Output-feedback Problem Research Articles

A new singular system approach to output feedback sliding mode control for fractional order nonlinear systems

This paper studies the problem of output feedback sliding mode control (OFSMC) for fractional order nonlinear systems. A necessary and sufficient condition for the existence of a sliding surface is obtained by a new singular system approach and a linear matrix equality (LMI), which reduces the conservativeness of the system. Then an OFSMC law is designed based on a fractional order Lyapunov method, which ensures that the resulting fractional closed-loop system is asymptotically stable and the states of the fractional closed-loop system converge to the sliding surface in finite time. A fractional electrical circuit is discussed to illustrate the effectiveness of the proposed approach.

Static output feedback H∞ control for active suspension system with input delay and parameter uncertainty

This article focuses on static output feedback [Formula: see text] control for active suspension system with input delay and parameter uncertainty. The parameter uncertainty of active suspension system model, input delay of actuator, input disturbance of road, and measurement output disturbance are simultaneously introduced in active suspension system. A kind of static output feedback [Formula: see text] controller is designed, which can consider the above factors, simultaneously. First of all, the mathematical model of quarter-vehicle active suspension system and the system state equation are established. Second, the static output feedback [Formula: see text] controller is designed by employing the Lyapunov–Krasovskii functional for system state equations without or with disturbance. The design problem of static output feedback [Formula: see text] controller for closed-loop system is transformed into the solving problem of linear matrix inequality. Finally, according to the designed controller and the specific vehicle parameters, the simulation model of quarter-vehicle active suspension system is established. And the simulations of three cases, for example, without disturbance, only with input disturbance, and with input disturbance and output disturbance, are exploited to demonstrate the feasibility and effectiveness of the proposed schemes.

Finite‐time distributed global optimal control for linear time‐varying multi‐agent systems: a dynamic output‐feedback perspective

This study presents a systematic procedure to solve the problem of finite-time distributed global optimal control for the leaderless and leader-follower homogeneous multi-agent systems (MASs). Each agent's dynamics is given in general form of continuous-time linear time-varying (LTV) systems. The communication network among the agents is also assumed to be undirected and directed under fixed topology. First, based on asymptotic stability principle, inverse optimal results of general LTV systems are constructed. Second, the necessary and sufficient conditions are given for the existence of the distributed optimal state feedback and optimal dynamic output feedback control that solves a global optimal control problem for MASs. Then, the sufficient condition for finite-time stability of both the state and the output feedback problems for MASs are stated. Finally, some numerical example results are provided to illustrate the effectiveness and applicability of the proposed scheme.

Multiobjective fault‐tolerant fixed‐order/PID control of multivariable discrete‐time linear systems with unmeasured disturbances

SummaryIn this paper, a multiobjective fault‐tolerant fixed‐order output feedback controller design technique is proposed for multivariable discrete‐time linear systems with unmeasured disturbances. Initially, a multiobjective fixed‐order controller is designed for the system by transforming the problem of tuning the parameters of the controller into a static output feedback problem and solving a mixed H2/H∞ optimization problem with bilinear matrix inequalities. Subsequently, the fixed‐order controller is used to construct the closed‐loop system and an active fault‐tolerant control scheme is applied using the input/output data collected from the controlled system. Motivated by its popularity in industry, the proposed method is also used to tune the parameters of proportional‐integral‐derivative controllers as a special case of structured controllers with the fixed order. Two numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed technique.

Static Output Feedback Stabilization of a Class of Switched Linear Systems with State Constraints

This paper will research the problem of static output feedback (SOF) stabilization of state-constrained switched linear systems via an improved average dwell time method (ADT). Firstly, an improved ADT method is adopted to establish sufficient conditions for SOF of the state-constrained switched linear systems in the form of matrix inequality. It has been shown that this method is less conservative than traditional ADT, which in view of different decay rates of a Lyapunov function related to an active subsystem on the basis of whether the saturations occur or not. Then, a new iterative algorithm is designed to solve the matrix inequality and a SOF controller can be added. In the iterative linear matrix inequality (ILMI) algorithm, it is important not only to overcome the typical bilinear matrix inequality (BMI) problem of SOF, but also to solve the non-convex problem caused by state constraints. Finally, the availability and the applicability of the proposed method is shown by the application of a boost converter.

Robust Finite–Time Fault–Tolerant Control of Uncertain Networked Control Systems via Markovian Jump Linear Systems Approach

This paper concerns the problem of static output feedback (SOF) fault–tolerant controller (FTC) design for uncertain networked control systems (NCSs) considering stochastic actuator faults. The NCSs in the presence of random delays and data packet dropouts are firstly modeled as Markovian jump linear systems (MJLSs) with partly unknown transition probabilities (TPs). Afterward, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to ensure finite–time stochastic stability (FTSS) of the closed–loop system. The Simulation results demonstrate the effectiveness and reliability of the controller.

