Robust Control Design Problem Research Articles

Improved Dynamic Event-Triggered Robust Control for Flexible Robotic Arm Systems with Semi-Markov Jump Process

In this paper, we investigate the problem of a dynamic event-triggered robust controller design for flexible robotic arm systems with continuous-time phase-type semi-Markov jump process. In particular, the change in moment of inertia is first considered in the flexible robotic arm system, which is necessary for ensuring the security and stability control of special robots employed under special circumstances, such as surgical robots and assisted-living robots which have strict lightweight requirements. To handle this problem, a semi-Markov chain is conducted to model this process. Furthermore, the dynamic event-triggered scheme is used to solve the problem of limited bandwidth in the network transmission environment, while considering the impact of DoS attacks. With regard to the challenging circumstances and negative elements previously mentioned, the adequate criteria for the existence of the resilient H∞ controller are obtained using the Lyapunov function approach, and the controller gains, Lyapunov parameters and event-triggered parameters are co-designed. Finally, the effectiveness of the designed controller is demonstrated via numerical simulation using the LMI toolbox in MATLAB.

Extension of iterative learning control design for batch processes with time-delay in the input subject to random cycle-varying uncertainties

For uncertain time-delay batch processes with repetitive nature, this work deals with an unresolved problem of robust iterative learning control (ILC) design, in which we simultaneously remove the conventional assumptions of cycle-invariant uncertainties in reference trajectories, initial states, external disturbances, process dynamics, and time-delay. Moreover, we consider the variation of all existing uncertainties from a random point of view. Based on the idea of the internal model control (IMC) and indirect ILC, a novel IMC-based ILC structure is proposed. Then, we derive the practical convergence conditions, which have two design functions. By introducing a simple method for adjusting these functions, not only can we ensure that the expected tracking error converges monotonically to zero-neighborhood (in the L2-norm sense) but we can also achieve an acceptable convergence rate. Moreover, it is shown that the satisfaction of derived convergence conditions can always be guaranteed for any process. Simulation tests are provided to demonstrate the effectiveness of the proposed design.

Robust stabilization for a class of complex production process systems based on multi-dimensional moving pattern

This paper studies robust stabilization problem and state feedback controller design problem for a class of complex production process systems by pattern class variable instead of state variable or output variable. Firstly, the maximum entropy clustering method is introduced and modeling method based on multi-dimensional moving pattern is given. Nonlinear state space models of systems with input-delay are established by using the trajectories of pattern class variable. Then sufficient conditions for robust stabilization of the system are obtained by Linear Matrix Inequality. In addition, a state feedback controller is designed based on this condition. Finally, the effectiveness of the methods is illustrated by taking the actual working conditions data as an example.

Robust observer-based controller design for nonlinear parameter-varying systems with uncertainty and external disturbances

This article investigates the robust observer-based controller design problem for nonlinear parameter-varying systems subject to uncertainty and external disturbances. First, a novel augment vector is constructed, and an corresponding model of the resulting closed-loop system is obtained. Second, by applying the Lyapunov stability theory, a class of state-and-parameter-dependent robust asymptotic stability criteria is established, and the state-and-parameter-dependent sufficient conditions for the design of the robust observer-based controller are then acquired to guarantee the stability of the resulting closed-loop system, which can be effectively solved by sum-of-squares techniques. Different from the previous researches, the proposed control algorithm enables the state-and-parameter-dependent observer and the state-and-parameter-dependent controller design of the nonlinear parameter-varying systems to enjoy the advantage of separate design. The advantage can effectively reduce the computational complexity. Finally, simulation results demonstrate that the proposed robust observer-based controller shows improved performance in presence of uncertainty and external disturbances.

Robust nonlinear observer-based controller design for one-sided Lipschitz switched systems with time-varying delays

The core objective of this paper is to investigate the problem of robust nonlinear observer-based controller design for one-sided Lipschitz (OLS) switched systems. This work considers nonlinear switched systems with norm-bounded uncertainties, time-varying delays, and external disturbances. By selecting appropriate Lyapunov-Krasovskii functions and applying the OSL condition together with the quadratic inner boundedness property, we drive certain necessary and sufficient conditions for the observer-based control of the underlying system that assure the exponential convergence of the system states, the observer states, and the error states to zero, in respect of linear matrix inequalities via average dwell-time approach. The devised scheme offers necessary robustness against L2-norm bounded perturbations. In the end, the proposed scheme has been validated a suitable practical example.

Robust control for a class of nonlinear systems with input constraints based on actor‐critic learning

AbstractThis article focuses on establishing a general robust actor‐critic online learning control structure for disturbed nonlinear continuous systems with input constraints. It enriches the existing studies for the robustness of input constraint systems. First, the problem of robust controller design is successfully transformed into optimal controller design, and this process is proven, in which a particular nonquadratic discount cost function is defined. Then, build two neural networks (NNs) to estimate the cost function together and update each other. In the update process of actor NN, a robust term related to the state is introduced, which can guarantee the system's stability during the online learning process, and the state information is more fully utilized. Furthermore, using Lyapunov's direct method, it is proved that the estimated weights of the closed‐loop optimal control system and the actor‐critic NNs are uniformly ultimately bounded (UUB). It also provides extended discussions and a simulation example to demonstrate the robustness verification results of the novel algorithm.

