Proposed Output Feedback Research Articles

Tracking consensus for uncertain nonlinear multi‐agent systems under cloud‐based event‐triggered coordination

AbstractThis paper considers the cloud‐based event‐triggered coordination problem of uncertain high‐order nonlinear multi‐agent systems. The communication among agents is realized by indirect and asynchronous access to a shared cloud database. A self‐triggered extended state observer (ESO) is first designed to estimate the total uncertainty. Based on the output of the ESO, an event‐triggered controller is proposed. It is proved that under the proposed output feedback controller, the multi‐agent system can track a virtual leader. We also show that Zeno behavior from output sampling or controller update will never happen. Finally, a numerical example and a vehicle platoon example are provided to corroborate the obtained theoretical results.

Memoryless parameter-dependent control strategy of stochastic strict-feedback time delay systems

For a class of stochastic strict-feedback nonlinear systems subject to different time delay states, this paper mainly concerns the problem of global asymptotic stabilization. Two new control strategies that the memoryless parameter-dependent state feedback control and the memoryless parameter-dependent output feedback control are taken into consideration, respectively. By skillfully constructing the Lyapunov-Krasovskii (L-K) functional, taking the proper determined parameter and employing the stochastic nonlinear time delay system (SNTDS) stability theory, the global asymptotic stability of the stochastic closed-loop system can be achieved. The proposed output feedback control scheme is finally utilized for the control design of the one-link manipulator system and two-stage chemical reactor system, which can verify the availability of the control approach.

Output-feedback control of viscous liquid–tank system and its numerical approximation

We solve the output-feedback stabilization problem for a tank with a liquid modeled by the viscous Saint-Venant PDE system. The control input is the acceleration of the tank and a Control Lyapunov Functional methodology is used. The measurements are the tank position and the liquid level at the tank walls. The control scheme is a combination of a state feedback law with functional observers for the tank velocity and the liquid momentum. Four different types of output feedback stabilizers are proposed. A full-order observer and a reduced-order observer are used in order to estimate the tank velocity while the unmeasured liquid momentum is either estimated by using an appropriate scalar filter or is ignored. The reduced order observer differs from the full order observer because it omits the estimation of the measured tank position. Exponential convergence of the closed-loop system to the desired equilibrium point is achieved in each case. An algorithm is provided that guarantees that a robotic arm can move a glass of water to a pre-specified position no matter how full the glass is, without spilling water out of the glass, without residual end point sloshing and without measuring the water momentum and the glass velocity. Finally, the efficiency of the proposed output feedback laws is validated by numerical examples, obtained by using a simple finite-difference numerical scheme. The properties of the proposed, explicit, finite-difference scheme are determined.

Finite-time adaptive fuzzy output tracking of switched nonlinear systems with ISD-ADT

This article is devoted to the initial state-dependent average dwell time (ISD-ADT) based output feedback control issue for switched systems. First, a switched observer is given to estimate the unmeasurable states. Based on the ISD-ADT method and backstepping technique, a novel switching law is established. Second, based on the smooth switch function (SSF), a novel fuzzy adaptive finite-time control algorithm is recursively fabricated, which availably surmounted the singularity hindrance derived from the differentiating virtual control law. Furthermore, the proposed output feedback control approach can steer the tracking error into an arbitrarily small residual set in a finite time. In addition, different switched filters and controllers are introduced to reduce the conservatism and restriction caused by employing the common filter and controller for different subsystems. Ultimately, the theoretical findings are validated through two simulation examples.

