Time-varying Output Feedback Research Articles

Output Feedback Observability of Switched Boolean Control Networks

This paper investigates the output feedback observability of switched Boolean control networks. According to time-varying output feedback (TVOF) and time-invariant output feedback (TIOF) controls, six types of observability are proposed and their relation is discussed. A technique called parallel extension and a new system named induced logical dynamic system are developed. Based on them, some necessary and sufficient conditions are obtained for these TVOF and TIOF observabilities. In addition, the relation between output feedback observability and the existing results about observability is analyzed. Furthermore, some examples are given to illustrate the validity of the main results.

Time-varying output feedback H∞ control for switched systems based on mixed switching

This article investigates time-varying dynamic output feedback H∞ control problem for discrete-time switched systems by using a time-varying Lyapunov function. A switching rule that depends on available information provided by measured output and time simultaneously is designed for the system with all unstable subsystems. Conditions for l 2-gain performance and time-varying controller synthesis are obtained under this switching rule. It provides a more general framework of analyzing discrete-time switched linear systems as it contains the min-switching as special cases when dwell time is not enforced. Finally, an example shows the effectiveness of the proposed method.

Simultaneous fault detection and control for discrete-time switched systems under relaxed persistent dwell time switching

This paper investigates the problem of robust control and fault detection for discrete-time switched systems. The main goals are to design controller/fault detectors and a switching rule to guarantee the control and detection objectives simultaneously. The switching rule is constructed based on persistent dwell time (PDT) with an average dwell time (ADT) constraint. The introduced ADT constraint can allow a much smaller PDT lower bound to be designed, which provides more freedom of designing switching signal. Next, some time-varying dynamic output feedback controllers/detectors matching different switching processes of PDT are constructed such that the closed-loop systems meet the desired objectives. The corresponding robust control and fault detection levels can be characterized by a class of non-weighted performance indexes. Finally, the effectiveness of the proposed results is illustrated by an example.

Leonov’s Method of Nonstationary Stabilization in the Theory of Linear Control Systems

A brief review on stabilization problem for linear control systems is presented. The statements of Pyragas’ and Brockett’s problems for stabilization of linear control systems by time-delayed feedback control and time-varying static output feedback are given. Leonov’s algorithms of nonstationary stabilization for solutions of Pyragas’ and Brockett’s problems are presented. Necessary and sufficient conditions for the stabilizability of two- and three-dimensional systems are given.

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.

Time-varying controller design for input saturated systems

This paper presents a time-varying controller design for input saturated system whose poles are all in the closed left-half plane by introducing a time-varying parameter. The time-varying state feedback controller and the observer-based time-varying output feedback controller are both designed based on the parametric Riccati equation and parametric Lyapunov equation to ensure the exponential stability of the closed-loop system. The dynamic performance improvement of the closed-loop system is obtained by the designed controllers. The effectiveness and the usefulness of the proposed method are illustrated by the numerical simulation.

Output feedback robust stabilisation for uncertain non‐linear systems with dead‐zone input

This study considers the output feedback robust stabilisation problem of non-linear systems with actuator non-symmetric dead zone and uncertain non-linearities including unmeasured states. Instead of constructing the dead-zone inverse, a robust control scheme is proposed. In particular, an input-driven observer is constructed, which uses the scaling gain to dominate non-linear terms. Based on non-separation principle and backstepping method, a time-varying and smooth output feedback controller is obtained to ensure that the resulting closed-loop systems are globally asymptotically stable. Also, the control scheme is generalised to more general non-linear systems in a lower triangular form. Finally, two examples are given to illustrate the effectiveness of the authors' results.

Control design with guaranteed transient performance: An approach with polyhedral target tubes

In this paper a novel approach is presented for control design with guaranteed transient performance for multiple-input multiple-output discrete-time linear polytopic difference inclusions. We establish a theorem that gives necessary and sufficient conditions for the state to evolve from one polyhedral subset of the state-space to another. Then we present an algorithm which constructs a time-varying output feedback law which guarantees that the state evolves within a time-varying polyhedral target-tube specifying the system’s desired transient performance. We present generalisations involving constraints on the control, and a bounded additive disturbance term. Our formulation is very general and includes reference tracking with any desired transient behaviour in the face of disturbances, as specified, for example, by the most popular step response specifications. The approach is demonstrated by an example involving the control of water levels in two coupled tanks.

Global feedback stabilisation of lower-triangular nonlinear systems in any prescribed finite time

In this paper, global state feedback and output feedback stabilisation problems are considered for a class of time-varying lower-triangular nonlinear systems in any prescribed finite time. The nonlinear terms admit an incremental rate depending on a time-varying continuous function. Firstly, by introducing a novel state transformation consisting of a time-varying gain and a scaling of the state by a function of time that grows unbounded towards the terminal time, the involved system is transformed into a new one easily designing a feedback controller. Then based on the Lyapunov theorem and choosing the time-varying gain, both state feedback and output feedback controllers are constructed respectively to globally stabilise the new system in the scaled state representation, yielding the global feedback stabilisation in any prescribed finite time of the involved system. Simulation examples are given to demonstrate the effectiveness of the proposed control strategies.

