Robust Dynamic Output Feedback Control Research Articles

Robust $H_{\infty }$ Dynamic Output-Feedback Control for CACC With ROSSs Subject to RODAs

This paper is concerned with the problem of dynamic output feedback control design for the cooperative adaptive cruise control (CACC) system with randomly occurring sensor saturations (ROSSs) subject to randomly occurring deception attacks (RODAs). The dynamics of the vehicle equipped with CACC system behave like a linear model in which the deviation of the position and velocity are chosen as the state variables. Sensor saturations and deception attacks are simultaneously taken into account, and two sets of Bernoulli random variables are utilized to characterize their nature of random occurrence. The main objective of this article is to develop a robust dynamic output feedback controller (RDOFC) such that, for all possible parameter uncertainties, sensor saturations as well as deception attacks, all the states can still be exponentially mean square stable and the <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance index is guaranteed. In light of the Lyapunov stability theory, a sufficient condition of the desired controller is firstly constructed, then the controller parameters are obtained relying on the solutions to a set of linear matrix inequalities (LMIs). Finally, the three-car platoon system is evaluated to validate the usefulness of the developed algorithm.

Robust DOF control for uncertain polynomial fuzzy systems in finite frequency domain

This study addresses the issue of robust dynamic output feedback control (DOF) for polynomial Takagi–Sugeno (T–S) fuzzy systems in the Finite Frequency (FF) domain. Sufficient conditions for designing the robust DOF control are derived in terms of the sum of squares (SOS). The proposed strategy is built in the FF domain to reduce conservation-generated by the techniques established in the whole frequency domain. In addition, there are no transformation matrices or equality constraints under these conditions, which simplifies the numerical solution. To show the validity of the suggested technique, several numerical examples are presented.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

Robust dynamic output feedback control of blood glucose level in diabetic rat with robust descriptor Kalman filter

This paper deals with the robust control problem for a model of blood glucose system in Type-1 diabetic rats with disturbances (food, physical activity, and insulin sensitivity parameter) and model uncertainties. The considered model has a special structure, which can be written as a descriptor model. The robust control law is designed such that the output of the system tracks the desired reference signal despite the parameter uncertainties. By utilizing the μ-synthesis-based and H∞ controller design methods, the desired input signals (insulin for injection) are designed for both approaches and compared with each other. Moreover, the control structure is considered in a way that the states are not essential to be directly measured, and instead, the states estimation is utilized which operates in the closed-loop system together with a control law. Due to the existence of the model uncertainties, external disturbances, and also the characteristics of the descriptor system, the robust descriptor Kalman filter is designed for this system. Finally, to demonstrate the efficiency of the proposed methods, they are applied to the model, and simulations are provided. The results show the closed-loop system including the descriptor model, robust controller, and robust descriptor Kalman filter can force the blood glucose level to maintain in the normal range successfully with an acceptable state estimation error.

Continuous-time synthesizing robust sampled-data dynamic output-feedback controllers for uncertain nonlinear systems in Takagi–Sugeno form: A descriptor representation approach

This paper discusses controller design techniques for robust sampled-data dynamic output-feedback (DOF) for nonlinear systems in the Takagi–Sugeno (T–S) fuzzy form with parametric uncertainties and L2/L∞ disturbances. We perform the sampled-data syntheses in a continuous-time domain based on an augmented sampled-data closed-loop model in descriptor form. Hence, the investigation does not require any (approximate) discrete-time model of a T–S fuzzy system, which is a significant obstacle in nonlinear sampled-data control system designs. Moreover, various cross-product terms among system matrices, to-be-designed DOF controller matrices, and other decision variables are reduced, yielding single-stage linear matrix inequality-based design conditions.

Multi-Objective Non-Fragile Robust Attitude Control for Flexible Microsatellite Close-Proximity Inspection

In this paper, the non-fragile robust attitude control problem is investigated for flexible microsatellite close-proximity inspection, with external disturbances, parameter uncertainties and input constraints. Firstly, the attitude motion model of microsatellite with flexible appendages is established. Secondly, a non-fragile robust dynamic output feedback controller (RDOFC) with multiplicative gain variations (MGV) is designed to satisfy the multi-objective requirements, including pole assignment, H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> disturbances attenuation and input constraints. Based on the Lyapunov stability theory, the design of the non-fragile robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> attitude control is formulated as the linear matrix inequality (LMI) condition. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed controller.