State Quantized Output Feedback Control for Nonlinear Systems via Event-Triggered Sampling

The current article proposes a novel output feedback event-triggered control scheme for nonlinear systems considering state quantization. First, we construct a state observer to track the unavailable system states. Second, a dynamic event-triggered and quantized mechanism is constructed to handle the state sampling and quantization. By designing the event-triggered mechanism to sample the system state, and using the quantizer to filtrate the sampled signals, the wasted resources in the data channels can be effectively reduced, and the communication efficiency can be improved. Then, based on the input-to-state stability method, the asymptotic stability is ensured for the closed-loop systems. Moreover, we propose an event-triggered and quantized control scheme for the nonlinear systems with input delay, and the asymptotic stability is ensured using the Lyapunov–Krasovskii functional method. The proposed output feedback event-triggered and quantized mechanisms can guarantee a positive lower bound of the transmission interval times of communication channels, which means that the Zeno behavior is avoided. Finally, a simulation example is presented to verify the feasibility of the proposed control schemes.

A novel observer-based approach for the exponential stabilization of the string PDE with cubic nonlinearities

The main objective of this study is to design an observer-based exponential output feedback controller for a one-dimensional vibrating string PDE with in-domain sources, and both anti-damper and anti-spring parameters and also both cubic velocity and nonlinear displacement at the boundary. Due to in-domain sources, the energy injection, cubic displacement and velocity nonlinearity, the unforced system is unstable and may represent a variety of dynamical behaviors. An exponential state feedback controller is first designed and also the well-posedness and the exponential stability of the closed-loop system is investigated. In addition, a novel exponential state observer is constructed, and then an observer-based exponential output feedback controller is proposed. At the end, the well-posedness and the exponential stability of the corresponding closed-loop system are obtained. The validity of the theoretical results is shown by numerical simulations. • Designing an exponential state feedback controller for a vibrating string with indomain sources, negative spring and damper, and two cubic nonlinearities. • Owing to the both negative spring and damper as well as cubic nonlinearities, the unforced plant is unstable and may cause chaotic oscillation and some other dynamical behaviors. • Presenting a new observer to obtain the exponential estimate of the real system containing indomain sources and cubic nonlinearities. • Designing an observer-based output feedback controller with exponential convergence for the underlying string PDE model. • Confirming the efficiency and validity performance of the proposed output feedback control method by simulation results.

An Output Feedback Controller for a Second-Order System Subject to Asymmetric Output Constraint Based on Lyapunov Function with Unlimited Domain

In this work, a new robust controller is designed for a second-order plant model, considering asymmetric output constraints. The tracking error convergence and output constraint are achieved by using a control law whose output feedback term is user-defined and bounded: it takes on large but finite and user-defined values for tracking error values equal to or higher than the constraint boundary, and it comprises a previously known user-defined function for tracking error values far from the constraint boundary. This is a significant contribution that remedies two important limitations of common output constraint control designs: the infinite control effort for tracking error equal to or higher than the constraint boundary, and the impossibility of using previously known user-defined functions in the output feedback function for tracking error values far from the constraint boundary. As another contribution, the control design is based on the dead-zone Lyapunov function, which facilitates the achievement of convergence to a compact set with user-defined size, avoidance of discontinuous signals in the controller, and robustness to model uncertainty or disturbances. The proposed output feedback term consists of the product between two functions of the tracking error, an increasing function and a sigmoid function, whose exact expressions are user-defined. Finally, the effectiveness of the developed controller is illustrated by the simulation of substrate concentration tracking in a continuous flow stirred bioreactor.

Particle-Swarm-Optimization-Based 2D Output Feedback Robust Constraint Model Predictive Control for Batch Processes

For the input and output constraints and uncertainties in batch processes, a 2D output feedback robust constrained model predictive control (MPC) method is designed by combining iterative learning control (ILC), MPC and output feedback. Firstly, an equivalent 2D-FM closed-loop prediction model is established by combining with the proposed output feedback controller. Then an optimization performance index function with terminal constraint is constructed to study its control optimization. According to the designed optimization performance index and Lyapunov stability theory, the feasible MPC problem is obtained by solving the linear matrix inequalities (LMIs). At the same time, the gain of the new output feedback control law is given to ensure that the performance index reaches the minimum upper bound under the constraints of input and output. In order to solve the manual adjustment problem of some parameters in the performance index function, the particle swarm optimization (PSO) algorithm is introduced, and a better solution is found near the controller by using the search optimization method. Finally, taking the injection molding process as an example and comparing with the existing method without using PSO algorithms, it is proved that the above method is more feasible.

