Unmeasured States Research Articles

Design and Control of an Aerial Manipulator With Invariant Center of Gravity for Physical Interaction

Abstract The deployment of manipulators enhances the versatility and flexibility of unmanned aerial vehicles (UAVs) in aerial physical interaction tasks but also challenges their designs and controls due to variations in the center of gravity (CoG), moment of inertia, and reaction wrenches. This work presents a novel design of a two-degree-of-freedom dual-tool manipulator with invariant-center-of-gravity (ICoG) property. The ICoG conditions are strictly deduced, and a practical optimization-based parameter tuning method is proposed. A novel adaptive extended state observer (AESO)-based impedance control method is developed with actuator dynamics taken into account. The AESO can estimate and compensate for both the lumped disturbance, including the influences of moment-of-inertia variation and counter torque, and the unmeasurable states for the controller. In addition, a switching adaptive law is proposed to attenuate the peaking phenomenon under high observer gains. The impedance controller is designed using an auxiliary impedance tracking error to overcome the difficulty of the increased system order. The Lyapunov approach is used to evaluate the stability of the entire system. The proposed approach is implemented on a fully actuated hexarotor with a prototype of the ICoG manipulator. Comparative experiments are conducted to validate the effectiveness and advantages of the proposed design and control methods.

Design and analysis of event‐triggered predictive sliding mode control for discrete‐time constrained system

AbstractThis paper presents a new approach for designing an event‐triggered predictive sliding mode control (SMC) for discrete‐time systems subject to constraints. The proposed controller is based on an existing reach‐law‐based SMC, and it formulates an optimization control problem (OCP) to generate predictive control actions that satisfy both state and input constraints. An event‐triggered strategy is introduced to reduce the frequency of OCP solving by taking into account the sliding mode controller and unmeasurable states between sampling instants. The paper also analyzes the recursive feasibility of the proposed controller, which ensures the feasibility of each OCP solution. Numerical simulations and comparison studies are performed to validate the theoretical results. The proposed approach offers an effective way to design event‐triggered predictive sliding mode controllers that reduce the computational burden of OCP solving while guaranteeing the satisfaction of system constraints.

State estimation of a physical system with unknown governing equations

State estimation is concerned with reconciling noisy observations of a physical system with the mathematical model believed to predict its behaviour for the purpose of inferring unmeasurable states and denoising measurable ones1,2. Traditional state-estimation techniques rely on strong assumptions about the form of uncertainty in mathematical models, typically that it manifests as an additive stochastic perturbation or is parametric in nature3. Here we present a reparametrization trick for stochastic variational inference with Markov Gaussian processes that enables an approximate Bayesian approach for state estimation in which the equations governing how the system evolves over time are partially or completely unknown. In contrast to classical state-estimation techniques, our method learns the missing terms in the mathematical model and a state estimate simultaneously from an approximate Bayesian perspective. This development enables the application of state-estimation methods to problems that have so far proved to be beyond reach. Finally, although we focus on state estimation, the advancements to stochastic variational inference made here are applicable to a broader class of problems in machine learning.

Event‐triggered distributed H∞$$ {H}_{\infty } $$ secure control for nonholonomic agents with dead‐zone inputs under attacks on sensors and actuators

SummaryDistributed optimal control has been extensively investigated for nonholonomic mechanical agents (NMA). However, the existing methods have not yet taken into account vulnerabilities caused by malicious attacks on sensors and dead‐zone actuator links. The aim of this paper is therefore to propose a novel control scheme that not only achieves bounded ‐gain consensus performance and rejects dead‐zone disturbance but also mitigates the burden of communication resources and the effects of sensor and actuator attacks. Firstly, to estimate unmeasurable states and the unknown model of the attacks, event‐triggered (ET) observers are designed. Secondly, ET‐augmented control is proposed to transform Euler‐Lagrange dynamics into consensus tracking dynamics, from which the ET‐robust optimal control problem is formulated. Thirdly, the ET‐distributed secure control strategies are approximated synchronously via adaptive dynamic programming (ADP) and multi‐player differential game theory. Finally, a numerical example illustrates, on a networked multi‐robot system, the effectiveness of the proposed method.

