Dynamic Output Feedback Control Law Research Articles

Solutions to the output regulation problem of time-varying descriptor systems

This paper studies the output regulation problem of time-varying descriptor systems and the problem of designing state feedback and dynamic measurement output feedback control laws which asymptotically achieves output regulation and disturbance rejection is considered. New regulator equations are proposed for time-varying descriptor systems in the form of differential-algebraic matrix equations. The unique solution of the proposed regulator equations is given as well. We prove that the output regulation problem of time-varying descriptor systems is solvable if and only if the given regulator equations are solvable. Based on the solution of the regulator equations, the state feedback and dynamic measurement output feedback control laws are designed to solve the output regulation problem. The work extends the existing results of output regulation problem for time-varying linear systems to the time-varying descriptor systems. Numerical examples are given to show the effectiveness of our methodology.

Output regulation and tracking for linear ODE-hyperbolic PDE–ODE systems

This paper proposes a constructive solution to the output regulation — output tracking problem for a general class of interconnected systems. The class of systems under consideration consists of a linear 2 × 2 hyperbolic Partial Differential Equations (PDE) system coupled at both ends with Ordinary Differential Equations (ODEs). The proximal ODE system, which represents actuator dynamics, is actuated. Colocated measurements are available. The distal ODE system represents the load dynamics. The control objective is to ensure, in the presence of a disturbance signal (regulation problem), that a virtual output exponentially converges to zero. By doing so, we can ensure that a state component of the distal ODE state robustly converges towards a known reference trajectory (output tracking problem) even in the presence of a disturbance with a known structure. The proposed approach combines the backstepping methodology and frequency analysis techniques. We first map the original system to a simpler target system using an invertible integral change of coordinates. From there, we design an adequate full-state feedback controller in the frequency domain. Following a similar approach, we propose a state observer that estimates the state and reconstructs the disturbance from the available measurement. Combining the full-state feedback controller with the state estimation results in a dynamic output-feedback control law. Finally, existing filtering techniques guarantee the closed-loop system robustness properties.

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

In this article, the robust output regulation problem of the linear uncertain system is investigated by the event-triggered control approach. Recently, the same problem is addressed by an event-triggered control law where the Zeno behavior may happen when time tends to infinity. In comparison, a class of event-triggered control laws is developed to achieve output regulation exactly, and meanwhile, explicitly exclude the Zeno behavior for all time. In particular, a dynamic triggering mechanism is first developed by introducing a dynamic changing variable with specific dynamics. Then, by the internal model principle, a class of dynamic output feedback control laws is designed. Later, a rigorous proof is provided to show that the tracking error of the system converges to zero asymptotically while prohibiting the Zeno behavior for all time. Finally, we give an example to illustrate our control approach.

Asynchronous sampled-data dynamic output feedback control for Markovian jump neural networks via a double-mode-dependent Lyapunov functional

This paper discusses the asynchronous switching problem of Markovian jump neural networks (MJNNs) with mode-dependent time delays. Due to the factors such as communication induced phenomena or the incomplete availability of system modes, asynchronous switching between the system mode and the controller mode is a common phenomenon. Therefore considering the mode mismatch phenomenon and the incomplete measurement of system state, we propose an asynchronous dynamic output feedback control (DOFC) law. Unlike the traditional DOFC, the sampled-data strategy is introduced into DOFC to alleviate the burden of the communication network. In light of the sampled-data DOFC, an augmented dynamic system is modeled. To fully employ the mode information of asynchronous switching and to relax the conservativeness of the results, a double-mode-dependent Lyapunov functional is constructed, which depends both on the system modes and the DOFC modes. Then, a less conservative stability condition is obtained to guarantee mean-square asymptotic stability (MSAS) of the augmented system. On the basis of the stability condition, a design algorithm is attained to solve the gain matrices of the asynchronous DOFC. Finally, a simulation example is given to illustrate the validity and superiority of the developed results.

