Unmeasured System States Research Articles

Output feedback control of electro-hydraulic servo actuators with matched and mismatched disturbances rejection

In this paper, two output feedback controllers are proposed for motion control of double-rod electro-hydraulic servo actuators with matched and mismatched disturbances rejection. All of them employ an linear extended state observer (LESO) to achieve real-time estimates of the unmeasured system states and matched disturbance, and a nonlinear disturbance observer (NDO) to estimate the largely unknown mismatched disturbance at the same time. Thus, the disturbances are compensated via their online estimates in a feedforward way when implementing the resulting control algorithms, respectively. Furthermore, a continuously differentiable friction model is employed to compensate the majority of nonlinear friction existing in the system and reduce the burden of the NDO. Specially, one of the proposed control schemes utilizes model-based compensation terms depending on the desired trajectory to be tracked instead of the estimated system states. By doing this, online computation burden can be reduced. The stability of the whole closed-loop system under each control scheme is guaranteed by theoretical analysis. Moreover, the applicability of each control scheme are validated by experiments in different working conditions.

Adaptive hybrid fuzzy output feedback control for fractional-order nonlinear systems with time-varying delays and input saturation

This paper studies the issue of adaptive hybrid fuzzy output feedback control for a class of commensurate fractional-order (FO) nonlinear systems with time-varying delays and input saturation. First, a hybrid fuzzy state observer is designed to estimate the unmeasured system states, where the neuro-fuzzy network systems (NFNSs) are introduced to handle the unknown nonlinear functions. Furthermore, based on DSC technique, a modified FO filter is designed to avoid the issue of the “explosion of complexity” generated by the traditional backstepping control design approach. Moreover, based on the recursive technique and an indirect Lyapunov method, an adaptive controller is constructed to ensure that all the signals of FO closed-loop systems are bounded. Finally, the simulation results are presented to demonstrate the effectiveness of the presented control scheme.

Networked controller and observer design of discrete-time systems with inaccurate model parameters

This paper develops a novel off-policy Q-learning method to find the optimal observer gain and the optimal controller for achieving optimality of network-communication based linear discrete-time systems using only measured data. The primary advantage of this off-policy Q-learning method is that it can work for the linear discrete-time systems with inaccurate system model, unmeasurable system states and network-induced delays. To this end, an optimization problem for networked control systems composed of a plant, a state observer and a Smith predictor is formulated first. The Smith predictor is employed to not only compensate network-induced delays, but also make the separation principle hold, thus the observer and controller can be designed separately. Then, the off-policy Q-learning is implemented for learning the optimal observer gain and the optimal controller combined with the Smith predictor, such that a novel off-policy Q-learning algorithm is derived using only input, output and delayed estimated state of systems, not the inaccurate system matrices. The convergences of the iterative observer gain and the iterative controller gain are rigorously proven. Finally, simulation results are given to verify the effectiveness of the proposed method.

Optimal Output Feedback Control of Nonlinear Partially-Unknown Constrained-Input Systems Using Integral Reinforcement Learning

The problem of output feedback optimal control of the partially-unknown nonlinear systems with constrained-input is investigated in this paper. Firstly, a neural network observer is proposed to estimate the unmeasurable system states. Secondly, synchronous integral reinforcement learning (SIRL) algorithm is used to solve the Hamilton–Jacobi–Bellman (HJB) equation associated with non-quadratic cost function and the optimal controller is obtained without knowing the system drift dynamics. This algorithm is implemented by a critic-actor structure and the novel weight update laws of the neural networks are designed and tuned simultaneously. Moreover, the weight estimation errors of all neural networks are proven uniformly ultimately bounded (UUB), and the stability of the whole closed-loop system is also guaranteed. Finally, two numerical simulation examples support the effectiveness of the proposed methods.

Sampled observer-based adaptive output feedback fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the sampled outputs-based adaptive fault-tolerant control problem for a class of strict-feedback uncertain nonlinear systems, where the nonlinear functions are allowed to include the unmeasured system states. Within the framework, a sampled output observer is introduced to jointly estimate the system states and parameters. By combining the estimated states and the supervisory switching strategy, an adaptive fault-tolerant controller is designed to achieve the desirable tracking performance. By using Lyapunov stability theory, it is proved that all the signals of the closed-loop systems are bounded and the tracking error converges to an adjustable neighbourhood of the origin eventually both in the fault free and faulty cases. Especially, if the outputs are available all the time, the proposed output feedback fault-tolerant control method can ensure the tracking error satisfy the prescribed performance bounds regardless of the faults. Finally, two examples are used to illustrate the effectiveness of the proposed method.

