Output Feedback Control Law Research Articles

Output feedback compensation to state and measurement delays for a first-order hyperbolic PIDE with recycle

This paper develops a novel observer-based output-feedback control law for a class of interconnected first-order hyperbolic partial integral differential equations (PIDEs) with in-domain, non-local coupling terms and measurement delay compensation. A transport PDE is introduced to account for in-domain recycle delay which results in an extended spatial domain with the PIDE and transport PDE being cascaded. Since standard backstepping approach cannot be applied, an affine Volterra integral transform is introduced which allows for the construction of a boundary controller for the PIDE and delay compensation. An observer backstepping transformation containing four kernels is realized, reconstructing the states throughout the delayed measurement. By the use of the backstepping method, a set of coupled kernel equations where one of the kernels has two boundary conditions is established. The existence and invertibility for the control and observer transformations are proved and the finite-time stability for the output system is established while results are illustrated by numerical simulations.

Nonlinear lateral motion stability control method for electric vehicle based on the combination of dual extended state observer and domination approach via sampled-data output feedback

This paper studies lateral motion stability control method for an electric vehicle (EV) with uncertain disturbances. Aiming to suppress the influence of uncertain disturbances, a novel method based on the combination of dual extended state observer (dESO) and domination approach is proposed. The proposed method enables the designed controller just to adopt a smaller scaling gain than the classic domination method, which is more practical for the controller in engineering. Firstly, a dESO is proposed to estimate the uncertain disturbances of the system. Also, a sampled-data output feedback domination approach is designed to dominate the disturbances by using a scaling gain. Then, the sampled-data output feedback control law is constructed based on the dESO and domination approach called dESOD. Furthermore, the stability analysis is presented to show that the proposed sampled-data controller can guarantee the closed-loop system globally asymptotically stable. Finally, the simulations and experiment results show the effectiveness of the proposed method.

Bipartite consensus of multi-agent systems with reduced-order observer-based distributed control protocols

This paper considers the bipartite consensus problem for multi-agent systems, in which both bipartite leaderless consensus and bipartite tracking problems are investigated under signed digraph. Two distributed output feedback control laws are proposed based on reduced-order observer design, respectively, for solving the bipartite leaderless consensus and bipartite tracking consensus problems. Some sufficient conditions are obtained for achieving the bipartite consensus of the multi-agent systems, by using the algebraic Riccati equation design and Jordan decomposition technique. Finally, two simulation examples are presented to illustrate the effectiveness of the obtained theoretical results.

Output Containment Control of Heterogeneous Linear Multiagent Systems With Unbounded Distributed Transmission Delays.

In this article, the output containment control problem of heterogeneous linear multiagent systems (MASs) with unbounded distributed transmission delays is considered. A key technical lemma is first established to show that the distributed observers under unbounded distributed transmission delays can be utilized to estimate the convex combination of the states of multiple leaders. Then, a novel distributed output feedback control law is proposed based on those distributed observers. It is shown that under our proposed control law, the output of each follower converges to the convex hull spanned by the outputs of the leaders. In addition, our results include relevant results on output containment control of MASs with bounded distributed or constant transmission delays as special cases. Finally, the effectiveness of the proposed control law is demonstrated by a simulation example.

Static output feedback control of a chain of integrators with input constraints using multiple saturations and delays

Using multiple saturations and delays, we present a time-domain static output feedback control approach for global stabilization of a chain of integrators with input constraints. In lieu of estimating the state by observers, we utilize the output with distinct delays to construct static output feedback control laws. A nested saturation design technique is employed to handle the nonlinearity in the control. An appealing feature of the proposed nonlinear controllers is that no observer is needed. The bounded and static output feedback control scheme is validated by an application to the triple integrators.

Time-Varying Tube-Based Output Feedback MPC for Constrained Linear Systems with Intermittently Delayed Data

Abstract This paper proposes a time-varying tube-based output feedback model predictive control (MPC) design for constrained linear systems in the presence of intermittently delayed observations, where the delayed/missing data patterns for each period satisfy a finite-length language. The design consists of a dynamic state estimator whose estimation errors satisfy equalized recovery (a weaker form of invariance with time-varying finite bounds), as well as an output feedback control law that extends existing tube-based output feedback MPC approaches to allow time-varying tubes for tightening the original state and input constraints. The resulting time-varying tube-based output feedback MPC design is robust to time-varying disturbances and errors, including when the observations are intermittently delayed. Further, we provide sufficient conditions for recursive feasibility and robust exponential stability of the proposed design. Simulation results demonstrate that the proposed approach is able to robustly stabilize and control a constrained linear system despite disturbances, noise and missing/delayed data.