Two-time-scale robust output feedback control for aircraft longitudinal dynamics via sliding mode control and high-gain observer

This paper presents output feedback control for longitudinal dynamics of fixed-wing aircraft using singular perturbation techniques. The longitudinal dynamic model is separated into two timescales. A composite feedback control law based on sliding mode control (SMC) is designed for slow and fast subsystems to track the aerodynamic velocity and flight path angle references. Additionally, two separate high-gain observers (HGO) are designed for the slow and fast subsystems to estimate system states. The proposed technique not only simplifies the design but also is computationally efficient. Simulations are performed in MATLAB/Simulink environment with results demonstrating that the proposed output feedback control method robustly achieves trajectory tracking.

Observer-Based Finite-Time Control for Distributed Path Maneuvering of Underactuated Unmanned Surface Vehicles With Collision Avoidance and Connectivity Preservation

This article addresses the distributed path maneuvering of underactuated unmanned surface vehicles (USVs) with collision avoidance and connectivity preservation. The USVs are guided by the multiple virtual leaders moving along the multiple parameterized paths and only a fraction of USVs have access to the virtual leaders. An observer-based finite-time control method is proposed to achieve a containment formation. Specifically, a finite-time extended state observer is employed to recover the unmeasured linear/angular velocities and estimate the total disturbances consisting of model uncertainties as well as ocean disturbances at first. Then, observer-based finite-time guidance laws using the information of neighbors are designed based on a containment scheme. An artificial potential field is incorporated into the distributed guidance law design to avoid collision and preserve connectivity. Finally, antidisturbance kinetic control laws are devised based on the finite-time convergent observers and nonlinear tracking differentiators. It is proven that all error signals in the closed-loop system are ultimately uniformly bounded, and the distributed path maneuvering formation pattern can be achieved in a finite time when USVs outside the collision avoidance and connectivity preservation region. Simulation results are given to verify the effectiveness of the proposed output feedback control method for the distributed path maneuvering of multiple USVs with position-yaw measurements only.

Output tracking for a radiative density optical communication system with unknown disturbance

This paper deals with boundary tracking problem for a radiative density parabolic equation (RDE) coming from an optical communication system. First, the radiative intensity is modeled by a radiative transfer equation (RTE). The idea of this work is to use the fact that the signal sent by the laser beam is collimated in consideration of the radiative density flux. Therefore, the control problem of the RTE model is transformed into a boundary control for an RDE based on the time-dependent SPN approximation. Then, we investigate a boundary output tracking problem of one dimensional parabolic density equation where the unknown disturbance enters the system from one part of the boundary. By utilizing one side boundary measurement, we construct an extended state observer to estimate the system state and the external disturbance. An output feedback boundary control is then designed using the states of the servo system and observer. It is shown that the closed-loop system and the control are uniformly bounded with output being tracking the reference and the closed-loop is internally exponentially stable. The numerical simulations are presented to illustrate the effectiveness of the proposed output feedback method.

Adaptive trajectory tracking control of a free-flying space manipulator with guaranteed prescribed performance and actuator saturation

In this paper, adaptive control schemes are proposed for the trajectory tracking control of a free-flying space manipulator with guaranteed prescribed performance in the presence of parametric uncertainties, external disturbances, and actuator saturation. Both full-state feedback control and output feedback control are considered. First, a model-based controller is designed by using the barrier Lyapunov function (BLF) to prevent the position tracking errors from exceeding the prescribed performance bounds. Then, a full-state feedback controller is designed by using the radial basis function neural network (RBFNN) to compensate for the lumped uncertainties. Finally, an output feedback controller is designed by using a high-gain observer to estimate the velocity of the space manipulator. Rigorous theoretical analysis for the semi-global uniform ultimate boundedness of the whole closed-loop system is provided. The proposed output feedback controller can guarantee the position and velocity tracking errors converge to the small neighborhoods about zero, while ensuring the position tracking errors within the prescribed performance bounds even without using velocity measurements. To the best of the authors’ knowledge, there are really limited existing controllers can achieve such excellent control performance in the same conditions. Numerical simulations demonstrate the effectiveness and strong robustness of the proposed control schemes.