Robust linear parameter-varying output-feedback control of permanent magnet synchronous motors

This paper investigates the design of a robust linear parameter-varying (LPV) controller for speed regulation of surface permanent magnet synchronous motors (SPMSMs). Motor dynamics is defined in the α–β stationary frame and a parameter-varying model formulation is provided to describe its nonlinear dynamics. A robust gain-scheduled LPV dynamic output-feedback controller is designed to guarantee the asymptotic stability and performance requirements, as well as, guarantee robustness against parameter perturbations and torque load disturbances. As a novel aspect in the SPMSM control, the real-time impact of temperature variation on the winding resistance and magnet flux during motor operation is explicitly considered in the LPV modeling as a scheduling parameter and the subsequent LPV control design compensating for demagnetization effects in the motor response. The controller synthesis conditions guaranteeing stability and robust performance to norm-bounded uncertainty in the system matrices are formulated in a convex linear matrix inequality (LMI) optimization framework. Finally, the validity of the proposed method is assessed in simulation studies. The closed-loop simulation studies demonstrate that the proposed LPV controller provides improved transient response with respect to settling time, overshoot, and disturbance rejection in tracking the velocity profile under the influence of parameter perturbation, temperature variations, and load disturbances.

Robust $$\mathcal {L}_{\infty }$$–$$l_{\infty }$$ Sampled-Data Dynamic Output-Feedback Control for Uncertain Linear Time-Invariant Systems Through Descriptor Redundancy

We discuss the robust sampled-data dynamic output-feedback controller design problem for linear time-invariant (LTI) systems subject to parametric uncertainties and $$\mathcal {L}_{\infty }$$ disturbances. The descriptor redundancy-based methods are proposed, and their main features are: (i) sampled-data syntheses are performed in a continuous-time domain; (ii) discrete-time modeling of sampled-data systems, which is adversely affected by uncertainties in LTI plant dynamics, is not required; (iii) linear matrix inequality conditions are presented for asymptotic stability and $$\mathcal {L}_{\infty }$$ – $$l_{\infty }$$ disturbance attenuation.

Optimal robust model predictive reset control design for performance improvement of uncertain linear system

This study aims to design a robust reset dynamic output feedback control (DOFC) for a class of uncertain linear systems. This procedure is performed as following. First, the elements of the robust DOFC are designed via the linear matrix inequality (LMI) technique such that closed-loop exponential stability is achieved. Second, reset law which contains value of after reset and a constraint for the reset action is determined. Genetic algorithm (GA) is applied to minimize the proposed objective function to find the reset times by using the specified after reset value for individual reset instances. To do this, a model-predictive-based optimization is adopted by using output information. The proposed robust controller is applied to two uncertain systems; distillation column, and B747-100/200 aircraft model. The merits of the proposed robust reset controller in improving transient performance are demonstrated by comparing its results with state-of-the-art methods.

Robust stabilisation of fractional-order interval systems via dynamic output feedback: an LMI approach

ABSTRACTThis paper addresses the problem of robust dynamic output stabilisation of FO-LTI interval systems with the fractional order , in terms of linear matrix inequalities (LMIs). Our purpose is to design a robust dynamic output feedback controller that asymptotically stabilises interval fractional-order linear time-invariant (FO-LTI) systems. Sufficient conditions are obtained for designing a stabilising controller with a predetermined order, which can be chosen to be as low as possible. The LMI-based procedures of designing robust stabilising controllers are preserved in spite of the complexity of assuming the most complete model of linear controller, with direct feedthrough parameter. Finally, some numerical examples with simulations are presented to demonstrate the effectiveness and correctness of the theoretical results.