Observer based stabilization of linear time delay systems using new augmented LKF

This paper addresses the stabilization problem of linear time-varying delay systems with unmeasurable states. A novel augmented Lyapunov–Krasovskii functional (LKF) is proposed that effectively accounts for the impact of time delays, and an observer based stabilization controller is developed employing linear matrix inequality (LMI) based optimization technique. The utilization of extended reciprocally convex matrix inequality (ERCMI) is employed in this work to establish less conservative stabilization conditions within the framework of linear matrix inequalities (LMIs). By formulating a convex optimization problem, the observer gain and controller gains are determined. Simulation results are used to validate the design, and two numerical examples are considered to prove the usefulness of the proposed method over existing methods.

Self-Healing Control for Wastewater Treatment Process Based on Variable-Gain State Observer

This paper proposes a variable-gain state observer-based sliding mode self-healing control (VSO-based SMSHC) method for a wastewater treatment process (WWTP) with changeable external disturbances and sensor failures. To reconstruct the disturbances and unmeasured system states, a novel VSO is developed, in which the VSO gains are adjusted by following an automatic variable-gain mechanism for adapting to the variation of external disturbances. An adaptive compensation coefficient of failure factor is designed to counteract the failure effects on observation and tracking performance. By utilizing the cubic absolute-value Lyapunov stability criterion, it is shown that system stability and tracking performance of WWTP are guaranteed. Experimental studies are carried out on a standardized platform of WWTP, and the results on dissolved oxygen and nitrate nitrogen regulation indicate that the proposed control strategy can ensure excellent control performance and reduce both failure and disturbance impacts.

Robust disturbances compensation for MIMO linear systems with unmeasured state vector and control delay

Robust disturbances compensation for MIMO linear systems with unmeasured state vector and control delay

Event-Triggered Adaptive Fuzzy Finite-Time Output Feedback Control for Stochastic Nonlinear Systems With Input and Output Constraints

This paper focuses on the problem of designing an adaptive fuzzy event-triggered finite-time output feedback control for stochastic nonlinear systems with input and output constraints. A fuzzy observer is designed to estimate the unmeasured states. The quartic asymmetric time-varying barrier Lyapunov function is established to ensure constraint satisfaction. By utilizing the stochastic theory, finite-time command filtered backstepping method and event-triggered mechanism, a finite-time event-triggered controller is recursively designed, which can not only guarantee finite-time convergent property, but also reduce communication pressure. Meanwhile, the matter of “explosion of complexity” is removed by introducing the finite-time command filter and the effect of filtered errors is offset by constructing error compensation signals. Moreover, an auxiliary system is introduced to handle the input constraint. Finally, the effectiveness of the theoretical results is demonstrated by the simulation example.

Robust output regulation of a class of smart actuators described by a minimum phase LPV dynamics

This paper presents a new control strategy for a class of minimum phase linear parameter-varying (LPV) systems representative of smart material actuators. In position control applications of such devices, one is typically interested in achieving output regulation with an arbitrary exponential decay rate. In principle, this problem can be tackled by assigning an exponential decay rate to the full system state, by means of well-established linear matrix inequalities (LMI) methods. For the class of systems under investigation, however, this approach leads to excessively large controller gains in case the desired decay rate is faster than the open-loop zero dynamics. In addition, the existence of unmeasurable state variables related to the material microstructure makes it not possible to directly implement full state feedback laws which are commonly adopted in LPV theory. To overcome these issues, a new design strategy is proposed. The key idea relies on arbitrarily shaping the output exponential decay rate without requiring fast convergence of the full state vector. This goal is achieved by means of a partial state feedback control law which solely depends on the measurable system states. A LMI algorithm is also developed to systematically address the design of the partial state feedback controller. The method is validated by means of simulations on generic examples, as well as via experiments on a mechatronic positioning system based on a dielectric elastomer membrane. In case the desired output convergence speed is faster than the open-loop zero dynamics, it is shown that the new approach leads to better transient behaviors and significantly smaller controller gains than standard LPV design techniques.

