Full-order Dynamic Output Feedback Research Articles

A new approach for dynamic output feedback control design of time-delayed nonlinear systems

This paper introduces a full-order dynamic output-feedback (DOF) controller for discrete-time nonlinear systems with time-varying delays represented by Linear Parameter-Varying (LPV) systems. The controller design is carried out by developing delay-dependent Linear Matrix Inequality based conditions using Lyapunov–Krasovskii stability arguments. A notable characteristic of the proposed approach is that the dynamic controller gains are directly obtained, without the need for variable transformations, equality constraints, or iterative algorithms. This feature sets it apart from many existing approaches in the literature and simplifies the design process. Furthermore, the proposed approach guarantees the local asymptotic stability of the origin of the closed-loop system and provides an estimated admissible initial condition region. The correct operation of the system is ensured once the state trajectories initiated within the admissible initial condition region remain enclosed in the validity domain of the LPV model. Numerical examples are provided to illustrate the potential and effectiveness of the proposed conditions.

Fuzzy Dynamic Output Feedback Force Security Control for Hysteretic Leaf Spring Hydro-Suspension With Servo Valve Opening Predictive Management Under Deception Attack

This article addresses the hierarchical resilient event triggered sampled-data security control and valve opening management problem for networked hysteretic leaf spring hydro-suspension with asymmetric actuator under false injected deception attack. For the derived Takagi–Sugeno (T–S) fuzzy model employed to tackle hysteresis nonlinearity, a new full-order dynamic output feedback top control with improved error and threshold functions for resilient event triggered mechanism is proposed to generate the target force so as to suppress the body and tire vibration under limited suspension chatter space. For the asymmetric cylinder hydraulic actuator over actuated by multiple servo valves, optimal servo valve openings are dynamic regulated to track the target force with weight adaptive nonlinear model predictive lower control. Benefiting from saved communication resource while more sparsely generating piecewise target force, as well as precise regulation by reasonably allocating over actuated valve openings to produce required force, the obtained results indicating more comfortable ride performance and less tire dynamic loads within smaller suspension chatter space favorably demonstrate the effectiveness of the proposed control strategy.

Dynamic Output Feedback Controller Design for Uncertain Takagi–Sugeno Fuzzy Systems: A Premise Variable Selection Approach

This article presents new design conditions of full-order dynamic output feedback controllers for continuous-time Takagi–Sugeno (T–S) fuzzy systems allowing the selection of premise variables to be used in the control law. The fuzzy output controller is allowed to have a different number of fuzzy rules and a different set of membership functions from the T–S model. This includes the cases of complete or partial immeasurable premise variables. The main aspect of the proposed methodology is to present conditions such that the control gains are independent of the premise variables that cannot be measured allowing flexibility for the designer in a realistic output feedback context. For this purpose, the design conditions are expressed as linear matrix inequality relaxations combined with scalar parameters that provide extra degrees of freedom. The proposed control methodology also deals with model uncertainties and the use of fuzzy Lyapunov functions. The effectiveness and applicability of the methodology are shown through numerical examples.

Robust l2−l∞ dynamic output feedback control design for uncertain discrete‐time switched systems with random time‐varying delay

SummaryThis article deals with the problem of robust output feedback control design for a class of switched systems with uncertainties and random time‐varying delay. Our purpose is focused on designing a full order dynamic output feedback controller and an appropriate switching rule to ensure the exponential mean square stability of the resulting closed‐loop switching system with an l2−l∞ performance level. The appealing aspects of the proposed control scheme include: (a) the development of LMI based delay‐dependent sufficient conditions for the exponential stability analysis of the stochastic hybrid systems using the appropriate choice of the augmented Lyapunov–Krasovskii functional, the partitioning technique and the average dwell time, (b) conservatism reduction of the unified design conditions, and (c) the controller designed exhibiting robustness with l2−l∞ performance against uncertainties and external disturbance. Finally, representative examples are given to demonstrate the validity and the merit of the proposed design technique.

