Output Feedback Regulation Research Articles

Periodic event‐triggered output feedback regulation for feedforward nonlinear systems with unknown measurement sensitivity

AbstractThis article addresses the global regulation by periodic event‐triggered output feedback control for a class of feedforward nonlinear systems. Particularly, the considered systems suffer from parameter uncertainties and unknown measurement sensitivity, which entail integrating advanced compensation strategies within the event‐triggered framework. To this end, a time‐varying gain is devised to tackle uncertain nonlinearities as well as the sampling error. Subsequently, a novel periodic event‐triggered output feedback controller is constructed based on the delicate choice of design parameters. Notably, the proposed control scheme is able to avoid the continuous monitoring of the system behavior, and guarantee that all closed‐loop system states are globally bounded and ultimately converge to zero. Finally, a practical example is given to illustrate the main results.

Periodic output regulation for 1-D wave equation subject to non-collocated control

In this paper, we focus on the periodic output regulation for a one-dimensional wave equation where the performance output is non-collocated with the control input. The exosystems considered here are multi-periodic time-varying, capable of generating periodic reference signals and disturbances within the domain and at the boundaries, each with distinct periods. Initially, a backstepping-based state feedback regulator is designed by tackling an ill-posed periodic regulator equation. Subsequently, leveraging an external matrix, we design a novel time-varying observer tailored for the transformed wave equation and the exosystems. An output feedback regulator is then obtained by replacing the states with their estimations. The tracking error is shown to decay exponentially and the closed-loop system is proved to be bounded. Some numerical simulations are presented to validate the results.

Output-Feedback Regulation of Nonlinear Networked Systems With Input Delay Under Event-Triggered and Quantized Mechanism

Output-Feedback Regulation of Nonlinear Networked Systems With Input Delay Under Event-Triggered and Quantized Mechanism

Global output feedback regulation of time-varying nonlinear systems via the dual-gain method

Global output feedback regulation of time-varying nonlinear systems via the dual-gain method

Event‐triggered adaptive output feedback regulation of a chain of integrators with an unknown time‐varying delay in the input

SummaryWe consider a global regulation problem for a chain of integrators with an unknown time‐varying input delay by event‐triggered output feedback control. We show that the considered system is globally regulated by the proposed event‐triggered output feedback controller with a dynamic gain‐scaling factor. Moreover, we show that interexecution times are lower bounded and these lower bounds can be increased with our control method. An example is given for clear illustration.

Cooperative output regulation for networks of hyperbolic systems using adaptive cooperative observers

This paper is concerned with the cooperative output regulation problem for heterogeneous networks of hyperbolic agents. Both the leaders’ output as well as the disturbances are generated by finite-dimensional signal models that are unknown to the followers. An adaptive cooperative reference observer is employed and an infinite-dimensional adaptive cooperative disturbance observer is designed using the backstepping approach to estimate both the states and the signal model parameters. By combining them with a local state feedback regulator, an adaptive cooperative output feedback regulator results. It is shown that the resulting network controlled multi-agent system achieves asymptotic leader–follower output synchronization. The results of the paper are illustrated for a heterogeneous network of three hyperbolic agents in simulations.

Noncollocated robust output regulation of an unstable heat equation with recycle

In this article, we study the output regulation of an unstable heat equation with recycle, where the right boundary heat flux is fed back to the other end through a recycle loop, and the reference signal and the disturbances in all channels are generated by an exosystem with known frequencies. By designing a static feedback with the noncollocated observation and choosing the proper control gain, we stabilize the heat system without disturbances. Then we solve the regulator equation and construct an observer based on the tracking error to obtain the robust output feedback regulator. The closed-loop system is proved to be well-posed and uniformly bounded, and the regulated output tracks the reference signal exponentially. The numerical simulations are carried out to demonstrate the effectiveness of the proposed control.

Boundary PID output regulation for Euler-Bernoulli beam equation

The paper deals with the output feedback regulation of Euler-Bernoulli beam system with the single boundary input and single boundary output. The PID control is designed to stabilize system and achieve output regulation. Based on an elaborated Lyapunov functional, it is proved that the closed-loop system is exponentially stable and the output tracks any given reference signal. Numerical simulations by the finite element method and the analysis of spectral distribution are carried out to validate the stabilization and regulation performance of our designed controller.

