Output Feedback Controller Design Research Articles

Policy gradient methods for designing dynamic output feedback controllers

This paper proposes model-based and model-free policy gradient methods (PGMs) for designing dynamic output feedback controllers for discrete-time partially observable deterministic systems without noise. To fulfill this objective, we first show that any dynamic output feedback controller design is equivalent to a state-feedback controller design for a newly introduced system whose internal state is a finite-length input–output history (IOH). Next, based on this equivalence, we propose a model-based PGM and show its global linear convergence by proving that the Polyak–Łojasiewicz inequality holds for a reachability-based lossless projection of the IOH dynamics. Moreover, we propose a model-free implementation of the PGM with a sample complexity analysis. Finally, the effectiveness of the model-based and model-free PGMs is investigated through numerical simulations.

Fuzzy control for networked systems with mixed data missing under quantization based event-triggered scheme

This paper presents an innovative event-triggered fuzzy control approach for networked systems operating over unreliable network channels. Traditional complicated modeling and analysis process of network induced issues is replaced by a bran-new logarithmic quantization based event-triggered scheme method. The joint characterization of mixed data missing, arising from the event-triggered mechanism and unreliable network channels, becomes a challenging issue due to disrupted data sequences and variable relations. Consequently, this paper contributes a formulated auxiliary stochastic sequence approach to overcome the difficulty of dynamics modeling. With an formulated event driven controller, the modeling and implementation of the closed-loop systems are constructed and further simplified. Considering the difference and relation between the membership functions of plant and controller, we present a new fuzzy output feedback controller design method to obtain feasible result via uncertainty based method. Finally, we verify the validity of the designed control policy via a simulation example.

Design and Implementation of an L1 Adaptive Proportional Output Feedback Controller

A new approach for output feedback L1 adaptive control based on a proportional adaptation law is presented. The effectiveness of this design is assessed in simulation and validated through real-time testing on an airfoil pitch control wind tunnel experimental rig. Experimental evaluation of the robustness of the controllers, assessed by introducing various disturbances into the control signals, shows that the adaptive control has a better performance compared to PID control, particularly in scenarios with reduced control effectiveness and time-varying disturbances. The experimental results demonstrate the efficacy of the proposed method in practical applications.

Global adaptive event-triggered output feedback control for p-normal feedforward nonlinear systems with uncertain output function

This paper concentrates on the global adaptive event-triggered output feedback controller design for a class of p-normal feedforward nonlinear systems with uncertain output function. Due to the existence of unknown growth rate and uncertain output function, the considered uncertain nonlinear systems contain more uncertainties. To overcome this difficulty, a dynamic gain technique is introduced and an elaborate adaptive law of the gain is designed. Then, a completely time-varying event-based strategy is presented, which can effectively eliminate the effects caused by event-triggered errors. Since the presented event-triggered controller is not differentiable, a new analysis manner is developed to prove that the system is Zeno-free. Meanwhile, the closed-loop system(CLS) states are asymptotically convergent with the proposed strategy. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

A new approach for dynamic output feedback control design of time-delayed nonlinear systems

This paper introduces a full-order dynamic output-feedback (DOF) controller for discrete-time nonlinear systems with time-varying delays represented by Linear Parameter-Varying (LPV) systems. The controller design is carried out by developing delay-dependent Linear Matrix Inequality based conditions using Lyapunov–Krasovskii stability arguments. A notable characteristic of the proposed approach is that the dynamic controller gains are directly obtained, without the need for variable transformations, equality constraints, or iterative algorithms. This feature sets it apart from many existing approaches in the literature and simplifies the design process. Furthermore, the proposed approach guarantees the local asymptotic stability of the origin of the closed-loop system and provides an estimated admissible initial condition region. The correct operation of the system is ensured once the state trajectories initiated within the admissible initial condition region remain enclosed in the validity domain of the LPV model. Numerical examples are provided to illustrate the potential and effectiveness of the proposed conditions.

High-Precision Position Tracking Control with a Hysteresis Observer Based on the Bouc–Wen Model for Smart Material-Actuated Systems

The Bouc–Wen model has been widely adopted to describe hysteresis nonlinearity in many smart material-actuated systems, such as piezoelectric actuators, shape memory alloy actuators, and magnetorheological dampers. For effective control design, it is of interest to estimate the hysteresis state that is not measurable. In this paper, the design of a state observer for the Bouc–Wen model is presented. It is shown that, with sufficiently high observer gains, the state estimate error, including that for the hysteresis state, converges to zero exponentially fast. The utility of the proposed hysteresis observer is illustrated in the design of a high precision output-feedback position tracking controller, and the resulting tracking error is shown to decay exponentially via Lyapunov analysis. Simulation and experimental results show that the proposed hysteresis observer and the high precision position tracking controller outperform a traditional extended state observer and the corresponding tracking controller, respectively.

