMA actuation control system, where load changes and control tasks with various frequencies are considered during experiments. Experimental results have demonstrated effectiveness and superiority of the proposed approach.

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.

Magnetic attitude control of bias momentum spacecraft by bounded linear feedback

This paper addresses the three-axis magnetic attitude control of small spacecraft with momentum bias configuration by bounded linear feedback. Necessary and sufficient conditions are derived to guarantee that the linearized dynamics and kinematics are stable in the Lyapunov sense. Explicit solutions to some Lyapunov equations associated with the considered open-loop system are obtained. Based on the explicit solutions to the Lyapunov equation, both explicit saturated linear state feedback controller and function observer based output feedback controller are designed. Globally asymptotic stability of the closed-loop systems is proved by constructing explicit Lyapunov functions. Simulations show the effectiveness of the proposed approach.

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.

Analytical solutions to the matrix inequalities in the robust control scheme based on implicit Lyapunov function for spacecraft rendezvous on elliptical orbit

In this study, the problem of robust control for spacecraft rendezvous on elliptical orbit, which contains parameter uncertainties and external disturbances, is investigated based on the implicit Lyapunov function method. A state-feedback controller is first designed, and its existence conditions are derived in terms of linear matrix inequalities (LMIs) which should be solved in real time. An analytical solution to these LMIs is provided to greatly reduce the computational burden. On the basis of the state-feedback analysis, an observer-based output-feedback controller is proposed, and it is proved finite-time stable by constructing an analytical solution to the parameterised nonlinear matrix inequalities (NLMIs). The advantage brought by the proposed analytical solution is that whether these NLMIs hold only need to be checked at two points, while in previous researches they were supposed to be checked at infinite points. The effectiveness of the theoretical results is illustrated by simulation examples.

Sampled-data output feedback control based on a new event-triggered control scheme

In this paper, a new event-triggered control (ETC) scheme is proposed to investigate the observer-based output feedback control problems. To reduce the usage of communication resources, the control input is designed as a specific time-varying signal between two consecutive event-triggering instants, which is different from the general ETC methods. For the continuous-time event detection case, it is shown that the obtained lower bound of the minimum inter-event interval is not smaller than the one using the existing method. In addition, a novel discrete-time event detection scheme and the corresponding ETC policy based on the sampling output is proposed. Employing the stability analysis method for the time-delay system, a sufficient condition on the existence of an observer-based controller is presented. Finally, the simulation results are given to show that the proposed ETC scheme is beneficial to further reduce the frequency of the communication between sensors and the control unit.

Local exponential stabilization via boundary feedback controllers for a class of unstable semi-linear parabolic distributed parameter processes

This paper addresses the problem of local exponential stabilization via boundary feedback controllers for a class of nonlinear distributed parameter processes described by a scalar semi-linear parabolic partial differential equation (PDE). Both the domain-averaged measurement form and the boundary measurement form are considered. For the boundary measurement form, the collocated boundary measurement case and the non-collocated boundary measurement case are studied, respectively. For both domain-averaged measurement case and collocated boundary measurement case, a static output feedback controller is constructed. An observer-based output feedback controller is constructed for the non-collocated boundary measurement case. It is shown by the contraction semigroup theory and the Lyapunov’s direct method that the resulting closed-loop system has a unique classical solution and is locally exponentially stable under sufficient conditions given in term of linear matrix inequalities (LMIs). The estimation of domain of attraction is also discussed for the resulting closed-loop system in this paper. Finally, the effectiveness of the proposed control methods is illustrated by a numerical example.

Observer-based output-feedback control of large-scale networked fuzzy systems with two-channel event-triggering

This paper concerns data transmissions for large-scale T–S fuzzy systems with event-triggering control, where each subsystem communicates its information via a two-channel network. We propose an event-triggering scheme in which two event-triggering mechanisms are used to verify the data transmissions. At first, a novel model transformation is presented, where the event-triggered control system is reconstructed as a constant-delay system with extra inputs and outputs. By using a relaxed Lyapunov–Krasovskii functional (LKF) without the requirement of positive definiteness for all Lyapunov matrices, and the scaled small gain (SSG) theorem, the co-design problem of desired observer and controller gains, event-triggering parameters, and the sampling period is resolved in the form of linear matrix inequalities (LMIs). It will be shown that the solution guarantees the stability of closed-loop fuzzy control system and the reductions of data communications in both the sensor-to-controller and controller-to-actuator channels. The proposed method is validated by using a numerical example.

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.

Dynamic Neural Network-Based Output Feedback Tracking Control for Uncertain Nonlinear Systems

A dynamic neural network (DNN) observer-based output feedback controller for uncertain nonlinear systems with bounded disturbances is developed. The DNN-based observer works in conjunction with a dynamic filter for state estimation using only output measurements during online operation. A sliding mode term is included in the DNN structure to robustly account for exogenous disturbances and reconstruction errors. Weight update laws for the DNN, based on estimation errors, tracking errors, and the filter output are developed, which guarantee asymptotic regulation of the state estimation error. A combination of a DNN feedforward term, along with the estimated state feedback and sliding mode terms yield an asymptotic tracking result. The developed output feedback (OFB) method yields asymptotic tracking and asymptotic estimation of unmeasurable states for a class of uncertain nonlinear systems with bounded disturbances. A two-link robot manipulator is used to investigate the performance of the proposed control approach.