A robust fractional-order controller design with gain and phase margin specifications based on delayed Bode’s ideal transfer function

In this study, a robust fractional-order controller design methodology for a type of fractional-order or integer-order model with dead time is proposed using phase and gain margin specifications. The delayed Bode’s ideal transfer function is used as a reference model to design the controller analytically. The delay term in delayed Bode’s ideal transfer function provides the exact determination of these frequency domain specifications when the system owns a dead time. The analytical robust controller design problem is transformed to solving four nonlinear equations with four unknown variables, two of which are the desired specifications; namely, phase and gain margins. The remaining two are the phase and gain cross-over frequencies. Next, some conditions are set based on the desired specifications so that nonlinear equations provide a unique solution. The proposed method is compared with the other existing robust controller methods based on the same frequency domain specifications. The simulation results reveal that the proposed method outperforms the other methods and also gives closer outcomes to the desired specifications.

Robust fuzzy control for non-linear systems with uncertainties: A Takagi- Sugeno model approach

This article studies the problem of robust control design for a class of uncertain nonlinear systems using the Takagi–Sugeno (TS) fuzzy models. The objective of this study is to design state feedback and an observer-based controller such that the closed-loop system is asymptotically stable. For this purpose, sufficient conditions are derived, and the corresponding controllers are designed by solving a set of linear matrix inequalities (LMIs). The effectiveness of the proposed design approach is provided via numerical simulations for a permanent magnet synchronous motor (PMSM).

An adaptive finite‐time stable control law for manipulator robots with unknown parameters

AbstractThis article develops an adaptive finite‐time stable control algorithm for an accurate manipulation of robot arms considering unknown model parameters and external disturbances. First, a state‐dependent twisting control algorithm is developed for the robust manipulation of robot arms under the consideration of bounded unknown uncertainties conditions. The more challenging problem of robust control design under consideration of totally unknown dynamical parameters is investigated in a second stage by supporting the control law with a suitable online parameters estimator. The objective of the parameters estimator is to drive the vector of estimated parameters to some level that ensures the establishment of real second‐order sliding mode without overloading the discontinuous controller gains. This approach based on combining both techniques of robust and adaptive algorithms allows overcoming large levels of uncertainties while preserving a high level of tracking accuracy without exciting the unwanted phenomena of chattering. The system finite‐time stability is proven by using Lyapunov theory and the weighted homogeneity principle. Practical tests are reported to support theoretical study results.

Robust fractional-order fixed-structure controller design for uncertain non-commensurate fractional plants using fractional Kharitonov theorem

This article deals with the problem of robust fractional-order fixed-structure controller design for commensurate and non-commensurate fractional-order interval systems using fractional Kharitonov theorem. The contribution of this study is to develop a simple control methodology to stabilize the fractional-order Kharitonov-defined vortex polynomials. Using the idea of robust stability testing function and extending it to the systems under study, the straightforward graphical and systematic procedures are proposed to investigate the robust stability of the system by searching for a non-conservative fractional-order Kharitonov region in the controller parameters plane. This region can establish all the fractional-order controllers that make the uncertain fractional-order systems stable. The relation between the fractional-order Kharitonov region and the parameters of the stabilizing controller is also found. Finally, comparison results with three relevant works are given to illustrate the feasibility of the proposed method.

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.

Stochastic faulty estimator-based non-fragile tracking controller for multi-agent systems with communication delay

A robust tracking control design problem for a class of linear multi-agent systems with fault signals is addressed in this study, where it is assumed that input signal of the leader is non-zero and unknown to the follower agents. An intermediate estimator, which bears stochastic failures, is designed to achieve the desired tracking performance and to estimate the combined unknown input signal of the leader input and the fault terms simultaneously. Assisted by the estimated terms, a robust non-fragile tracking control protocol that takes into account communication delays is proposed to eliminate the influence of the combined input signal. With the help of the Lyapunov-Krasovskii functional approach, a delay-dependent sufficient criterion is established to ensure that the resulting tracking error system states are uniformly bounded. On the basis of this criterion, the design procedure of the considered non-fragile control gain and the intermediate estimator gain matrices are presented. Two numerical examples, including a practical example, are used to reflect the validity and usefulness of the designed tracking control protocol.