Observer-based adaptive fuzzy funnel control for strict-feedback nonlinear systems with unknown control coefficients

This paper proposes an adaptive fuzzy funnel controller for a class of strict-feedback nonlinear systems with unknown control coefficients. A fuzzy state observer is designed to estimate the unmeasurable system states. An improved funnel error is given and embedded in the procedure of control design. Furthermore, based on the backstepping method, an observer-based adaptive fuzzy funnel controller is constructed, which can guarantee that the output tracking error remains in a pre-set funnel and converges to a prescribed interval in finite time as long as the initial error is in the funnel. All the signals in the closed-loop system are also semi-globally uniformly and ultimately bounded. Simulation results demonstrate the effectiveness of the developed controller.

Data-driven adaptive dynamic programming for partially observable nonzero-sum games via Q-learning method

ABSTRACTThis paper concerns with a class of discrete-time linear nonzero-sum games with the partially observable system state. As is known, the optimal control policy for the nonzero-sum games relies on the full state measurement which is hard to fulfil in partially observable environment. Moreover, to achieve the optimal control, one needs to know the accurate system model. To overcome these deficiencies, this paper develops a data-driven adaptive dynamic programming method via Q-learning method using measurable input/output data without any system knowledge. First, the representation of the unmeasurable inner system state is built using historical input/output data. Then, based on the representation state, a Q-function-based policy iteration approach with convergence analysis is introduced to approximate the optimal control policy iteratively. A neural network (NN)-based actor-critic framework is applied to implement the developed data-driven approach. Finally, two simulation examples are provided to demonstrate the effectiveness of the developed approach.

Security Control of Networked T–S Fuzzy System Under Intermittent DoS Jamming Attack with Event-Based Predictor

In this paper, the security issue of networked T–S fuzzy system (NTFS) is investigated under intermittent DoS jamming attack (I-DoS-JA). This kind attack often causes the hiatus of control input and output feedback in communication channels. In order to compensate the missing data caused by attacks, a model-based predictive control framework is proposed by embedding predictors within the closed-loop NTFS, in which: (1) a T–S fuzzy model is formulated with the consideration of I-DoS-JA. Based on this model, a fuzzy observer is constructed to estimate the unmeasurable system states; (2) the predictors embedded in remote plant and local controller are modeled as a synchronous T–S fuzzy system; and (3) an event-trigger mechanism is integrated in the observer-based predictor, which would take great advantages in saving bandwidth sources. Finally, a nonlinear system is given as an example to substantiate the work of this paper.

Observer-based fuzzy adaptive stabilization of uncertain switched stochastic nonlinear systems with input quantization

This paper proposes an observer-based fuzzy adaptive output feedback control scheme for a class of uncertain single-input and single-output (SISO) nonlinear stochastic systems with quantized input signals and arbitrary switchings. The SISO system under consideration contains completely unknown nonlinear functions, unmeasured system states and quantized input signals quantized by a hysteretic quantizer. By adopting a new nonlinear disposal of the quantized input, the relationship between the control input and the quantized input is established. The hysteretic quantizer that we take can effectively avoid the chattering phenomena. Furthermore, the introduction of a linear observer makes the estimation of the states possible. Based on the universal approximation ability of the fuzzy logic systems (FLSs) and backstepping recursive design with the common stochastic Lyapunov function approach, a quantized output feedback control scheme is constructed, where the dynamic surface control (DSC) is explored to alleviate the computation burden. The proposed control scheme cannot only guarantee the boundedness of signals but also make the output of the system converge to a small neighborhood of the origin. The simulation results are exhibited to demonstrate the validity of the control scheme.

Output feedback model predictive control of hydraulic systems with disturbances compensation

Enhancing the robustness of output feedback control has always been an important issue in hydraulic servo systems. In this paper, an output feedback model predictive controller (MPC) with the integration of an extended state observer (ESO) is proposed for hydraulic systems. The ESO was designed to estimate not only the unmeasured system states but also the disturbances, which will be synthesized into the design of the output prediction equation. Based on the mechanism of receding horizon and repeating optimization of MPC, the output prediction equation will be updated in real time and the future behavior of the system will be accurately predicted since the disturbances are compensated effectively. Hence, the ability of the traditional MPC to suppress disturbances will be improved evidently. The experiment results show that the proposed controller has high-performance nature and strong robustness against various model uncertainties, which verifies the effectiveness of the proposed control strategy.