LMI relaxations for robust gain‐scheduled control of uncertain linear parameter varying systems

This study deals with the problem of robust gain-scheduled dynamic output feedback control for uncertain discrete-time linear parameter varying systems. The obtained controller guarantees an upper bound on the induced $l_2$l 2 -gain performance of the closed-loop system. The system matrices are assumed to depend polynomially on both the scheduling and uncertain parameters which are supposed to belong to intervals with a priori known bounds. To formulate the design problem in a linear matrix inequality (LMI) setting, a required auxiliary matrix is initially determined using a necessary condition for finding a gain-scheduled controller by the proposed method. Then, a robust gain-scheduled controller is designed by LMI conditions combined with a scalar search using the obtained auxiliary matrix. The method is applied to an inverted pendulum on a cart to illustrate the benefits and applicability of the proposed method.

Dynamic output-feedback control for nonlinear continuous-time systems based on parametric uncertain subsystem and interval type-2 fuzzy model

This paper addresses the interval type-2 fuzzy robust dynamic output-feedback control problem for a class of nonlinear continuous-time systems with parametric uncertainties and immeasurable premise variables. First, the parametric uncertainties are assumed to be a subsystem based on the control input matrix and output matrix, and described as a linear fractional. Secondly, the nonlinear continuous-time systems are described by the interval type-2 fuzzy model. Thirdly, the new dynamic output feedback controller is designed based on the interval type-2 fuzzy model and the linear fractional (parametric uncertainties), the sufficient conditions for robust stabilization are given in the form of linear matrix inequalities (LMIs). Compared with previous work, the developed methods not only have abilities to handle the fuzzy system with immeasurable premise variables but also can deal with the parametric uncertainties effectively. The results are further extended to a mobile robot case and a chemical process case. Finally, two simulation examples are performed to show the effectiveness of the propose methods.

Robust fixed‐order dynamic output feedback controller design for fractional‐order systems

This study deals with designing a robust fixed-order dynamic output feedback controller for uncertain fractional-order linear time-invariant systems by means of linear matrix inequalities (LMIs). The authors’ purpose is to design a low-order controller that stabilises the fractional-order linear system in the presence of model uncertainties. No limiting constraint on the state space matrices of the uncertain system is assumed in the design procedure. Furthermore, adopting the most complete model of linear controller, with direct feedthrough parameter, does not disturb the LMI-based approach of developing robust stabilising control. Eventually, the authors illustrate the advantages of the proposed method by some examples and their numerical simulation.

Output Feedback Control of a Class of Uncertain Systems Under Control-derivative dependent disturbances

This paper addresses the design of robust dynamic output feedback control for highly uncertain systems in which the unknown disturbance might be excited by the derivative of the control input. This context appears in many industrial problems such as the speed control of the hydraulic turbines and the frequency stabilization in micro grids to cite but few examples. A key feature that has to be carefully addressed in this context is that too agressive feedback might lead to the loss of controllability and/or a significant drop in the closed-loop performance. The paper formulates the problem, underlines its relevance and gives a rigorous solution in which a dynamic output feedback is given together with a realistic set of sufficient conditions on the controller’s parameters that enable to assess the behavior of the closed-loop under different circumstances. A numerical example is given to illustrate the relevance of the proposed successful design characterization

A multiobjective robust controller synthesis approach aided by multicriteria decision analysis

This paper proposes a methodology for robust dynamic output-feedback control synthesis of uncertain linear systems represented by polytopic models. This control problem results in a semi-infinite optimization problem. The proposed synthesis procedure improves a previous two-step procedure, composed of synthesis and analysis, by employing both a multiobjective evolutionary algorithm (MOEA) and a multiple criteria decision making (MCDM) strategy in the synthesis step. The analysis stage is performed via a Branch and Bound (B&B) algorithm, enabling the validation of the former step. In the proposed multiobjective approach, the project aim is to meet the specifications of (i) reference signal tracking response, (ii) disturbance rejection and (iii) measurement noise attenuation. The project specifications are quantified in terms of H∞ and H2 norms of closed-loop transfer functions. Essentially, this technique combines the flexibility of a dedicated MOEA together with the minimax semi-infinite programming problem. Since a MOEA evolves a set of candidate solutions in parallel, the suggested strategy provides a diverse set of controller designs, which is very useful for an a posteriori decision-making process. A proposed multicriteria decision-aid strategy is employed, in addition, as a controller design tool, aiming to incorporate the decision-maker preferences throughout the process, which (i) enables a guided evolutionary search to a trade-off region (of solutions) of practical interest and (ii) assists the definition of an adequate final controller, characterized by a reasonable practical trade-off concerning the criteria. The application of the suggested framework is illustrated on three case studies in order to demonstrate the effectiveness of the method presented.