Design of all feasible output feedback controllers for robust output tracking of Boolean control networks

This paper devotes to the design of all feasible output feedback controllers for the robust output tracking of Boolean control networks with disturbances (DBCNs). First, the output feedback–based robust control invariant set (RCIS) is defined, and a calculation method to find all output feedback–based RCISs of a given set is derived via the truth matrix technique. Second, a class of complete family of robust reachable sets (CFRRSs) is developed; the solvability of robust output tracking problem by output feedback control is verified. Furthermore, a constructive algorithm of all feasible output feedback controllers is presented. Finally, the study of a network about Escherichia coli lactose operon shows the effectiveness of the theoretical results.

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.

Adaptive Output Feedback Control for Uncertain Nonlinear Systems with Unknown Modeling Errors

AbstractIt is well known that unknown modeling errors cannot be avoided in practice. Such unmeasured uncertainties are usually denoted as unknown nonlinear functions that exist in every channel of the system equation. This paper aims to develop an output feedback adaptive control scheme by constructing state estimation filters to address such unknown modeling errors. In the controller design, these uncertainties caused by modeling errors will be accumulated to the last step for compensation. Unknown parameters existing in the upper bound functions of unknown nonlinear functions and system parameters are estimated synchronously based on tuning function approaches. It is shown that the designed output feedback controller can ensure the stability and tracking performance of the closed‐loop system, and the transient performance in terms of a truncated norm is also established.

Synthesizing Negative-Imaginary Systems With Closed-Loop H∞-Performance Via Static Output Feedback Control

Abstract This paper develops an algorithm for synthesizing negative imaginary (NI) systems with a specified H∞-norm bound by exploiting the convex relaxation technique in the static output-feedback (SOF) control design framework. This scheme improves the robustness objective since the present framework can handle both NI and H∞-norm-bounded unstructured uncertainty of the system. The non-strict inequality involved in the NI system description that creates a major difficulty in the SOF control design, can efficiently be tackled by the developed convex relaxation-based iterative algorithm. The advantages of the algorithm are shown using several examples and the results are compared with the existing works.

Pinning Asymptotic Observability of Distributed Boolean Networks.

Asymptotic observability of distributed Boolean networks (DBNs) is studied in this article. Via a parallel extension method, asymptotic observability of the original system is converted to reachability at a fixed point of the extended system. Based on the structure matrix of the extended system, a necessary and sufficient condition is presented for asymptotic observability. Further, for unobservable systems, mode-dependent pinning control is first introduced and applied to achieve asymptotic observability, including the selections of pinning nodes, the design of output feedback controls, and the adding approaches. Then, a set of matrices is defined for the construction of the desired structure matrix. Based on it, a necessary condition is given to guarantee the solvability of the corresponding output feedback controls and the adding approaches. Finally, a numerical example is presented to show the effectiveness of the obtained results.

Amplitude Saturated Nonlinear Output Feedback Controller Design for Underactuated 5-DOF Tower Cranes Without Velocity Measurement

Amplitude Saturated Nonlinear Output Feedback Controller Design for Underactuated 5-DOF Tower Cranes Without Velocity Measurement

Inverse optimally adaptive neural output‐feedback control of stochastic nonlinear systems

SummaryIn this article, for a class of stochastic nonlinear systems with non‐strict feedback, a neural adaptive inverse optimal output feedback control design scheme is presented. First, according to the existing inverse optimal criterion, an auxiliary system is established. On this basis, a novel observer is built to evaluate the unpredictable states. Second, in the control process, neural networks (NNs) are applied to estimate the unknown functions. Based on NNs and the backstepping technology, an adaptive neural inverse optimal output feedback controller is established. It is indicated that the proposed scheme could ensure the semi‐globally uniformly ultimately bounded of the closed‐loop system and also achieve the objective of inverse optimality. Eventually, an example is applied to testify the feasibility of this scheme.

Event-triggered output feedback control design for polynomial fuzzy systems

This paper presents a novel approach to event-triggered output feedback control of polynomial fuzzy systems that exhibit unmeasurable system states. To stabilize the system state, a fuzzy model-based event-triggered control scheme is proposed based on output measurement information. The transmission frequency is modulated using a periodic event-trigger protocol, which is scheduled by resorting to a set of historically released packets to ensure better dynamic performance. The event-triggering condition uses the current samples to determine the next trigger and also takes into account the triggering time-dependent gain parameter, thereby significantly reducing network burden. The proposed approach ensures the existence of both polynomial controller gain and event-triggered parameters by satisfying sufficient conditions based on the sum-of-squares approach and the polynomial fitting approximation algorithm. The addressed system’s stability conditions are solved using MATLAB SOSTOOLS. Three numerical examples, including an invented pendulum model, illustrate the superiority and applicability of the methodology. The main contributions of this work are the introduction of a triggering instant dependent periodic event-triggered output feedback control design, which reduces network traffic and enhances dynamic performance. The approach is validated through numerical examples, which demonstrate its superiority and applicability.