Stop-and-go suppression in two-class congested traffic

This paper develops an output feedback control law in order to damp out traffic oscillations in the congested regime of the linearized two-class Aw-Rascle (AR) traffic model. The macroscopic second-order two-class AR traffic model consists of four hyperbolic partial differential equations (PDEs) describing the dynamics of densities and velocities on freeway. Each vehicle class is characterized by its own vehicle size and driver’s behavior. The considered equilibrium profiles of the model represent evenly distributed traffic with constant densities and velocities of both classes along the investigated track section. After linearizing the model equations around those equilibrium profiles, it is observed that in the congested traffic one of the four characteristic speeds is negative, whereas the remaining three are positive. Backstepping control design is employed to stabilize the 4 × 4 heterodirectional hyperbolic PDEs. The control input actuates the traffic flow at outlet of the investigated track section and is realized by a ramp metering. The output feedback controller is obtained by designing an anti-collocated observer and combining it with a full state feedback result. Overall, the output feedback control law achieves the damping of stop-and-go waves in finite time by measuring the velocities and densities of both vehicle classes at the inlet of the investigated track section. The performance of the developed controller is verified by simulation of the linearized model and quantified by performance indices for the fuel consumption, comfort and total travel time.

Adaptive Neural Output Feedback Tracking Control of Underactuated Ships Against Uncertainties in Kinematics and System Matrices

Adaptive neural output feedback tracking control is developed for underactuated ships with uncertainties in kinematics (i.e., kinematic uncertainties) and uncertain off-diagonal terms in the matrices of their system dynamics (i.e., dynamic uncertainties), where radial basis function networks are incorporated. As the kinematic uncertainties unavoidably exist in the off-diagonal terms of system matrices and only the posture information (position variables and yaw angle) of the ship is available, the velocities should be observed and the kinematic and dynamic uncertainties should be simultaneously compensated to achieve the satisfactory ship tracking control performance. Therefore, the kinematic and dynamic uncertainties of the underactuated ship are rigorously derived. The kinematic equations with uncertainties are then derived such that the proposed nonlinear velocity observer can be used to estimate the combined velocities and kinematic uncertainties using the posture information irrespective of the ship dynamics. The dynamic uncertainties are also derived while taking into consideration the uncertainties in the system matrices. An adaptive neural uncertainty observer is then proposed to estimate the dynamic uncertainties. In this way, the proposed adaptive neural output feedback control law can compensate for the uncertainties in both the kinematics and dynamics. The estimation errors in the combined velocities and kinematic uncertainties and the dynamic uncertainties are rigorously considered in the proposed controller design. A stability analysis and the simulation results of the ship tracking control system are provided to demonstrate the validity of the proposed method.

An LMI-Based Algorithm to Compute Robust Stabilizing Feedback Gains Directly as Optimization Variables

This article addresses the problem of robust stabilization of uncertain linear systems by static state- and output-feedback control laws. The uncertainty is supposed to belong to a polytope and both continuous- and discrete-time systems are investigated. Contrarily to the main stream of the linear matrix inequality (LMI)-based robust stabilization methods available in the literature, where the product between the Lyapunov (or slack variable) and control gain matrices is transformed in a new variable, this article proposes a change of paradigm, avoiding the standard change of variables and providing synthesis conditions that deal directly with the control gain as an optimization variable. The design procedure is formulated in terms of a locally convergent iterative algorithm based on LMIs, having as main novelties the following points: Both the Lyapunov and the closed-loop dynamic matrices appear affinely in the conditions; the iterative scheme involves the slack variables only, avoiding the classic alternation between the Lyapunov matrix and the control gain; an extra degree of freedom is created in terms of an additional scalar variable, which also appears affinely in the conditions and represents a scaling on the closed-loop dynamic matrix; a smart termination for the algorithm through a stability analysis condition. Numerical experiments based on exhaustive simulations show that all these features combined provide a robust stabilization technique capable to outperform the best available methods in the literature in terms of effectiveness, being specially suitable to address static output-feedback and decentralized control problems.

Distributed Output Regulation for a Class of Nonlinear Multiagent Systems With Dynamic Edges.

In this article, an output regulation problem is considered for nonlinear multiagent systems with unity relative degree, in which nodes are coupled by dynamic edges. The inputs of the edge dynamic systems are determined by the error outputs of the node dynamic systems. Similarly, the neighboring inputs of the node dynamic systems are formed by the outputs of the edge dynamic systems and can influence node outputs. By introducing some coordinate transformations, we can transform the output regulation problem into a robust stabilization problem for an augmented system. Then, using the relative outputs of neighboring agents, we design a distributed output-feedback control law and suitable dynamic couplings between the nodes. Finally, it is shown that the global stabilization of the augmented system can be achieved using the proposed controller. An example is presented to demonstrate the effectiveness of our control strategy.