Nonsingular Practical Fixed-Time Adaptive Output Feedback Control of MIMO Nonlinear Systems.

This article studies the nonsingular fixed-time control problem of multiple-input multiple-output (MIMO) nonlinear systems with unmeasured states for the first time. A state observer is designed to solve the problem that system states cannot be measured. Due to the existence of the unknown system nonlinear dynamics, neural networks (NNs) are introduced to approximate them. Then, through the combination of adaptive backstepping recursive technology and adding power integration technology, a nonsingular fixed-time adaptive output feedback control algorithm is proposed, which introduces a filter to avoid the complicated derivation process of the virtual control function. According to the fixed-time Lyapunov stability theory, the practical fixed-time stability of the closed-loop system is proven, which means that all signals of the closed-loop system remain bounded in a fixed time under the proposed algorithm. Finally, the effectiveness of the proposed algorithm is verified by the numerical simulation and practical simulation.

Improved Nonlinear Extended Observer Based Adaptive Fuzzy Output Feedback Control for a Class of Uncertain Nonlinear Systems With Unknown Input Hysteresis

This study focuses on the problem of adaptive fuzzy dynamic surface output feedback control for a class of uncertain nonlinear systems subjected to unknown input hysteresis. A Prandtl–Ishlinskii (PI) model is applied to the uncertain nonlinear system for describing the unknown input hysteresis, making the controller design feasible. In addition, a nonlinear extended state observer (NESO) is designed for simultaneously estimating the unmeasurable states and generalized disturbances, including the nonlinear hysteresis term of the PI model and external disturbances. In addition, a novel nonlinear function is designed to replace the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$fal(\cdot)$</tex-math></inline-formula> function of the general NESO to address a modification that increases the convergence speed. Considering the incorporation of the improved nonlinear extended state observer (INESO), an adaptive output feedback control scheme is proposed based on fuzzy logic system and dynamic surface techniques. A command filter is employed to avoid the “explosion of complexity” problem inherent in the backstepping technique, while compensating the filtering error caused by adopting the filter. The Lyapunov approach is used to demonstrate the stability of the entire closed-loop system. Experiments regarding a piezoelectric micro–positioning stage are conducted, the results of which illustrate that the proposed adaptive fuzzy output feedback control method can guarantee a satisfactory tracking performance.

Neural learning-based dual channel event-triggered deployment control of space tethered system with intermittent output

In this paper, we investigate the dual-channel event-triggered deployment control for the space tethered system with intermittent output. Two different dynamic event-triggered mechanisms are designed to implement the event-based state sampling and the event-based input sampling, in which the data transmission frequencies are reduced at the dual channel, namely sensor-to-controller and controller-to-actuator. Then, the neural network (NN) state observer based on the intermittent output is designed to estimate the unmeasurable state under external disturbance, and the observer-based sliding mode controller is designed. Furthermore, because of the non-periodic sampling of the state signal and the output signal, the closed-loop system is proved via the analysis of the hybrid system, and the Zeno behavior is avoidance under these two event-triggered conditions. Finally, the simulation tests are implemented to verify the effectiveness of the proposed scheme.