Active vibration control of axisymmetric membrane through partial pole placement

Abstract This paper deals with the problem of active vibration control for a flexible axisymmetric membrane. This mechanical system is equipped with two piezoelectric circular chips where one of them works as an actuator, whereas the other is used as a sensor. Both are glued on the membrane, one on each side, and centered according to its axis of symmetry. The model of this system is obtained from a finite element modelling, leading to a linear state-space model. The design of the proposed controller is based on delayed proportional actions. We exploit a property called Coexisting Real Roots inducing Dominancy to an assignment of spectral values in an appropriate sector corresponding to a desired damping. The aim of this work is to examine the performances of the proposed output feedback controller in terms of vibration damping of the main observable and controllable vibrating modes.

A delay‐independent output feedback law for discrete‐time linear systems with bounded unknown input delay

AbstractBounded input delay frequently arises in discrete‐time linear systems. The standard predictor feedback design requires the exact knowledge of the delay. Such a requirement on the availability of the delay knowledge poses challenges in the design of robust control laws when only the knowledge of an upper bound of the delay is known. We propose such a design in this article. Based on the delay‐independent truncated predictor state feedback design, an observer‐based output feedback law is constructed that does not contain any explicit information of the delay. For a general, possibly exponentially unstable, discrete‐time linear system, the proposed output feedback law stabilizes the system as long as the delay does not exceed a certain amount. For the special case of systems with all the open‐loop poles on or inside the unit circle, a low gain feedback design is presented. This low gain design allows us to establish that, when all the open‐loop poles of a system are at z = 1 or inside the unit circle, stabilization can be achieved for an arbitrarily large bounded delay as long as the value of the low gain parameter is chosen small enough.

Output feedback control of two-lane traffic congestion

This paper develops output feedback boundary control to mitigate traffic congestion of an unidirectional two-lane freeway segment. The macroscopic traffic dynamics are described by the Aw–Rascle–Zhang (ARZ) model respectively for both the fast and slow lanes. The traffic density and velocity of each of the two lanes are governed by coupled 2 × 2 nonlinear hyperbolic partial differential equations (PDEs). Lane-changing interactions between the two lanes lead to exchanging source terms between the two pairs second-order PDEs. Therefore, we are dealing with 4 × 4 nonlinear coupled hyperbolic PDEs. Based on driver’s preference for the slow and fast lanes, a reference system of lane-specific uniform steady states in congested traffic is chosen. To stabilize traffic densities and velocities of both lanes to the steady states, two distinct variable speed limits (VSLs) are applied at outlet boundary, controlling the traffic velocity of each lane. Using backstepping transformation, we map the coupled heterodirectional hyperbolic PDE system into a cascade target system, in which the traffic oscillations are damped out through actuation of the velocities at the downstream boundary. Two full-state feedback boundary control laws are developed. We also design a collocated boundary observer for state estimation with sensing of the densities at the outlet. Output feedback boundary controllers are obtained by combining the collocated observer and full-state feedback controllers. The finite time convergence to equilibrium is achieved and a performance improvement in fuel consumption, drivers’ comfort and total travel time is demonstrated with the proposed output feedback controllers for some parameter choice, compared with the open-loop system. The proposed output feedback design is also validated for different congested traffic scenarios and compared with one-lane backstepping and PI control designs.