New Passivity Conditions for Linear Time Varying Output Feedback Systems

The paper presents new passivity conditions for square linear time varying (LTV) output feedback systems. The new conditions enable the formulation of a new simple test for almost strict passivity, which is necessary for the closed loop to be output strictly passive. The new test requires the solution of an algebraic Riccati equation in the linear time invariant (LTI) case and the solution of a forward differential Riccati equation in the LTV case. The proposed test simplifies the synthesis and design of output strictly passive systems. The examples discussed in the paper demonstrate the efficiency of the test.

A time-varying high-gain approach to feedback regulation of uncertain time-varying nonholonomic systems

In this paper, novel state feedback and output feedback control strategies are proposed to regulate a class of uncertain time-varying nonholonomic systems with lower-triangular nonlinearities. The nonlinearities admit an incremental rate depending on an unknown parameter and an essential time-varying function. By means of the input-state-scaling technique, the involved systems are firstly transformed into a class of lower-triangular systems. The time-varying high-gain method is then introduced to tackle the system uncertainties and essential time-varying features simultaneously, and based on this, the time-varying state feedback controllers are constructed to achieve the state feedback regulation of the involved systems. Finally a time-varying high-gain observer is proposed to effectively compensate for system uncertainties and essential time-varying features, and on the basis of this, the time-varying output feedback controllers are constructed to achieve the output feedback regulation of the involved systems. Two illustrative examples are provided to demonstrate the effectiveness of the proposed control strategies.

Velocity-free spacecraft attitude stabilization using two control torques

The attitude stabilization of an inertial-pointing underactuated rigid-body spacecraft using two torques under time-varying disturbances and inertia matrix uncertainties is examined. An observer-based time-varying output feedback control law is proposed where angular velocity measurements are not available. The stability of the combined controller–observer system is proven rigorously to show local ultimate boundedness of all states. A comprehensive numerical example is presented with sampled-data implementation of the observer-based control law to demonstrate convergence even with very large initial attitude errors.

An adjoint network approach to design stabilizable switching signals of switched Boolean networks

In this paper, two kinds of stabilizability of switched Boolean networks (SBNs), consistent stabilizability and stabilizability under time-varying output feedback (TVOF), are investigated on the basis of adjoint logical networks (ALNs), which are constructed via switching signals. Firstly, globally consistent stabilizability of SBNs is equivalently converted into local (one state) pointwise stabilizability of ALNs, under which all suitable finite-time switching signals can be designed. Then the method is generalized to design stabilizable TVOF switching signals. Finally, to show the effectiveness of obtained results, two types of stabilizability of a shift register are discussed.

Non-fragile consensus control for nonlinear multi-agent systems with uniform quantizations and deception attacks via output feedback approach

In this paper, we handle the non-fragile consensus control problem for a class of discrete time-varying nonlinear multi-agent systems with uniform quantization and randomly occurring deception attacks. The quantization error is described by a noise distributed uniformly in certain interval, and the phenomenon of the randomly occurring deception attacks is depicted by the Bernoulli distributed random variables with known probabilities. Here, the measurement output utilized in the controller side is not only from a single agent itself, but also from its adjacent agents, where the corresponding transmissions are carried out under a given topology. In particular, the controller gain perturbations are characterized by the multiplicative noises. We focus on the design of non-fragile time-varying output feedback controller such that, when the randomly occurring deception attacks, uniform quantization effects as well as controller gain perturbations exist simultaneously, and the desired consensus performance is guaranteed by designing the controller parameters. Accordingly, a sufficient condition is derived to ensure the existence of the desired control scheme, where the feasibility of conducted problem can be tested by solving a set of matrix inequalities. Moreover, the optimal consensus performance is addressed by employing an optimization problem. Finally, we utilize the simulations to illustrate the feasibility of the proposed output feedback control strategy.

Global stabilisation via time-varying output feedback for the systems with inherent nonlinearities and coarse disturbance

ABSTRACTThis paper is devoted to the global output-feedback stabilisation for a class of nonlinear systems with inherent nonlinearities and coarse disturbance. Remarkably, the disturbance may be non-periodic, non-differentiable and/or of unknown magnitude, and hence some critical requirements on the disturbance in the existing related literature are successfully removed. Recognising that the strategies of disturbance compensation, such as internal model principle, sliding mode control method, learning method and active disturbance rejection control method, are quite hard or even impossible to apply, a time-varying design scheme is developed in the paper. Moreover, the serious unknowns and time-variations reflected in the growth rate of the system are also dealt with by the proposed scheme. By designing a time-varying output-feedback controller, all the signals of the resulting closed-loop system are globally bounded, and the original system state and the observer state ultimately converge to zero.