Tensor Product model based PID controller optimisation for propofol administration

This study investigates the computer-regulated propofol administration in anesthesia during medical interventions considering output feedback and robust PID control. The paper applies the Affine Tensor Product Model Transformation to derive the appropriate polytopic quasi-LPV representation of the closed-loop dynamics. This model form enables the use of LMI-based optimisation techniques to evaluate the closed loop performance. Despite the highly non-convex nature of this output feedback problem, the PID gains can be locally tuned through simplex optimisation. The proposed method provides a systematic way of tuning PID-controlled propofol administration for individual patients with theoretically established worst-case performance measures.

Dynamic output‐feedback stabilisation for Markovian jump systems with incomplete transition description and input quantisation: linear matrix inequality approach

In this study, a dynamic output-feedback stabilisation problem for Markovian jump systems (MJSs) with incomplete transition description and input quantisation is investigated. While the previous researches about output-feedback stabilisation for MJSs assumed that the transition rates are completely known, a more general situation where the transition rates are partly unknown is considered. Moreover, the proposed controller includes non-linear control part to eliminate the effect of input quantisation. Two numerical examples are provided to demonstrate the feasibility of the proposed dynamic output-feedback controller.

Gain-scheduled static output feedback controller synthesis for discrete-time LPV systems

ABSTRACTThis study is concerned with the problem of gain-scheduled static output feedback H∞ controller synthesis for discrete-time linear parameter varying systems. The scheduling parameters, which may affect all the system matrices, and their deviations are supposed to lie in a known hyper-rectangle. A design procedure is presented in terms of sequentially solving three parameter-dependent linear matrix inequality (LMI) optimisation problems. The parameter-dependent LMIs are solved through finite-dimensional LMI relaxations exploiting homogeneous polynomial matrices of arbitrary degree. One of the advantages of the new method lies in its less conservatism which is theoretically shown in comparison with some available approaches. By an iterative scheme, the performance of the method can be improved. Numerical examples reveal the effectiveness of the new method.

Guest editorial: special issue on Consensus‐based Applications in Networked Systems

Guest editorial: special issue on Consensus‐based Applications in Networked Systems

Output Feedback Distributed Containment Control for High-Order Nonlinear Multiagent Systems.

In this paper, we study the problem of output feedback distributed containment control for a class of high-order nonlinear multiagent systems under a fixed undirected graph and a fixed directed graph, respectively. Only the output signals of the systems can be measured. The novel reduced order dynamic gain observer is constructed to estimate the unmeasured state variables of the system with the less conservative condition on nonlinear terms than traditional Lipschitz one. Via the backstepping method, output feedback distributed nonlinear controllers for the followers are designed. By means of the novel first virtual controllers, we separate the estimated state variables of different agents from each other. Consequently, the designed controllers show independence on the estimated state variables of neighbors except outputs information, and the dynamics of each agent can be greatly different, which make the design method have a wider class of applications. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed method.

Output Containment Control of Linear Heterogeneous Multi-Agent Systems Using Internal Model Principle.

This paper studies the output containment control of linear heterogeneous multi-agent systems, where the system dynamics and even the state dimensions can generally be different. Since the states can have different dimensions, standard results from state containment control do not apply. Therefore, the control objective is to guarantee the convergence of the output of each follower to the dynamic convex hull spanned by the outputs of leaders. This can be achieved by making certain output containment errors go to zero asymptotically. Based on this formulation, two different control protocols, namely, full-state feedback and static output-feedback, are designed based on internal model principles. Sufficient local conditions for the existence of the proposed control protocols are developed in terms of stabilizing the local followers' dynamics and satisfying a certain H∞ criterion. Unified design procedures to solve the proposed two control protocols are presented by formulation and solution of certain local state-feedback and static output-feedback problems, respectively. Numerical simulations are given to validate the proposed control protocols.

Higher Accuracy Output Feedback Sliding Mode Control of Sampled-Data Systems

The problem of output feedback sliding mode control for sampled-data systems in the presence of external disturbances is considered. The proposed output feedback control strategy helps obtain a quasi sliding mode with an $O(T^{3})$ boundary layer, where $T$ is the sampling period. This outperforms the $O(T^{2})$ result induced by the one-step delayed disturbance approximation method. The proposed scheme is applicable to linear systems which are relative degree one and minimum phase. An example is given to illustrate the efficacy of the new method.