Output feedback control of uncertain Euler–Lagrange systems by internal model

In this paper, we investigate the trajectory tracking control problem of a class of uncertain Euler–Lagrange systems subject to disturbances. In sharp contrast to existing approaches where the position, the velocity, and the acceleration of the reference trajectory are assumed to be measurable, we propose a class of dynamic output feedback control laws which depends on the tracking error of the position and that of the velocity. Specifically, by characterizing the reference trajectory and the disturbances with an exosystem, we design an internal model to learn the desired feedforward input such that the reference trajectory can be tracked in spite of unknown system parameters and disturbances. The effectiveness of the proposed approach is illustrated by its application to trajectory tracking control of a three-link cylindrical robot arm.

Codesign of Quantized Dynamic Output Feedback MPC for the Takagi–Sugeno Model

We present a co-design of measurement quantized dynamic output feedback model predictive control (DOFMPC) for Takagi-Sugeno model with bounded disturbance. The system output is quantized by a dynamic quantizer before it is transmitted to the DOFMPC controller. Hence, we utilize the dynamic output feedback control law with quantized output signal and consider the mixed input and quantized output constraint for the controller design. By optimizing the quantizer and controller paramters on-line, the control performance is enhanced. Moreover, we formulate a 2-leveled optimizations, with the upper level optimizing the performance index and the lower level optimizing the soft constraint in a lexicographic order, for the co-design of the DOFMPC controller and dynamic quantizer. Thus, there are more degrees of freedom for tighting the soft constraints. The recursive feasibility and stability of the proposed approaches are guaranteed. The applicability of the proposed approach is illustrated by a simulation example.

Periodic event-triggered dynamic output feedback control for networked control systems subject to packet dropouts

This paper proposes a co-design method of dynamic output feedback control law and periodic event-triggered control (PETC) strategy to tolerate a maximum allowable number of successive packet dropouts (MANSDs) in networked control systems (NCSs). For the purpose of striking a balance between saving limited communication resources and reducing complexity of the transmission implementation, we present the periodic event-triggering mechanism (PETM), in which the triggering conditions only needs to be monitored at each event-verifying instant. In NCSs, packets often suffer from some interference in network transmission, such as packet losses. For packet dropouts, we introduce a dropout variable and model the whole closed-loop systems as a hybrid system. Furthermore, some stability conditions for co-design are given by a novel Lyapunov function and stability theorems of hybrid systems, and the explicit designs parameters of controller and triggering conditions are presented to ensure L2 stability. Finally, two illustrated examples are given to show the effectiveness of the proposed design methods.

Guest Editorial: Learning, optimisation and control of cyber‐physical systems

Guest Editorial: Learning, optimisation and control of cyber‐physical systems

Output feedback control with time-varying asymmetric constraints for nonlinear cascade systems

In this paper, the output feedback problem is studied for a class of nonlinear cascade systems with integral input to state stability (iISS) inverse dynamics and an unknown control direction. The tan-type barrier Lyapunov function (UBLF) is introduced for an asymmetric time-varying output constraint, which can be equal to the standard Lyapunov function of an unconstrained system, thereby solving the requirement for the asymmetric time-varying output constraint. A design strategy based on backstepping is proposed to construct a dynamic output feedback control law, and an output feedback controller is designed using the barrier function. The proposed strategy satisfies the constraint condition while keeping all other closed-loop signals bounded. Finally, the effectiveness of the proposed strategy is proven by the simulation results.

An event-triggered round-robin protocol to dynamic output feedback control for nonhomogeneous Markov switching systems

This paper addresses the dynamic output feedback control issue for nonhomogeneous Markov switching systems with an event-triggered round-robin protocol. The transition probability matrix of the nonhomogeneous Markov process is time-varying, which can be characterized by a polytopic structure. To alleviate the communication burden in a shared network, as a first effort, a novel dynamic event-triggered round-robin protocol is forwarded to regulate whether to release the measurements and which ones to release. In light of the dynamic event-triggered round-robin protocol, an asynchronous dynamic output feedback control law is constructed, which reflects the mismatching phenomenon of modes switching between the nonhomogeneous Markov switching systems and the desired controllers. By resorting to a novel Lyapunov functional, sufficient conditions are attained to guarantee the stochastic stability of the augmented dynamic. At last, two examples are addressed to verify the effectiveness and applicability of the theoretic results.