H∞ Dynamic Output Feedback Controller Design For Disturbed Fractional-Order Systems

In this work, the synthesis of a full order dynamic output feedback controller (DOFC) for Fractional-Order Systems with a derivative order 1 < α < 2 under norm-bounded disturbances is investigated. The designed DOFC must ensure the internal stability of the closed loop system and satisfy a disturbance rejection criterion which quantifies the disturbances effect on the desired output. This kind of problems is referred as H∞ control. The existence conditions and design of DFOS are given. An LMI-based minimization problem is derived based on the H∞-norm computation for fractional order systems. Finally, simulation results are presented to illustrate the performance of the proposed methodology.

Robust H∞ dynamic output feedback control for spacecraft rendezvous with poles and input constraint

ABSTRACTThis paper is concerned with the output feedback control problem for spacecraft rendezvous subject to target angular velocity uncertainty and controller uncertainty, external disturbance and input constraint. A general full-order dynamic output feedback (DOF) controller is proposed. As a stepping-stone, the H∞ performance requirement, poles and input constraint are analysed separately via linear matrix inequalities (LMIs). Then, with the obtained results, the controller design problem is cast into a convex problem subject to a set of LMI constraints through a critical change of controller variables. Furthermore, when the system states are all available, a reduced sufficient condition of the non-fragile state feedback controller is given. Compared with existing results, the designed controller has overcome the disadvantage of strictly proper DOF controller, where the initial value of the control input is zero. Besides, the constraint on poles placement is relaxed. A numerical simulation is performed to verify the effectiveness of the proposed method.

Full-Order Dynamic Output-Feedback Compensator for Time-Stamped Networked Control Systems

We present a method for the synthesis of a full-order dynamic output-feedback compensator for time-stamped Networked Control Systems (NCS). The methodology is obtained from the use of a polytopic approximation for the NCS representation, based on the exact discretization of the originally linear time-invariant system. The dynamics of the proposed compensator depends on the delays induced by the network, which are considered not to be greater than the sampling period and can be computed from information provided by time-stamped messages. A parameter-dependent Lyapunov function is associated to the closed-loop system to ensure stability and some time-performance. The synthesis of the compensator is described in terms of Linear Matrix Inequalities. Some numerical experiments are proposed to illustrate the applicability of the methodology.

Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T–S fuzzy approach

By utilising Takagi–Sugeno (T–S) fuzzy set approach, this paper addresses the robust H∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics’ enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T–S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T–S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.

Simultaneous fault detection and control for stochastic time-delay systems

This paper is concerned with the simultaneous fault detection and control problem for Itô-type stochastic time-delay systems. A full-order dynamic output feedback controller is designed to achieve the desired control and detection objectives. The main contributions of this paper are as follows: (1) for stochastic time-delay systems, the controller design with multiple objectives can be addressed by employing the multiple Lyapunov functions approach, (2) the dynamic output feedback controller synthesis conditions described by linear matrix inequalities (LMIs) are derived and (3) within the proposed fault detection and control framework, a better integrated control and detection performance can be obtained. Some numerical examples including the comparison results are presented to show the advantages of the proposed method.

Robust H ∞ output feedback control with pole placement constraints for uncertain discrete-time fuzzy systems

This paper investigates the problem of multi-objective control for a class of uncertain discrete-time fuzzy systems. The state-space Takagi---Sugeno T---S fuzzy model with linear fractional parameter uncertainties is adopted. Based on a linear matrix inequality approach and via so-called dynamic parallel distributed compensation, a fuzzy full-order dynamic output feedback controller is developed such that the L 2 gain performance from the exogenous input signals to the controlled output is less than or equal to some prescribed value and, for all admissible uncertainties, the closed-loop poles of each local system are within a pre-specified sub-region of complex plane. Two numerical examples are provided to illustrate the effectiveness of the proposed design method.