Robust dynamic output feedback control for attitude stabilization of spacecraft with nonlinear perturbations

This paper investigates the robust dynamic output feedback non-fragile control (RDOFNFC) strategy for spacecraft attitude stabilization problem with nonlinear perturbations. The spacecraft attitude dynamics model takes the actuator saturation limits, external disturbances, controller perturbation and model parameter uncertainty into account. To make spacecraft attitude system satisfy H∞ performance and quadratic stability, with respect to the additive perturbation in initial state and multiplicative perturbation in decay phase, the corresponding RDOFNFC is designed respectively. Based on Lyapunov theory, the controller design is transformed into a multi-objective convex optimization problem based on linear matrix inequalities (LMIs). Simulation results based on the on-orbit servicing spacecraft show good performance under external disturbances, model parameter uncertainty and controller perturbation, which validates the effectiveness and feasibility of the proposed control method.

Mixed‐Objective Robust Dynamic Output Feedback Controller Synthesis for Continuous‐Time Polytopic Lpv Systems

AbstractA robust dynamic output feedback controller synthesis algorithm considering H∞/H2 performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.

Reduced-order dynamic output feedback control of uncertain discrete-time Markov jump linear systems

ABSTRACTThis paper deals with the problem of designing reduced-order robust dynamic output feedback controllers for discrete-time Markov jump linear systems (MJLS) with polytopic state space matrices and uncertain transition probabilities. Starting from a full order, mode-dependent and polynomially parameter-dependent dynamic output feedback controller, sufficient linear matrix inequality based conditions are provided for the existence of a robust reduced-order dynamic output feedback stabilising controller with complete, partial or none mode dependency assuring an upper bound to the or the norm of the closed-loop system. The main advantage of the proposed method when compared to the existing approaches is the fact that the dynamic controllers are exclusively expressed in terms of the decision variables of the problem. In other words, the matrices that define the controller realisation do not depend explicitly on the state space matrices associated with the modes of the MJLS. As a consequence, the method is specially suitable to handle order reduction or cluster availability constraints in the context of or dynamic output feedback control of discrete-time MJLS. Additionally, as illustrated by means of numerical examples, the proposed approach can provide less conservative results than other conditions in the literature.

Fuzzy robust dynamic output feedback control of nonlinear systems with linear fractional parametric uncertainties

In this paper, the problem of robust dynamic output feedback control for a class of discrete-time nonlinear systems with parametric uncertainties is studied. The parametric uncertainties are assumed to be of a linear fractional form. First, the Takagi–Sugeno (T–S) fuzzy model is employed to represent the nonlinear system. Then, novel approaches are developed to design the dynamic output feedback controller and sufficient conditions for robust stabilization are obtained in the form of linear matrix inequalities (LMIs). The proposed approaches not only have abilities to effectively handle the parametric uncertainties but also are suitable for the fuzzy system with immeasurable premise variables. Simulation examples are presented to illustrate the design procedures and the effectiveness of the proposed methods.

Dynamic output-feedback control for continuous-time interval positive systems under L1 performance

This paper is concerned with the design of L1-induced dynamic output-feedback controller for continuous-time positive systems with interval uncertainties. A necessary and sufficient condition for stability and L1-induced performance of positive linear systems is proposed in terms of linear inequalities. Based on this, conditions for the existence of robust dynamic output-feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions. One illustrative example is provided to show the effectiveness and applicability of the theoretical results.