Output feedback MPC for uncertain delayed system and control of a wind tunnel system

We propose an output feedback model predictive control (MPC) strategy for a class of uncertain systems with state delay and unknown disturbance. In order to handle the state delay, we formulate an augmented dynamic system that includes the delayed states, as well as the original system state, as the augmented state. Then, we utilize a dynamic output feedback control law, which is based on the current estimated state instead of the augmented state, for stabilizing the system. As a result, the order of the controller is much reduced. The benefits of utilizing the reduced order controller are the reduced computational burden and guaranteed recursive feasibility. We apply the proposed approach to a wind tunnel system for regulating the Mach number in the test section to the reference value. The simulation result verifies the effectiveness and practicality of the proposed approach.

Predictive Descriptor Observer Design for a Class of Linear Time-Invariant Systems With Applications to Quadrotor Trajectory Tracking

This article deals with sensor fault tolerant control design and large delay compensation for a class of linear time-invariant systems. Based on predictor-based state transformation and predictive descriptor observer design, both the state and output feedback control laws are constructed. Within the framework of Lyapunov–Krasovskii functionals, a set of stability conditions are identified. The closed-loop systems is globally asymptotically stable at the origin under the state feedback and is ultimately bounded under the output feedback. Finally, the proposed design is validated through numerical simulations and then implemented on a quadrotor trajectory tracking test. Both simulation and experimental results demonstrate the effectiveness of the proposed design.

Event-triggered robust control for quadrotors with preassigned time performance constraints

In this paper, an event-triggered robust control for quadrotors with preassigned time performance constraints is presented. In order to prolong operational time and enhance mission completion efficiency subject to limited onboard power, a switching threshold event-triggered strategy is embedded in controller-to-actuator and sensor-to-controller channels, where switching threshold event-triggered based extended state observers (SET-ESO) are respectively established in the trajectory and attitude subsystems to accomplish the real-time estimation of linear velocity, angular velocity along with lumped disturbances using intermittent measurements, and the quantitative analysis between the ultimate observation error and parameters of SET-ESO is revealed. Based on the estimation results, an event-triggered output feedback control law including a robust compensation term is established to realize an anti-disturbance time-varying trajectory tracking without involving Zeno phenomena. Moreover, to eliminate severe fluctuations at the transient inherent in traditional prescribed performance control (TPPC) with a fast convergent rate, a tracking differentiator-based prescribed performance control (TDPPC) mechanism is exploited to ensure the trajectory state converge to a pre-given region with a preassigned prescribed time, such that a smooth and pre-specified finite-time tracking capability independent of control parameters is preserved. Next, with the aid of Lyapunov synthesis, all the signals involved in the closed-loop quadrotor system are proved to be bounded, and the preassigned time performance constraints are not violated. The simulation and comparison results are shown to validate the effectiveness of the proposed control scheme.

Input-to-state stabilization of an ODE-wave system with disturbances

In this paper, we consider the input-to-state stabilization of an ODE-wave feedback-connection system with Neumann boundary control, where the left end displacement of the wave equation enters the ODE, while the output of the ODE is fluxed into boundary of the wave equation. The disturbance is appeared as a nonhomogeneous term in the ODE. Based on the backstepping approach, a state feedback control law is designed to guarantee the exponential input-to-state stability of the closed-loop system. The resulting closed-loop system has been shown to be well-posed by the semigroup approach. Moreover, we construct an exponentially convergent state observer based on which an output feedback control law is obtained, and the closed-loop system is proved to be input-to-state stable.

Laser Sintering Control for Metal Additive Manufacturing by PDE Backstepping

Metal additive manufacturing (AM) has been intensively advanced due to numerous industrial applications, such as automobiles, aerospace, consumer electronics, and medical devices. The dynamics of the melt pool via laser sintering for metal AM has been studied by means of the thermodynamic phase change model known as the “Stefan problem”. In this article, we develop a control design for the laser power to drive the depth of the melt pool to the desired set point. The governing equation is described by a partial differential equation (PDE) defined on a time-varying spatial domain, which is dependent on the PDE state, and the optical penetration of the laser energy affects the PDE dynamics in the domain as well as at the surface boundary. First, we design the full-state feedback control law utilizing the entire spatial profile of the temperature in the melt pool and the moving interface position. The closed-loop system is proven to satisfy some conditions to validate the physical model, and its origin is shown to be exponentially stable. Next, we propose an observer-based output feedback control law by reconstructing the temperature profile with the availability of only the measured interface position and prove the analogous properties of the closed-loop system. Numerical simulation for a controller designed on a single-phase Stefan model is conducted on a more complex and realistic two-phase Stefan model, which incorporates the cooling effect from the solid phase. In addition, a bias in the interface location measurement is considered. The numerical results illustrate the robustness of the proposed feedback. By lowering the initial temperature in the solid and by increasing the interface sensor bias to more extreme levels, which leads to the controller’s failure (where the failure is exhibited through the entire metal freezing and the melt pool disappearing), we explore the limits of how much uncertainty our control law can handle.