Adaptive output-feedback control design with prescribed performance for switched nonlinear systems

In this paper, an output feedback control method with prescribed performance is proposed for single-input and single-output (SISO) switched non-strict-feedback nonlinear systems. It is assumed that nonlinear functions of the concerned systems are unknown, switching signals are unknown and arbitrary, and the states are unmeasured. A linear state observer is designed to estimate the unmeasured states, and an observer-based output feedback control scheme is developed. The key advantages of the proposed control strategy are that virtual control gains of the concerned non-strict-feedback nonlinear systems are not required to be known, and only one tuning parameter is needed. Based on Lyapunov stability theory, it is shown that all the signals in the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by a numerical example.

Reliable Output Feedback Control for T-S Fuzzy Systems With Decentralized Event Triggering Communication and Actuator Failures.

Due to the unavailability of full state variables in many control systems, this paper is concerned with the design of reliable observer-based output feedback controller for a class of network-based Takagi-Sugeno fuzzy systems with actuator failures. In order to better allocate network resources under the case that the sensor nodes are physically distributed, the decentralized event triggering communication scheme is adopted such that each sensor node is capable to determine the transmission of its local measurement information independently. Considering that the implementation of the controller may not be synchronized with the plant trajectories due to asynchronous premise variables with such communication mechanism, a novel piecewise fuzzy observer-based output feedback controller is developed. By applying a piecewise Lyapunov function and some techniques on matrix convexification, an approach to the design of observer and controller gain is derived for the augmented closed-loop system to be asymptotically stable with a guaranteed H∞ performance and reduced transmission frequency. Finally, two examples are given to show the effectiveness of the developed method.

Non-fragile observer-based output feedback control for polytopic uncertain system under distributed model predictive control approach

ABSTRACTIn this paper, a non-fragile observer-based output feedback control problem for the polytopic uncertain system under distributed model predictive control (MPC) approach is discussed. By decomposing the global system into some subsystems, the computation complexity is reduced, so it follows that the online designing time can be saved.Moreover, an observer-based output feedback control algorithm is proposed in the framework of distributed MPC to deal with the difficulties in obtaining the states measurements. In this way, the presented observer-based output-feedback MPC strategy is more flexible and applicable in practice than the traditional state-feedback one. What is more, the non-fragility of the controller has been taken into consideration in favour of increasing the robustness of the polytopic uncertain system. After that, a sufficient stability criterion is presented by using Lyapunov-like functional approach, meanwhile, the corresponding control law and the upper bound of the quadratic cost function are derived by solving an optimisation subject to convex constraints. Finally, some simulation examples are employed to show the effectiveness of the method.

Observer-Based Output Feedback Control for Discrete-Time T-S Fuzzy Systems With Partly Immeasurable Premise Variables

This paper is concerned with the observer-based output feedback control problem for Takagi and Sugeno fuzzy systems with partly immeasurable premise variables. By using measurable premise variables and estimations of immeasurable premise variables of fuzzy models as the premise variables of fuzzy controllers, a new fuzzy control scheme is proposed. Further by constructing a set-theoretic description of fuzzy systems, the equivalence class theory in set theory is applied for designing fuzzy controllers, then the partly measurable premise variables are effectively used in the proposed conditions. In the existing fuzzy control schemes, the fuzzy weight functions are unaccessible on line due to the partly immeasurable premise variables, so that the partly measurable premise variables cannot be directly used, which might introduce some conservatism. Different from the existing results, the new condition can make better use of measurable premise variables via the proposed control scheme. A numerical example is given to illustrate the effectiveness of the proposed method.

Adaptive quantised observer‐based output feedback control for non‐linear systems with input and output quantisation

This study investigates the case of simultaneous input and output quantisation for a class of non-linear output feedback systems subject to uncertain non-linear dynamics and non-zero initial states. An adaptive quantised observer-based output feedback controller is designed to guarantee bounded stability and H∞ performance despite input and output quantisation. In comparison with the existing work, the main contributions of this study are that: (i) an important lemma is proposed to remove the matrix equality constraint used in many existing results, and three new design methods in strict terms of linear matrix inequality techniques are proposed; (ii) this study focuses on eliminating the impact of both input and output quantisation errors. Since the impact of input and output quantisation errors cannot be fully eliminated, the estimation error is proved to be ultimately bounded and to converge to a residual set; and (iii) an adaptive compensation term is constructed to compensate for the time-variant effects caused by non-linear dynamics and uncertain parameter vectors. Finally, two numerical examples are given to show the efficacy and advantages of the proposed methods.

Adaptive Fuzzy Output Feedback Control for Switched Nonstrict-Feedback Nonlinear Systems With Input Nonlinearities

This paper studies adaptive fuzzy output feedback tracking control problem for nonstrict-feedback switched nonlinear systems. The switched systems under consideration contain unknown nonlinearities, unmeasured states, and unknown deadzones. Fuzzy logic systems are utilized to approximate the unknown nonlinearities, and a switched fuzzy state observer is designed, and thus, the immeasurable states are estimated via it. In the framework of observer-based output feedback control, and by using the certainty equivalence deadzone inverse, a novel adaptive fuzzy output feedback control design method with the parameters adaptation laws is developed. The stability of the closed-loop system and the convergence of the tracking error are proved based on Lyapunov function and the average dwell-time methods. Two simulation examples are provided to check the effectiveness of the proposed approach.

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.