Reduced-order dynamic output feedback control of continuous-time T–S fuzzy systems

The problem of reduced-order dynamic output feedback control design for continuous-time Takagi–Sugeno fuzzy systems with H∞ guaranteed cost is addressed. The proposed approach is based on a line-integral fuzzy Lyapunov function with arbitrary polynomial dependence on the premise variables, allowing the membership functions, modeled as multi-simplexes, to vary arbitrarily. The controller is obtained by transforming the problem into a static output feedback control design problem solved by means of a two-stages linear matrix inequality procedure. The main appeal of the approach is that the order of the output feedback controller as well as the dependence of the premise variables are customizable for control implementation purposes. Examples illustrate the flexibility of the method and also that the proposed strategy can provide less conservative results when compared to other methods for full order dynamic output feedback controllers from the literature of continuous-time Takagi–Sugeno fuzzy systems.

Dynamic output feedback control synthesis for stochastic time-delay systems

This article deals with the dynamic output feedback control synthesis problem for Itô-type stochastic time-delay systems. Our aim is to design a full order dynamic output feedback controller to achieve the desired control objectives. We will formulate the controller design problem as an H ∞ optimisation problem in the mean-square sense. The main contributions of this article are as follows: (i) for stochastic systems, the design of a controller with multiple objectives can be addressed without employing a unique Lyapunov function; (ii) using an inequality technique and Finsler Lemma, we provide convex controller synthesis conditions described by linear matrix inequalities (LMIs). Some examples are presented to show the effectiveness of the developed theoretical results.

Dynamic output feedback control for Markovian jump systems with time-varying delays

This study investigates the problems of delay-dependent H∞ output feedback control for Markovian jump systems with time-varying delays. Firstly, the improved delay-dependent stochastic stability is obtained by constructing a new Lyapunov–Krasovskii functional. Neither free-weighting matrix approach nor model transformation is involved in the derivative of the criterion. Then, a new bounded real lemma (BRL) for Markovian jump systems is established. Based on the proposed BRL, a full-order dynamic output feedback controller is designed to ensure the stochastic stability and a prescribed H∞ performance level for the closed-loop systems. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed approaches.

Dynamic output feedback [formula omitted] control of switched linear systems

This paper is devoted to dynamic output feedback H ∞ control design of switched linear systems in both continuous and discrete-time domains. More specifically, the main purpose is to jointly design a switching rule and a full order dynamic output feedback switched controller that render the associated closed-loop switched linear system globally asymptotically stable and impose a pre-specified upper bound to the L 2 gain. An example of practical importance is presented to illustrate the validity and efficiency of the theory.

H ∞ output feedback control for stochastic systems with mode-dependent time-varying delays and Markovian jump parameters

This paper deals with the H∞ control problems of Markovian jump systems with mode-dependent time delays. First, considering the mode-dependent time delays, a different delay-dependent H∞ performance condition for Markovian jump systems is proposed by constructing an improved Lyapunov-Krasovskii function. Based on this new H∞ disturbance attenuation criterion, a full-order dynamic output feedback controller that ensures the exponential mean-square stability and a prescribed H∞ performance level for the resulting closed-loop system is designed. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.

New Dilated LMI Characterization for the Multiobjective Full-Order Dynamic Output Feedback Synthesis Problem

This paper introduces new dilated LMI conditions for continuous-time linear systems which not only characterize stability and performance specifications, but also, performance specifications. These new conditions offer, in addition to new analysis tools, synthesis procedures that have the advantages of keeping the controller parameters independent of the Lyapunov matrix and offering supplementary degrees of freedom. The impact of such advantages is great on the multiobjective full-order dynamic output feedback control problem as the obtained dilated LMI conditions always encompass the standard ones. It follows that much less conservatism is possible in comparison to the currently used standard LMI based synthesis procedures. A numerical simulation, based on an empirically abridged search procedure, is presented and shows the advantage of the proposed synthesis methods.