Full-Order and Reduced-Order Exponential Observers for Discrete-Time Nonlinear Systems With Incremental Quadratic Constraints

This paper considers the observer design problem for a class of discrete-time system whose nonlinear time-varying terms satisfy incremental quadratic constraints. We first construct a circle criterion based full-order observer by injecting output estimation error into the observer nonlinear terms. We also construct a reduced-order observer to estimate the unmeasured system state. The proposed observers guarantee exponential convergence of the state estimation error to zero. The design of the proposed observers is reduced to solving a set of linear matrix inequalities. It is proved that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. Compared to some previous results in the literature, this work considers a larger class of nonlinearities and unifies some related observer designs for discrete-time nonlinear systems. Finally, a numerical example is included to illustrate the effectiveness of the proposed design.

Robust observer based Fault Tolerant Tracking Control for T–S uncertain systems subject to sensor and actuator faults

This paper investigates the sensor and actuator fault (SAF) estimations and the fault tolerant tracking control (FTTC) problem for uncertain systems represented by Takagi–Sugeno (T–S) fuzzy model affected by Unknown Bounded Disturbance (UBD). A robust descriptor adaptive observer based FTTC is firstly designed to simultaneously estimate the unmeasurable system states and SAF vectors and then to track reference trajectories. Sufficient design conditions are developed in terms of Linear Matrix Inequalities (LMIs). The gains of both observer and fault tolerant controller are computed by solving a set of LMI constraints in single step. Robustness against external disturbances is analysed using the H∞ performance index to attenuate its effect on the tracking error for bounded reference inputs. Finally, simulation results are illustrated by considering three types of actuator faults. Moreover, two comparisons are presented to show the mentioned process effectiveness.

Output feedback control for unknown LTI systems driven by unknown periodic disturbances

This paper considers unknown minimum-phase LTI systems with known relative degree and system order. The main aim is to reject the unknown, unmatched sinusoidal disturbances and make the output track a given trajectory with the output feedback. The essence of the control design is composed of disturbance parametrization, K-filter technique and adaptive backstepping procedure. Firstly, the unmeasured system states are represented in terms of filtered input and output signals. Then, the disturbance information in the output signal is parametrized and the problem is converted to an adaptive control problem. After that, the K-filter approach is employed to redefine the system states that enable to use a backstepping technique. An adaptive output feedback controller is designed recursively. It is proven that the equilibrium at the origin is globally uniformly stable and the output signal tracks the reference signal asymptotically. Finally, the effectiveness of the controller is illustrated with a numerical simulation. The robustness of the closed loop system with respect to an additive unmodelled noise is also discussed.

Tube-based explicit model predictive output-feedback controller for collective pitching of wind turbines

Abstract Collective pitch control is the main tool used to regulate the speed and power of wind turbines while operating above their rated wind speeds. The main challenges that face collective pitch control designs are the constraints on the control actions, the unmodeled uncertainties, and the unmeasured system states. A tube – based explicit model-predictive output-feedback controller is designed to control the collective pitch angle. The proposed controller is capable of handling the constraints challenge, reducing the on-line computational time and producing the optimal control sequence. Furthermore, the proposed controller is robust against the unmodeled uncertainties. The challenge of unmeasured system states is eliminated since this is an output feedback controller. The performance of the proposed controller is compared to the performance of a gain-scheduled PI controller which is commonly adopted in industry. Simulation results through application to a typical 5-MW offshore wind turbine are obtained. Further, experimental results with hardware in loop are obtained for a reduced scale wind turbine model to demonstrate the feasibility of the controller for real time applications. Simulation and experimental results show the superiority of the proposed controller over the gain-scheduled PI controller.