Design of output feedback proportional–integral controller for polynomial fuzzy systems

AbstractIn this paper, the design of dynamic output feedback control law for polynomial fuzzy systems is studied. The main purpose is to design a tracker control law for fuzzy polynomial systems that are subject to external bounded disturbances. The structure of the control law is considered as fuzzy proportional–integral control. The conditions for deriving the control law are formulated in the form of a sum of square (SOS) feasibility problem. The designed control law will be able to force the system state vector to follow the state vector of a stable reference model in addition to guaranteeing the performance measure. The simulation results show the efficiency of the proposed method exposed to external disturbance.

A Characterization of approximate decentralized fixed modes of time‐delay systems

AbstractThe concept of decentralized fixed mode (DFM) is crucial in determining the output feedback stabilizability by linear time‐invariant (LTI) decentralized controllers. However, in some cases, although a system has no DFMs, some of its modes may be very close to being fixed. It is thus important to characterize these modes, which are called approximate DFMs (ADFMs). In this paper, the characterization of ADFMs is discussed for LTI neutral (possibly descriptor‐type) time‐delay systems under static and dynamic decentralized output feedback control laws, and a mode mobility measure is proposed to provide quantitative information about ADFMs. To analytically compare the proposed measure, some of the commonly used quantitative measures for the characterization of ADFMs of finite‐dimensional systems have also been extended to the considered type of systems. The herein proposed approach allows multiple time delays and does not require additional expansions or preliminaries for multi‐input multi‐output systems, like some other commonly used methods. Thus, characterization with this measure, in general, requires less computational load, while it can provide more explicit information about the controller effort than the other considered measures.

Distributed Robust Containment Control of Linear Heterogeneous Multi-Agent Systems: An Output Regulation Approach

In this paper, we consider the robust output containment problem of linear heterogeneous multi-agent systems under fixed directed networks. A distributed dynamic observer based on the leaders' measurable output was designed to estimate a convex combination of the leaders' states. First, for the case of followers with identical state dimensions, distributed dynamic state and output feedback control laws were designed based on the state-coupled item and the internal model compensator to drive the uncertain followers into the leaders' convex hull within the output regulation framework. Subsequently, we extended theoretical results to the case where followers have nonidentical state dimensions. By establishing virtual errors between the dynamic observer and followers, a new distributed dynamic output feedback control law was constructed using only the states of the compensator to solve the robust output containment problem. Finally, two numerical simulations verified the effectiveness of the designed schemes.

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.

Output‐based event‐triggered control of networked systems subject to bilateral packet dropouts

In this paper, an output‐based event‐triggered control problem of discrete‐time networked control systems (NCSs) subject to bilateral packet dropouts is investigated. In view of stochastic sequences of packet dropouts in the measurement channels (from sensors to controller) and the control channels (from controller to actuators), the NCS is converted into a closed‐loop stochastic parameter system. In the aid of a Lyapunov functional based on stochastic variables, the sufficient conditions on design of a dynamic output feedback control law and bilateral event‐triggering conditions are derived to guarantee the exponentially mean‐square stability for NCSs. Furthermore, an improved iterative algorithm is given to obtain the output‐based control law and event‐triggering parameters from a set of nonconvex inequalities. Finally, a numerical example and the corresponding simulation results are given to illustrate the validity and applicability of the developed techniques.

Design of Robust Dynamic Output Feedback Event-Triggering Controllers for Nonlinear Uncertain Systems

This paper presents a design of dynamic output feedback event-triggering control for nonlinear uncertain networked control systems. The plant and actuator asynchronously transmit the measurement and control signals over two different communication channels. We address the norm-bounded time-varying parameter uncertainties in a nonlinear plant. First, considering the exogenous disturbances and noises in the control and measurement signals, sufficient conditions for the <i>L</i>₂ stability of the nonlinear networked control systems are given in the presence of the uncertainties. Then, we propose design conditions to choose the dynamic output feedback control and triggering laws in terms of linear matrix inequalities (LMIs). The proposed conditions enable the controller and event-triggering parameters to be jointly optimized to lessen the number of transmissions, guaranteeing a certain level of <i>L</i>₂ gain. Numerical examples demonstrate the effectiveness of the proposed method.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

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.

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.