Velocity observer-based robust control of piezoelectric compliant motion systems with disturbance and hysteresis estimation

This paper proposes a velocity observer-based robust control methodology for piezoelectric compliant motion systems with both unmeasurable hysteresis states and unknown disturbances. A dynamic asymmetric Bouc–Wen model is introduced to describe hysteresis behaviors of the piezoelectric compliant motion systems, a nonlinear state estimator is constructed to compensate the hysteresis nonlinearities. With the aid of the hysteresis state estimation, a velocity and disturbance observer is designed to simultaneously achieve output feedback control and disturbance rejection. Based on the estimations of the hysteresis state, the velocity, and the disturbance, a novel gain adaptation sliding mode control (SMC) structure is developed to robustly stabilize the tracking error without the requirement of velocity measurements, where the hyperbolic tangent function is employed to avoid the chattering, and the gain of the SMC is captured by an adaptive observer. By means of Lyapunov stability theory, the convergence of the hysteresis state estimation error, the velocity observation error, and the disturbance estimation error is analyzed, and the stability of such a control system is rigorously proved. Finally, the proposed control approach is applied to a piezoelectric compliant motion system without velocity sensors. The parameters of the asymmetric Bouc–Wen model are identified by using practical experimental data from the piezoelectric compliant motion system. Simulation and experimental results based on the identified model are provided to demonstrate the proposed control approach achieves excellent tracking performance with the relative error less than 0.6%. Compared with recently reported control approaches, more than 74.42% improvement on the control accuracy is confirmed in the complicated multifrequency trajectory tracking experiments.

Nonlinear Filter-Based Adaptive Output-Feedback Control for Uncertain Fractional-Order Nonlinear Systems with Unknown External Disturbance

This study is devoted to a nonlinear filter-based adaptive fuzzy output-feedback control scheme for uncertain fractional-order (FO) nonlinear systems with unknown external disturbance. Fuzzy logic systems (FLSs) are applied to estimate unknown nonlinear dynamics, and a new FO fuzzy state observer based on a nonlinear disturbance observer is established for simultaneously estimating the unmeasurable states and mixed disturbance. Then, with the aid of auxiliary functions, a novel FO nonlinear filter is given to approximately replace the virtual control functions, together with the corresponding fractional derivative, which not only erases the inherent complexity explosion problem under the framework of backstepping, but also completely compensates for the effects of the boundary errors induced by the constructed filters compared to the previous FO linear filter method. Under certain assumptions, and in line with the FO stability criterion, the stability of the controlled system is ensured. An FO Chua–Hartley simulation study is presented to verify the validity of the proposed method.

Observer-Based Fixed-Time Adaptive Fuzzy Consensus DSC for Nonlinear Multiagent Systems.

This article studies the output-feedback fixed-time fuzzy consensus control problem for nonlinear multiagent systems (MASs) under the directed communication topologies. Since the controlled systems contain the unmeasurable states and unknown dynamics, the unmeasurable states are reconstructed via linear state observers, and fuzzy logic systems are utilized to identify the unknown internal dynamics. By constructing the integral type Lyapunov function, a fixed-time adaptive fuzzy consensus control scheme is developed by introducing the nonlinear filter technique into the backstepping recursive technique adaptive control algorithm. The presented consensus control method can not only guarantee the controlled system is semi-global practical fixed-time stable (SGPFTS), but also avoid the singular problem in existing backstepping recursive control design methods. Finally, an application of unmanned surface vehicles is provided to verify the effectiveness of the presented fixed-time fuzzy consensus control method.

Finite-Time Adaptive Fuzzy Event-Triggered Output-Feedback Containment Control for Nonlinear Multiagent Systems With Input Saturation

This paper considers the finite-time containment output-feedback control problem for a class of nonlinear multi-agent systems (MASs) with unmeasurable states and input saturation. Fuzzy logic systems (FLSs) and a smooth function are first employed to model unknown agent's subsystems and input saturation, respectively. Then, a novel fuzzy state observer is established via the intermittent output signal. By introducing first-order filter and using the sampled estimating states and triggered output signals, an event-triggered mechanism consisting of the sensor-to-controller and controller-to-actuator is formulated. Consequently, under the framework of the finite-time stability criterion and adaptive backstepping control design technique, a finite-time adaptive fuzzy event-triggered output-feedback containment control design method is proposed and the semiglobal finite-time stability of the controlled system is rigorously proved. Finally, the simulation results are given to confirm the effectiveness of the proposed control scheme.