Output feedback stabilization of stochastic feedforward systems with unknown control coefficients and unknown output function

This paper investigates the problem of output feedback control for a class of stochastic feedforward systems with unknown control coefficients and unknown output function. Since many unknowns occur into the systems, all the states of the systems are unmeasurable or unknown which means that they are not available in the control scheme. To compensate these unmeasurable/unknown states, a new form of K-filters with time-varying low-gain is introduced in our design. As long as output function belongs to any close sector included in the maximal sector region of systems’ output function, we can design a time-varying output feedback control law by integrating the well-known backstepping framework with the time-varying technique. Later, based on the improved LaSalle-type theorem, we analyze the regulation of the closed-loop systems. Finally, an induction heater circuit system with unknown inductance/capacitance is given to show the effectiveness of our control scheme.

Mean-Square $H_\infty $ Consensus Control for a Class of Nonlinear Time-Varying Stochastic Multiagent Systems: The Finite-Horizon Case

This paper deals with the consensus control problem for a class of nonlinear discrete time-varying stochastic multiagent systems (MASs) over a finite horizon via static output feedback. The measurement output available for the controller is not only from the individual agent itself but also from its neighboring ones according to the given topology. The nonlinearities described by statistical means can encompass several classes of well-studied nonlinearities in the literature. A new index of mean-square consensus performance, which quantifies the deviation level from the state of individual agent to the average value of all agents’ states, is proposed to reflect the transient consensus behavior of the MAS. The purpose of the addressed problem is to design a time-varying output feedback controller such that: 1) the ${H}_{\infty }$ consensus performance defined over a given finite horizon is guaranteed with respect to the additive noises and 2) at each time step, the mean-square consensus performance satisfies the prespecified upper bound constraint. By using a set of recursive matrix inequalities, sufficient conditions are derived for the existence of the desired control scheme for achieving both $H_{\infty }$ and mean-square consensus performance requirements. Finally, a simulation example is utilized to illustrate the usefulness of the proposed control protocol.

Output Feedback Passification of Saturated Switched Systems Under the Improved State-Dependent Switching

This paper focuses on the passivity analysis and feedback passification of discrete-time switched systems with actuator saturation. The proposed framework consists of a switching law and a bank of time-varying output feedback controllers. The switching law is depending on partial state measurements and switching-delay slack matrix, which avoid the possible too frequent switching caused by the classical state-dependent switching law. The resulting time-varying saturated controllers associated with the switching law are constructed to guarantee the passivity of the closed-loop systems. In addition, the performance index measuring the level of unknown input tolerance capacity of the systems can be also estimated. Sufficient conditions for the existence of the switching law and controllers are provided via Lyapunov---Metzler inequalities. Finally, the effectiveness of the theoretical results is illustrated through an example derived from the stirred tank reactor.

Variance-constrained [formula omitted] control for a class of nonlinear stochastic discrete time-varying systems: The event-triggered design

In this paper, a general event-triggered framework is set up to deal with the variance-constrained H∞ control problem for a class of discrete time-varying systems with randomly occurring saturations, stochastic nonlinearities and state-multiplicative noises. Based on the relative error with respect to the measurement signal, an event indicator variable is introduced and the corresponding event-triggered scheme is proposed in order to determine whether the measurement output is transmitted to the controller or not. The stochastic nonlinearities under consideration are characterized by statistical means which can cover several classes of well-studied nonlinearities. A set of unrelated random variables is exploited to govern the phenomena of randomly occurring saturations, stochastic nonlinearities and state-dependent noises. The purpose of the addressed multiobjective control problem is to design a set of time-varying output feedback controller such that, over a finite horizon, the closed-loop system achieves both the prescribed H∞ noise attenuation level and the state covariance constraints. A recursive matrix inequality approach is developed to derive the sufficient conditions for the existence of the desired finite-horizon controllers, and the analytical characterization of such controllers is also given. Simulation studies are conducted to demonstrate the effectiveness of the developed controller design scheme.

Global output-feedback stabilization for high-order nonlinear systems with unknown growth rate

Summary This paper considers the global stabilization via time-varying output-feedback for a class of high-order uncertain nonlinear systems with rather weak assumptions. Essentially different from the existing literature, the systems under investigation simultaneously have more serious nonlinearities, unknowns, immeasurableness, and time-variations, which are indicated from the unknown time-varying control coefficients and the higher-order and lower-order unmeasured states dependent growth with the rate of unknown function of time and output. Recognizing that adaptive technique is quite hard to apply, a time-varying design scheme is proposed by combining time-varying approach, certainty equivalence principle and homogeneous domination approach. One key point in the design scheme is the selection of the design functions of time, in order to compensate/capture the serious unknowns and serious time-variations, and another one is the design of a time-varying observer to rebuild the unmeasured system states. With the appropriate choice of the involved design functions, the designed controller makes all the signals of the closed-loop system globally bounded and ultimately converge to zero. Copyright © 2016 John Wiley & Sons, Ltd.