Quantized output regulation of minimum‐phase linear uncertain systems

SummaryThis article investigates the robust output regulation problem of a class of minimum‐phase linear uncertain systems subject to limited measurement information. A novel dynamic quantized output feedback control law together with a hybrid quantized feedback control policy is developed. By means of Lyapunov analysis, it is shown that the tracking error tends to zero asymptotically in spite of system uncertainties, disturbances, and limited measurement information. In addition, a special case of the main result leads to the solution of the robust stabilization problem of minimum‐phase linear systems subject to system uncertainties, disturbances, and the quantized output.

Cooperative output regulation of heterogeneous linear multi-agent systems based on the event-triggered distributed control under switching topologies

This paper studies the cooperative output regulation (COR) problem of heterogeneous linear multi-agent systems (MAS)s based on two kinds of event-triggered control protocols under time-varying topologies. Firstly, a state feedback distributed control scheme is designed to achieve COR problem and eliminate Zeno behavior of the MASs with only intermittent communication between neighbors. The design of such a controller requires the assumption that the states of all agents are measurable. Secondly, we design a dynamic output feedback control law which does not need to assume that all states are measurable in the MASs. The COR problem of MASs is also implemented without Zeno behavior existing. Under the proposed two kinds of triggering mechanisms, each agent sends information to its neighbors only at its switching and triggering times. Finally, several examples are introduced to illustrate effectiveness and practicability of the theoretical results. And we add a comparative experiment to highlight the advantages of the design methods in this paper.

Dynamic stabilisation for an Euler–Bernoulli beam equation with boundary control and matched nonlinear disturbance

In this paper, we are concerned with dynamic stabilisation for a one-dimensional Euler–Bernoulli beam equation with boundary moment control and matched nonlinear uncertain disturbance. In the case of no disturbance, we show that a boundary feedback control law exponentially stabilises the system and Riesz basis generation holds for the closed-loop system. The well-posedness of the system in the sense of Salamon-Weiss, which is essentially important for the design of observer, is verified. We design an infinite-dimensional disturbance estimator, which doesn't need slow variation or high gain or boundedness of the derivation of the disturbance, to estimate the total disturbance. Based on the disturbance estimator, we design an output feedback control law. The Riesz basis generation and exponential stability of a couple system including the original equation is proved. Moreover, the boundedness of the closed-loop system is verified. Some numerical simulations are presented to illustrate the results.

Output-Feedback Flocking Control of Multiple Autonomous Surface Vehicles Based on Data-Driven Adaptive Extended State Observers.

This article addresses an output-feedback flocking control problem for a swarm of autonomous surface vehicles (ASVs) to follow a leading ASV guided via a parameterized path. The leading and following ASVs are subject to completely unknown model parameters, external disturbances, and unmeasured velocities. A data-driven adaptive anti-disturbance control method is proposed for establishing a flocking behavior without any prior knowledge of model parameters. Specifically, a data-driven adaptive extended state observer (ESO) is proposed such that unknown input gains, unmeasured velocities, and total disturbance are simultaneously estimated. For the leading ASV, an output-feedback path-following control law is developed to follow a predefined parameterized path. For following ASVs, an output-feedback flocking control law is developed based on an artificial potential function for collision avoidance and connectivity preservation, in addition to a distributed ESO for estimating the velocity of the leading ASV through a cooperative estimation network. The simulation results are discussed to substantiate the efficacy of the proposed path-guided output-feedback ASV flocking control based on data-driven adaptive ESOs without measured velocity information.

Robust Output Regulation of Linear Systems by Event-Triggered Dynamic Output Feedback Control

In this article, we study the robust output regulation problem of linear systems by an event-triggered output feedback control law. We first summarize the solvability of the linear robust output regulation problem by the internal model design. Then, we implement this continuous-time control law by an event-triggered output feedback control law together with an output-based triggering mechanism. We show that, under almost the same solvability conditions as those for the linear robust output regulation problem, the robust output regulation problem can also be solved by an event-triggered output feedback control law without incurring Zeno phenomenon. Furthermore, we show that, it is possible to solve the robust output regulation problem practically while preventing the interevent time from approaching zero as time tends to infinity.