Output feedback and adaptive output feedback control design for input-affine nonlinear systems based on Riemannian metrics

This paper deals with output feedback and adaptive output feedback control design for input-affine nonlinear systems on the basis of Riemannian metrics. Firstly, an observer for the considered class of nonlinear systems is proposed. Then, it is shown that by combining the introduced observer with state-feedback controllers in a suitable way, output tracking can be achieved. Moreover, the obtained results are extended to be used for adaptive output feedback stabilization of uncertain nonlinear systems. The introduced adaptive controller is more general than the existing adaptive output feedback ones because it does not assume any constraint on the structure of the system and the parametric uncertainty. Simulation results are presented to verify the effectiveness of the proposed control methods.

Improved Event-Triggered Dynamic Output Feedback Control for Networked T-S Fuzzy Systems With Actuator Failure and Deception Attacks.

This article addresses the problem of event-triggered dynamic output feedback controller design for networked Takagi-Sugeno (T-S) fuzzy systems subject to actuator failure and deception attacks. In order to save network resources effectively, two event-triggered schemes (ETSs) are introduced to test whether the measurement output and control input are transmitted under network communication. While the ETS brings advantages, it also leads to a mismatch between the premise variables of the system and the controller. To solve this problem, an asynchronous premise reconstruct method is considered, which relaxes the condition of the previous results that the premises of the plant and the controller are synchronous. Furthermore, two crucial factors, including actuator failure and deception attacks, are taken into consideration simultaneously. Then, the mean square asymptotic stability conditions of the resultant augmented system are derived by utilizing the Lyapunov stability theory. Besides, controller gains and event-triggered parameters are co-designed with the help of linear matrix inequality techniques. Finally, a cart-damper-spring system and a nonlinear mass-spring-damper mechanical system are presented to verify the theoretical analysis.

Output Feedback Control Design for Switched Systems with Unmatched Uncertainties Based on the Switched Robust Integral Sliding Mode

This paper proposes an output feedback sliding-mode control design based on a switched robust integral sliding mode for switched systems with unmatched uncertainties. First, the control task based on the observer is given while the system state information cannot be measured directly. Then, the switched robust integral sliding mode is constructed on the space of the estimated state, while the parameters of the switched robust integral sliding mode are selected ensuring that the system state in the sliding mode is robustly and exponentially stable. Linear matrix inequality conditions for the stabilization switching rule and the common Lyapunov function criterion are achieved. Consequently, the corresponding sliding-mode controller is designed based on the state estimation and the switched robust integral sliding mode. Finally, the application simulation results in a one-link manipulator with the load change validate the effectiveness and feasibility.

Asynchronous Event-Triggered Output-Feedback Control of Singular Markov Jump Systems.

This study focused on the asynchronous event-triggered output-feedback controller design problem for discrete-time singular Markov jump systems (MJSs). A hidden Markov model (HMM) was employed to estimate the system mode, which cannot always be ideally detected in practice. Because the full state is also difficult to obtain in practical scenarios, an output-feedback control scheme was used. In addition, an HMM-based event-triggered mechanism was also employed in the design of the controller to reduce the communication burden of the networked system. Sufficient conditions for the stochastic admissibility of a closed-loop singular MJS with a prescribed H∞ performance index were established using the Lyapunov functional technique. Finally, design procedures for an asynchronous event-triggered controller were summarized as a linear-matrix-inequality-based optimization algorithm. Two examples were considered to verify the effectiveness of the asynchronous event-triggered output-feedback controller design method.

Neural networks-based adaptive output-feedback control design for nonlinear systems with dead zone output and uncertain disturbances

This work focuses on the issue of neural networks-based adaptive output-feedback control for nonlinear systems with dead zone output and immeasurable states. Radial basis function neural networks (RBFNN) are utilised to approximate the unknown functions and an input-driven filter is used to estimate the immeasurable states. Nussbaum function is employed to address the issue of uncertain virtual control coefficient, which is brought by the dead zone in the output mechanism, and the presented control scheme requires only one adaptive law, making the structure of the controllers very realistic. Based on the approximation capabilities of NNs and the backstepping method, an adaptive controller is designed. Based on the Lyapunov stability theory, all signals in closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small area near the origin. The effectiveness of the proposed adaptive control method is proved with the help of two examples.

Adaptive optimal output regulation of unknown linear continuous-time systems by dynamic output feedback and value iteration

This paper proposes a value iteration based learning algorithm to solve the optimal output regulation problem for linear continuous-time systems, which aims at achieving disturbance rejection and asymptotic tracking simultaneously. Notably, the state is unmeasurable and the system dynamics is completely unknown, which greatly increases the challenge of solving the output regulation problem. Firstly, we present a dynamic output feedback controller design method by combining the internal model, setting a virtual exo-system, and constructing the augmented internal state without using any knowledge of system. Then, by establishing a novel iterative learning equation which requires no repeated finite window integral operations, an adaptive dynamic programming based learning algorithm with employing value-iteration scheme is proposed to estimate the optimal feedback control gain, which may lead to a reduction of the computational load. The analysis on solvability and convergence shows that the estimated control gain converges to the optimal control gain. Finally, a physical experiment on control of an unmanned quadrotor illustrates the effectiveness of the proposed algorithm.