Robust error feedback output regulation of a 2 × 2 hyperbolic system

Abstract In this paper, we consider the robust error feedback output regulation problem for a linear $ 2 \times 2 $ hyperbolic system with system uncertainties and disturbance signals. Using the backstepping method, the state feedback controller for the system without the system uncertainties and the external disturbance signals (nominal system) is designed. In terms of the measurable regulation error, an observer system is designed to recover the state of the nominal system, and an observer-based error feedback controller is obtained to solve the robust output regulation problem. Moreover, we prove that the controller is robust to the system uncertainties and the disturbance signals, and show that the state of the closed-loop system is bounded. The numerical simulations are presented to illustrate the effectiveness of the theoretical results.

Semiglobal Leader-Following Output Consensus of Discrete-Time Heterogeneous Linear Systems Subject to Actuator Position and Rate Saturation

Motivated by the fact that physical systems are usually subject to actuator position and rate saturation, we consider in this article the semiglobal leader-following output consensus problem of a group of discrete-time heterogeneous linear systems with position and rate-limited actuators by output feedback control law. Distributed observers are designed for followers to estimate the state of the leader and the follower itself, based on which a novel distributed control law is proposed. We show that, via the low gain feedback design technique and output regulation theory, the semiglobal leader-following output consensus of discrete-time heterogeneous linear systems can be achieved by the consensus protocol if each follower is reachable from the leader in a directed communication topology.

Output regulation for general heterodirectional linear hyperbolic PDEs coupled with nonlinear ODEs

This paper considers general heterodirectional linear hyperbolic PDEs with boundary actuation and collocated measurement, that are bidirectionally coupled with nonlinear ODEs at the unactuated boundary. An output feedback regulator is designed to have the control output track a reference in the presence of disturbances, with a nonlinear signal model generating the reference and the disturbances. This leads to new challenges for both the observer and controller design. The regulator design makes use of results from output regulation theory for nonlinear lumped-parameter and distributed-parameter systems. The derivation of the state feedback regulator requires solving a new type of regulator equations, which consist of a Cauchy problem for linear and semilinear hyperbolic PDEs. A key component of the novel observer design is a nonlinear retarded observer for a finite-dimensional subsystem. Both the controller and the observer design are systematic in nature and derived in several successive steps, that include backstepping transformations and, most notably, predictions of PDE and ODE states. The latter are shown to be the unique solution of general nonlinear Volterra integro-differential equations. Combining the observer with the state feedback regulator is proven to achieve output regulation for the closed-loop system. A numerical example illustrates and confirms the theoretical results.

Output feedback regulation for a class of output‐constrained nonlinear systems with iISS inverse dynamics

This paper studies the output feedback problem for nonlinear systems with integral input-to-state stability (iISS) inverse dynamics, output constraint, and unknown control direction. First, a nonlinear mapping is introduced to transform the output constrained system into a new unconstrained system. Second, the influence of the change of iISS supply rate is discussed. By introducing an observer and using the time-varying Riccati equation, a dynamic output feedback control law is constructed with a backstepping-based design strategy. Besides, the value of gain P is determined to make it meet the stability equation. The output results do not violate the constraints.

On the Output-Feedback Regulation for a Second-Order System with Unknown Parameters: An I&I and MRAC Based Approach

On the Output-Feedback Regulation for a Second-Order System with Unknown Parameters: An I&I and MRAC Based Approach

Semi-global leader-following output consensus of heterogeneous systems subject to actuator position and rate saturation

We study in this paper a semi-global leader-following output consensus problem for multiple heterogeneous linear systems in the presence of actuator position and rate saturation over a directed topology. For each follower, via the low gain feedback design technique and output regulation theory, both a state feedback consensus protocol and an output feedback consensus protocol are constructed. In the output feedback case, different distributed observers are designed for the informed followers and uninformed followers to estimate the state of the leader and the follower itself. We show that the semi-global leader-following output consensus of heterogeneous linear systems can be achieved by the two consensus protocols if each follower is reachable from the leader in the directed communication topology.

Adaptive output feedback regulation for a class of uncertain feedforward stochastic nonlinear systems

This paper addresses the global output feedback regulation problem for a class of uncertain feedforward stochastic nonlinear systems. Unlike the previous works, the drift’s growth rate depends not only on an unknown constant but also on an output polynomial function and an input function. Moreover, the diffusion’s growth rate depends on an unknown constant or an output polynomial function and an input function. By using the general stochastic convergence theorem, an output controller is constructed to guarantee the boundedness and stochastic convergence of the resulting closed-loop system.