Neural networks-based adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances

This paper focuses on the problem of adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances. Radial basis function neural networks (NNs) are employed to approximate the unknown functions and an NN observer is constructed to estimate the unmeasurable system states. Moreover, an auxiliary system is introduced to compensate for the effect of input delay. With the aid of the backstepping technique and Lyapunov stability theorem, an adaptive NN output feedback controller is designed which can guarantee the boundedness of all the signals in the closed-loop systems. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Observer and Adaptive Fuzzy Control Design for Nonlinear Strict-Feedback Systems With Unknown Virtual Control Coefficients

This paper considers the problems of designing a robust observer and developing a backstepping-based adaptive fuzzy control scheme for a class of strict-feedback systems, in which the virtual control coefficients are unknown. By using convex combination method, a robust fuzzy observer has been constructed to estimate the unmeasurable system state variables. Further, an observer-based adaptive fuzzy control scheme has been proposed. During the controller design procedure, fuzzy logic systems are used to model the unknown nonlinear functions, adaptive technique and backstepping are combined to construct the ideal virtual and the real laws. The proposed adaptive fuzzy output feedback controller guarantees that the tracking error converges to a small neighborhood of the origin and all the signals in the adaptive closed-loop system are bounded. Simulation results are provided to demonstrate the effectiveness of the presented approach.

Adaptive Observer‐Based Global Sliding Mode Control for Uncertain Discrete‐Time Nonlinear Systems with Time‐Delays and Input Nonlinearity

AbstractA new discrete‐time adaptive global sliding mode control (SMC) scheme combined with a state observer is proposed for the robust stabilization of uncertain nonlinear systems with mismatched time delays and input nonlinearity. A state observer is developed to estimate the unmeasured system states. By using Lyapunov stability theorem and linear matrix inequality (LMI), the condition for the existence of quasi‐sliding mode is derived and the stability of the overall closed‐loop system is guaranteed. Finally, simulation results are presented to demonstrate the validity of the proposed scheme.

High-Order Sliding Mode Observer Based OER Control for PEM Fuel Cell Air-Feed System

This paper presents oxygen excess ratio (OER) control methods for proton exchange membrane fuel cell systems based on high-order sliding mode (HOSM) observer. The nonlinear and strong coupling characteristics make it difficult for the nonlinear uncertain systems to realize OER closed-loop feedback control. An improved HOSM observer is developed to observe the unmeasurable system states. Even under the interference of model parametric uncertainties, external disturbances, and measurement noises, the HOSM observer can still show fast convergence and good robustness. With the output error injection feature of improved HOSM algorithm, OER can be reconstructed in finite time. The proposed two stage sliding mode based on super twisting algorithm plus feedforward (TS_SM_STW+FF) controller and TS_SM_STW plus fuzzy feedforward (TS_SM_STW+Fuzzy_FF) controller are applied to regulate the estimated OER to track optimal value, respectively. The dynamic performance of OER with proposed methods is validated through the RT-LAB hardware-in-loop platform. The experimental results have shown the feasibility and effectiveness of proposed controllers as compared with conventional strategies.

Boundary output feedback control of a flexible spacecraft system with input constraint

This study is concerned with vibration control of a flexible spacecraft system in the presence of disturbances and input saturation constraint. The dynamics of the spacecraft consisting of a rigid body and two flexible appendages is presented by the coupled partial differential equations and ordinary differential equations. The first boundary state feedback control is adopted when the spacecraft system states can be measured. The second boundary output feedback control is employed when there exists the unmeasurable state in the proposed control law. A high-gain observer is developed to estimate the unmeasurable system state, two auxiliary systems are designed to prevent the presence of input saturation from destroying the system performance and two disturbance observers are established to handle the unknown boundary disturbances. The well-posedness and stability of the spacecraft system are proved. Simulation results are presented to demonstrate the effectiveness of the proposed control schemes.

Adaptive fault estimation and fault‐tolerant tracking control for a class of non‐linear systems with output constraints

This study investigates the problem of adaptive fault estimation and fault-tolerant control for a class of non-linear systems with output constraints. In order to estimate system faults and unmeasurable system states, a novel non-linear fault estimator with adaptive update law is constructed, which can receive better estimation accuracy, and the fault estimation error can be confined into a prescribed region. Moreover, a fault-tolerant tracking controller is designed to compensate the effect of faults based on backstepping techniques. It is proved that all the closed-loop system signals are uniformly ultimately bounded and the system output tracking error converges to a desired neighbourhood of origin. Finally, simulation results are provided to illustrate the efficiency of the proposed approach.