Cooperative game-oriented optimal design in constraint-following control of mechanical systems

This paper proposes a cooperative game-oriented optimal design problem of robust control for uncertain mechanical systems. State of the concerned system is affected by (possibly fast) time-varying but bounded uncertainty. The task is to drive the system to obey a set of prescribed constraints. A $$\beta $$ -measure is defined to gauge the constraint-following error; based on which, a robust control with two tunable parameters is then proposed to render the system to be uniform boundedness and uniform ultimate boundedness. For the seeking of the optimal design parameters, two cost functions, each of which is dominated by one tunable parameter, are developed, and thereout a two-player cooperative game is formulated. Finally, the optimal design problem is successfully solved: with the existence, uniqueness, and analytical expression of the Pareto-optimality. This paper is the first ever endeavor to cast both constraint following and cooperative game into control framework for uncertain mechanical systems.

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.

Finite-time reliable stabilization of uncertain semi-Markovian jump systems with input saturation

Abstract In this study, we concentrate on the design problem of robust reliable control for uncertain semi-Markovian jump systems with input saturation over a specified finite interval of time. To exhibit the reality, a delay function that varies with respect to time and a more practical actuator fault model are included in the addressed system and the control design, respectively. By coupling the linear matrix inequality technique and the Lyapunov stability method with the finite-time theory, the required finite-time stabilization conditions are established to the system under consideration. The proposed reliable control gain matrices can be subsequently acquired by solving the aforementioned conditions with the support of existing convex optimization algorithms. To testify the correctness of the developed theoretical results and display the effectiveness of the proposed control design, an academic example is presented.

Robust Adaptive Fuzzy Tracking Control for Uncertain MIMO Nonlinear Nonminimum Phase System

Parameter uncertainty and unmodeled dynamics are inevitable for an actual nonlinear system, and are hard to deal with in control design, especially when the internal dynamics of this nonlinear system are unstable. The control design for a multiinput multioutput nonlinear nonminimum phase system with parameter uncertainty and unmodeled dynamics is discussed in this paper. The internal dynamics of nonminimum phase system are unstable, the control of this kind of system is challenging. Ideal internal dynamics (IID) based controller design method are utilized here, and a partially linearized model is constructed. A state tracking model is constructed on account of the partially linearized model and IID. Then the robust fuzzy controller design problem is discussed and a fuzzy logical system is utilized to identify the parameter uncertainty and unmodeled dynamics. A robust adaptive fuzzy controller is proposed for the stability of the nonlinear nonminimum phase system with parameter uncertainty and unmodeled dynamics. Finally, by simulations on vertical takeoff and landing aircraft, the availability of the presented adaptive fuzzy controller is validated.

Discrete-time robust fuzzy control synthesis for discretized and perturbed ship fin stabilizing systems subject to variance and pole location constraints

A discrete-time robust fuzzy controller design problem for the discretized and perturbed nonlinear ship fin stabilizing systems is studied in this paper. The discrete-time Takagi–Sugeno fuzzy model is used to represent the nonlinear ship fin stabilizing systems. The control performance considered in this paper includes stability requirement, pole location constraint, individual state variance constraint, and minimum output variance. Applying the Lyapunov theory, a discrete-time robust fuzzy controller is designed based on parallel distributed compensation technology and the relevant conditions are deduced in the form of linear matrix inequalities. By solving these conditions, a discrete-time robust fuzzy controller can be obtained to satisfy the above performance constraints. At last, a simulation for controlling a discrete-time nonlinear ship fin stabilizing system is provided to show the feasibility and applicability of the proposed robust fuzzy control method.

Robust Performance in Parametric Control System Design With Application to Power Systems

This article deals with the problem of robust low-order controller design for systems with multimodel representations. Such models are frequently used for the description of nonlinear and complex industrial power systems over an operating profile. We first develop a generalized complex extension of convex direction based on the interpolation and edge theorems. Subsequently, for plant models with parametric-type uncertainty, new vertex results related to robustness margins and system performance are derived. Based on this, new tools to design robust low-order controllers for such systems are presented.

Robust Stability and Stabilisation of Delayed Boolean Networks With Disturbance

In this paper, we study a type of delayed Boolean networks(DBNs) which are affected by disturbances. We study the stability problems of this kind of DBNs based on algebraic form, which can be constructed by the semi-tensor product(STP) method. Firstly, the robust stability of DBNs without control is investigated, and the decision condition for robust stability is derived. Then, the robust stabilisation and control design problems are considered. Based on the algebraic representation of the delayed Boolean control networks(DBCNs), a necessary and sufficient condition is established to judge the robust stabilisation of the system, moreover, a state feedback control is also designed to robustly stabilize the DBCNs. Finally, we give an example to support our new results.

Robust Adaptive Control for Uncertain Input Delay MIMO Nonlinear Non-Minimum Phase System: A Fuzzy Approach

In this paper, the robust controller design problem of uncertain multi-input multi-output nonlinear non-minimum phase system is discussed. The nonlinear system is suffering from both uncertainty and input delay, so the controller design is difficult. The traditional stable inversion controller is utilized and extended to uncertain case. An integral of past control input is constructed and fuzzy logical system is utilized for approaching the unknown state matrix and input matrix. Then a robust adaptive control strategy is presented. Finally, a numerical simulation on vertical takeoff and landing aircraft is given to show the effectiveness of the proposed method.