Output feedback regulation of large-scale feedforward systems with discrete and distributed delays

This paper proposes an output feedback control strategy to achieve the global regulation of a class of large-scale feedforward nonlinear systems with discrete and distributed delays. The nonlinear terms are assumed to be bounded by the continuous functions of inputs multiplied by an unknown constant, and the discrete and distributed delays are allowed in the inputs and states. A novel design approach, namely dynamic gain construct method, is given to design the observers and the output feedback controllers. On the basis of the Lyapunov–Razumikhin theory, the global regulation of the closed-loop system is proved. Different from the existing results, a dynamic gain is online updated by the systems outputs and the observers states. Moreover, the time-varying gain with the logarithmic form is first constructed under a unified framework, which is also a valid control algorithm in coping with the uncertainty of the concerned systems. A simulation example is provided to demonstrate the effectiveness of the theoretic results.

Cooperative output regulation for a network of parabolic systems with varying parameters

This paper is concerned with the cooperative output regulation problem for a network of agents with different dynamics described by parabolic PDEs subject to spatially- and time-varying parameters. Firstly, a networked controller is designed achieving output synchronization for identical finite-dimensional reference models, which deliver the state of the global reference model required for the synchronization to the parabolic agents. The latter can be subject to local disturbances acting in-domain, on all boundaries and on the anti-collocated output to be controlled. The cooperative output regulation problem is solved by designing local output feedback regulators for the parabolic agents. This requires the solution of time-varying regulator equations and the design of disturbance observers for parabolic systems with spatially- and time-varying coefficients. For this, a systematic backstepping approach is provided and it is shown that cooperative output regulation with exponential convergence is ensured for the resulting multi-agent system. The results of the paper are applied to the cooperative output regulation of a heterogeneous network of four parabolic agents in the presence of local disturbances.

A new integral boundary control for de Saint-Venant Partial Differential Equations

The paper deals with output feedback regulation of exponentially stable systems by an integral controller. We have recently proposed an appropriate Lyapunov functional to prove exponential stability of the closed-loop system. The approach is dedicated in this paper to hyperbolic systems and especially to the de Saint-Venant equations giving explicitly the gains to ensure an exponentially stabilized integral controller: the parameters expression is deduced directly of the Lyapunov functional based on the Forwarding approach. Numerical simulations illustrate this approach.

Discrete-time modeling and output regulation of gas pipeline networks

In this work, a discrete-time output regulator design is proposed for a class of gas pipeline networks to meet various operating requirements in energy scheduling. Based on the isothermal Euler equations, linearized continuous-time gas pipeline network models with boundary actuation and sensing in the infinite-dimensional space are established, with consideration of Rankine–Hugoniot conditions at junction joints. Cayley–Tustin bilinear transformation is applied for model time discretization without any spatial approximation, by which the continuous-time model with unbounded operators is transformed into an infinite-dimensional discrete-time system with all bounded operators and essential continuous-time properties are invariant under this transformation. Based on the internal model principle, the discrete output regulator is constructed and its solvability conditions are provided. Considering the unavailability of the full state information, observer design methods for state estimation of exogenous and pipeline systems are proposed in order to construct an output feedback regulator. Additionally, a stability analysis of the considered pipeline system is provided. Finally, two simulation examples representing a single gas pipeline and a star-shaped pipeline network are given to demonstrate the applicability of the proposed method.

Output feedback regulation of a class of high‐order feedforward nonlinear systems with unknown time‐varying delay in the input under measurement sensitivity

SummaryAn output feedback regulation problem is considered for a class of high‐order feedforward nonlinear systems with delay in the input under measurement sensitivity. The key features are that the considered systems have uncertain high‐order feedforward nonlinearity and unknown time‐varying delay in the input. Then, the controller is supposed to be engaged where the output feedback information is distorted by measurement sensitivity. Our proposed controller has two gains—fixed and adaptive gains. The fixed gain is first designed to compensate for measurement sensitivity, and the adaptive gain is next utilized to dominate both unknown input delay and uncertain high‐order feedforward nonlinearity. Simulation examples are given to highlight the advantage of our control scheme.