Finite-time observer-based backstepping control of a flexible launch vehicle

In this paper, a longitudinal model of a space launch vehicle was developed using the Lagrange mechanism and a free–free Euler–Bernoulli beam model. The aim was to propose a model including one flexible mode plus a nonlinear aerodynamic coefficient for nonlinear control design. We then studied the output feedback problem raised by using such a nonlinear model. The main achievement is to propose a new finite-time state observer when the measured outputs are corrupted by an unidentified flexible mode. This effect may destabilize a classical backstepping control law applied to the rigid model. To achieve this, a backstepping control law was redesigned to damp out the flexible mode, once measured and characterized. Hence a new adaptive finite time observer was developed. Closed-loop simulations show the effectiveness of the observer in combination with a redesigned backstepping control law when sensors and the launcher nozzle are collocated.

Output-feedback adaptive optimal control of interconnected systems based on robust adaptive dynamic programming

This paper studies the adaptive and optimal output-feedback problem for continuous-time uncertain systems with nonlinear dynamic uncertainties. Data-driven output-feedback control policies are developed by approximate/adaptive dynamic programming (ADP) based on both policy iteration and value iteration methods. The obtained adaptive and optimal output-feedback controllers differ from the existing literature on the ADP in that they are derived from sampled-data systems theory and are guaranteed to be robust to dynamic uncertainties. A small-gain condition is given under which the overall system is globally asymptotically stable at the origin. An application to power systems is given to test the effectiveness of the proposed approaches.

Boundary feedback stabilisation for the time fractional‐order anomalous diffusion system

In this study, the authors attempt to explore the boundary feedback stabilisation for an unstable heat process described by fractional-order partial differential equation (PDE), where the first-order time derivative of normal reaction–diffusion equation is replaced by a Caputo time fractional derivative of order α∈(0, 1]. By designing an invertible coordinate transformation, the system under consideration is converted into a Mittag–Leffler stability linear system and the boundary stabilisation problem is transformed into a problem of solving a linear hyperbolic PDE. It is worth mentioning that with the help of this invertible coordinate transformation, they can explicitly obtain the closed-loop solutions of the original problem. The output feedback problem with both anti-collocated and collocated actuator/sensor pairs in one-dimensional domain is also presented. A numerical example is given to test the effectiveness of the authors' results.

A Static Output Feedback Approach for Inverting a Dynamic System

Inverting a state-space system A,B,C,D is a problem implying that the transmission zeros, of the system we want to invert, lie in the open left half plane. This is solved by finding an appropriate D matrix. We will show that finding D turns into a static output feedback problem, that can be addressed by solving a non-convex problem of rank minimization under LMI constrains. A numerical example will show the effectiveness of this approach.

Global output feedback sampled‐data stabilization for upper‐triangular nonlinear systems with improved maximum allowable transmission delay

SummaryThis paper addresses the problem of output feedback sampled‐data stabilization for upper‐triangular nonlinear systems with improved maximum allowable transmission delay. A class of hybrid systems are firstly introduced. The transmission delay may be larger than the sampling period. Then, sufficient conditions are proposed to guarantee global exponential stability of the hybrid systems. Based on these sufficient conditions and a linear continuous‐discrete observer, an output feedback control law is presented to globally exponentially stabilize the feedforward nonlinear system. The improved maximum allowable transmission delay is also given. The results are also extended to output feedback sampled‐data stabilization for lower‐triangular nonlinear systems. Finally, illustrative examples are used to verify the effectiveness of the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.

Decentralised output-feedback control design for switched fuzzy large-scale systems

ABSTRACTThis paper investigates the output-feedback control design problem for a class of switched Takagi–Sugeno fuzzy large-scale systems with non-measurable premise variables. The considered fuzzy large-scale systems consist of several interconnected subsystems with different switching modes and there exists the asynchronous switching between the system switching modes and the controller switching modes. A decentralised state observer is proposed to estimate the unmeasured states, and a new output-feedback decentralised control scheme is developed by using the state observers and the switching functions. Based on the theory of Lyapunov stability and average dwell-time methods, the sufficient conditions of ensuring the switched control system stability are proposed and proved, which are formulated in the form of linear matrix inequalities. An applicable example is provided to show the effectiveness of the obtained theoretical results.

Robust static output feedback infinite horizon RMPC for linear uncertain systems

This work studies the problem of static output feedback (SOF) infinite horizon robust model predictive control (RMPC) for linear uncertain systems with input constraints. In contrast with the existing RMPC design methods, this approach computes the vector of control actions directly from the observed variables while the system states are unmeasurable. For the unavailable states, an ellipsoidal set is used to obtain an estimation and applied in the RMPC optimization problem. This set is updated at every time instant which may cause the loss of the recursive feasibility. In order to handle this drawback, a new design condition is adopted. Then, the design method is formulated in terms of a convex optimization problem with linear matrix inequality (LMI) constraints. The effectiveness of the proposed RMPC method is demonstrated by a numerical example.