Robust H∞ control for uncertain delayed nonlinear systems based on standard neural network models

A neural-network-based robust output feedback H ∞ control design is suggested for control of a class of nonlinear systems both with time delays and with uncertainties. In this paper, a full-order dynamic output feedback controller is designed for the delayed uncertain nonlinear system approximated by the neural network (e.g. multilayer perceptron, recurrent neural network, etc.), of which the activation functions satisfy the sector conditions. The closed-loop neural control system is transformed into a novel neural network model both with uncertainties and with time delays termed standard neural network model (SNNM). Based on the optimal robust H ∞ performance analysis of the SNNM, the parameters of output feedback controllers can be obtained by solving some linear matrix inequalities (LMIs). The optimal H ∞ controller ensures the robust global asymptotic stability of the closed-loop system and eliminates the effect of approximation errors, parametric uncertainties, and external disturbances. Finally, a simple example is presented to illustrate the effectiveness and the applicability of the proposed design approach.

Dynamic output feedback H ∞ control of discrete-time fuzzy systems: a fuzzy-basis-dependent Lyapunov function approach

This article deals with an output feedback H ∞ control problem for a class of discrete-time fuzzy dynamic systems. A full-order dynamic output feedback H ∞ control design approach is developed by combining a fuzzy-basis-dependent Lyapunov function and a transformation on the controller parameters, which leads to sufficient conditions in the form of strict linear matrix inequalities (LMIs). The fuzzy-basis-dependent results are less conservative due to the generality of the fuzzy-basis-dependent Lyapunov function used which includes the fuzzy-basis-independent one as a special case. It has been shown that the underling full-order dynamic output feedback H ∞ control problem can be solved as LMI optimization problems that can be computed numerically very efficiently. Finally, two numerical examples, concerning the control of a discrete-time chaotic Lorenz system and an inverted pendulum, are given to demonstrate the applicability of the proposed approach.

DYNAMIC OUTPUT FEEDBACK STABILIZATION FOR NONLINEAR SYSTEMS BASED ON STANDARD NEURAL NETWORK MODELS

A neural-model-based control design for some nonlinear systems is addressed. The design approach is to approximate the nonlinear systems with neural networks of which the activation functions satisfy the sector conditions. A novel neural network model termed standard neural network model (SNNM) is advanced for describing this class of approximating neural networks. Full-order dynamic output feedback control laws are then designed for the SNNMs with inputs and outputs to stabilize the closed-loop systems. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. It is shown that most neural-network-based nonlinear systems can be transformed into input-output SNNMs to be stabilization synthesized in a unified way. Finally, some application examples are presented to illustrate the control design procedures.

Final comments by the authors

are a little different when it comes for feedback control and packet dropouts between controller and actuator. As demonstrated by [7], depending on the packet dropout rates and the weights of the optimization variable, better results can be obtained with zero-input or with hold-input schemes. Hence, the design of the mode-dependent filter could be simplified by considering a null input whenever a dropout occurs, but some simulation should be done before deciding what the best strategy for the control input is. The output feedback control is built based on an internal model state observer interconnected with a state gain. For themode-dependentH2 control problem, a Separation Principle has been proved by [1], but there is no similar result for the H∞ control problem, to the best of my knowledge. Therefore, it would make more sense to work with a full-order dynamic output feedback controller, as indicated in [4]. Finally, it seems to me that using a limit for the number of consecutive dropouts in the communication channels, indicated in the article as lk and hk , has increased too much the complexity of the problem. By considering an upper bound for that variable, the stochastic nature of the dropout is not Bernoulli anymore and the formulas for the expected values should be different. Moreover, most of the complexity on the Lyapunov function used by the authors comes from the fact that their closed loop system is represented as a discrete-timeMarkov jump systemwith time-delays. In summary, the association of a mode-dependent dynamic output feedback controller with the quantization effects and the discussion of when to apply hold-input or zero-input strategies would be a good direction for future work by the authors, given the developments they have achieved in the article under discussion.