Optimal Power Flow With State Estimation in the Loop for Distribution Networks

In this article, we propose a framework for running optimal control-estimation synthesis in distribution networks. Our approach combines a primal-dual gradient-based optimal power flow solver with a state estimation feedback loop based on a limited set of sensors for system monitoring, instead of assuming exact knowledge of all states. The estimation algorithm reduces uncertainty on unmeasured grid states based on certain online state measurements and noisy “pseudomeasurements.” We analyze the convergence of the proposed algorithm and quantify the statistical estimation errors based on a weighted least-squares estimator. The numerical results on a 4521-node network demonstrate that this approach can scale to extremely large networks and provide robustness to both large pseudomeasurement variability and inherent sensor measurement noise.

Adaptive output-feedback control for uncertain nonlinear systems with function control coefficients

This article addresses the global adaptive output-feedback state regulation problem for a class of uncertain nonlinear systems with generalized control coefficients. Remarkably, the system under investigation simultaneously possesses function control coefficients, input matching uncertainty, and unknown growth rate, which is essentially different from the closely related existing literature. Such nonlinearities from function control coefficients and uncertainties from unknown growth rate bring great technical difficulties to controller design. A novel dynamic gain is introduced to deal with the extra system nonlinearities from function control coefficients and unknowns from the growth rate. In addition, the extended state observer is developed to reconstruct the unmeasured states of the system. By integrating the dynamic gain and extended state observer, an adaptive output-feedback controller is designed, which ensures that the states of the system globally converge to zero, and the estimation of the input matching uncertainty converges to its actual value. Two simulation examples are given to demonstrate the effectiveness of the proposed method.

Collision-Free Adaptive Fuzzy Formation Control for Stochastic Nonlinear Multiagent Systems

This article considers the collision-free fuzzy output-feedback formation control problem for stochastic nonlinear multiagent systems (MASs) with immeasurable states. The fuzzy state observers are established to estimate the unmeasurable states of MASs, and fuzzy-logic systems (FLSs) are utilized to identify the unknown internal dynamics. The prescribed performance functions (PPFs) are introduced to establish the collision avoidance conditions between the follower agent and its leader agent. Then, a novel collision-free adaptive output-feedback formation controller is constructed by utilizing a suitable error transformation. The presented formation control method can guarantee all the variables of the stochastic nonlinear MASs are bounded in probability and each follower agent and the leader agent are free of collision. Finally, the presented formation control method is applied to the unmanned surface vehicle (USV) systems, and the effectiveness and superiorities are checked by the simulation results and comprehensive comparisons.

Pump-Controlled AGC Micro-Displacement Position Control of Lithium Battery Pole Strip Mill Based on Friction Model

Electrode roll-forming refers to rolling a battery electrode into a preset thickness through the electro-hydraulic servo pump-controlled hydraulic roll gap thickness automatic control system (known to as pump-controlled AGC). Compared with the motor servo system, the friction problem of the electro-hydraulic servo system is more serious and the friction problem of the actuator itself is very prominent. Moreover, low-speed performance is one of its core indicators, the friction phenomenon is the most abundant during the low-speed stage and the impact on the servo system is also the most obvious. Therefore, for high-performance electro-hydraulic servo control, friction compensation is not only unavoidable, but also a very difficult problem. Aiming to influence the friction on the position control of the pump-controlled system of a lithium battery pole strip mill, the rolling mechanism and process procedure under micro-displacement position control based on the friction model were studied and compared from the perspective of considering friction factors, and a friction compensation controller based on the LuGre model was designed. The control precision of a pump-controlled AGC system was improved through combination with an adaptive robust controller. Because of the diversity of unmeasurable states of the system, a dual observer was designed, and the known model of the system was added to the observer. In the final comparative experiment, the steady-state accuracy of the friction adaptive robust compensation controller system based on the LuGre model reached ±0.3 μm, which is superior to the fuzzy IMC compensation and traditional PID control strategies.