Adaptive Reinforcement Learning Strategy with Sliding Mode Control for Unknown and Disturbed Wheeled Inverted Pendulum

This paper develops a novel adaptive integral sliding-mode control (SMC) technique to improve the tracking performance of a wheeled inverted pendulum (WIP) system, which belongs to a class of continuous time systems with input disturbance and/or unknown parameters. The proposed algorithm is established based on an integrating between the advantage of online adaptive reinforcement learning control and the high robustness of integral sliding-mode control (SMC) law. The main objective is to find a general structure of integral sliding mode control law that can guarantee the system state reaching a sliding surface in finite time. An adaptive/approximate optimal control based on the approximate/adaptive dynamic programming (ADP) is responsible for the asymptotic stability of the closed loop system. Furthermore, the convergence possibility of proposed output feedback optimal control was determined without the convergence of additional state observer. Finally, the theoretical analysis and simulation results validate the performance of the proposed control structure.

Bipartite output synchronization of heterogeneous time-varying multi-agent systems via edge-based adaptive protocols

This paper considers a bipartite output synchronization problem for heterogeneous linear multi-agent systems with time-varying communication networks using an adaptive distributed observer-based control strategy. Based on the relative output information from neighboring agents, a reduced-dimensional distributed observer is proposed to estimate the unavailable state information of each agent. Meanwhile, an edge-based adaptive law is designed for each agent to assign the time-varying interaction weight such that the connectivity of the communication network is preserved. Theoretical analysis is presented for the convergence of the output tracking errors under the proposed output feedback control strategy. Some numerical results are also presented to validate the proposed control strategy.

LMI conditions for output feedback control of switched systems based on a time-varying convex Lyapunov function

This paper proposes novel sufficient conditions expressed in terms of linear matrix inequalities for the dynamical output feedback control design of discrete-time switched linear systems. More specifically, an output-dependent switching function together with a full order switched controller are determined in order to assure exponential stability and a guaranteed H2 performance level. The proposed output feedback conditions have some useful properties: (a) they are based on a time-varying convex Lyapunov function, which contributes to reducing conservatism, (b) the controller parameters are independent of the Lyapunov matrices, which lead to time-invariant controller matrices, and (c) the conditions are expressed in terms of linear matrix inequalities being easier to solve, but not necessarily more conservative than other techniques available in the literature. Two academic examples are used for validation and comparison with other techniques from the literature.

Global output feedback regulation of nonlinear time delay systems subject to sensor measurement faults

SummaryThis article studied the global output feedback regulation problem for a class of uncertain nonlinear time delay systems subject to unknown measurement faults on sensors. Different from the existing works, we consider the unknown time‐varying delays on the system states and relax their conservative condition on nonlinear functions. By introducing two novel time‐varying gains, a new global output feedback regulation algorithm is proposed, which ensures control parameters can be chosen flexibly. The proposed linear‐like controller is independent of the unknown time‐varying delays. Moreover, it has a simple structure, which is convenient for the implementation in practice. Based on the Lyapunov stability theory, it is strictly proved that all signals of the resulting closed‐loop system are globally bounded with the designed controller. Finally, a simulation example is presented to illustrate the effectiveness of the proposed output feedback regulation algorithm.

Boundary output tracking for an Euler–Bernoulli beam equation with unmatched perturbations from a known exosystem

In this paper, we consider boundary output regulation for an Euler–Bernoulli beam equation which can describe typically the flexible arm of robots. The reference signal and disturbance are generated by a finite-dimensional exosystem. The measurements are angular and angular velocity of the right end where the control is imposed. However, the performance output is on the left end which is non-collocated with control, a difficult case in practice where the control takes time to perform its force from the right end to the left. The objective is to design an output feedback controller to regulate the displacement of the left end to track the reference signal. We first design a state feedback regulator to make the performance output track the reference signal exponentially. An observer is then constructed to recover the state, with which, an output feedback regulator is designed by replacing state feedback with its estimation. The closed-loop system is shown to admit a unique bounded solution and the tracking error converges to zero exponentially. Some numerical simulations are presented to illustrate the effectiveness of the proposed output feedback regulator.