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Abstract This paper develops a robust gain-scheduled proportional–integral–derivative (PID) controller design method for a linear-parameter-varying (LPV) system with parametric uncertainty. It is recognized in the literature that the robust fixed-order controller design can be formulated as a feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP hard problem in general. Previous researchers have applied a linearization method, such as a variable change technique or a congruence transformation, to transform the BMI into a LMI. The applicability of the linearization method depends on the specific structure of the problem at hand and cannot be generalized. This paper instead formulates the gain-scheduled PID controller design as a feasibility problem of a quadratic matrix inequality (QMI) constraint, which covers the BMI constraint as a special case. An augmented sequential LMI optimization method is proposed to search for a feasible solution of the QMI constraint iteratively. As an illustrative application, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world output feedback control design system. [ABSTRACT FROM AUTHOR]

Design of controllers in the form of a state-feedback coupled to a state observer is studied in the context of uncertain systems. The classical approach by Luenberger is revisited. Results provide a heuristic design procedure that mimics the independent state-feedback/observer gains design by minimizing the coupling of observation error dynamics on the ideal state-feedback dynamics. The proposed design and analysis conditions apply to linear systems rationally-dependent on uncertainties defined in the cross-product of polytopes. Convex linear matrix inequality results are given thanks to the combination of a descriptor multi-affine representations of systems and the S -variable approach. Stability and H ∞ performances are assessed by multi-affine parameter-dependent Lyapunov matrices. [ABSTRACT FROM AUTHOR]

The maximum capability of feedback control for discrete-time systems under a nonparametric Lipschitz uncertainty was first established in Xie and Guo (2000) for the simplest dynamical control system. It was shown that the necessary and sufficient condition for the adaptive stabilizability is of the form L < 3 2 + 2 , where L is the Lipschitz constant of the uncertainty. This result was extended in Huang and Guo (2012) to a basic class of scalar discrete-time minimum-phase control systems under an additional parametric uncertainty, and the adaptive stabilization was achieved with the use of an impracticable infinite memory feedback based on a brute-force search over a sufficiently fine grid in the prior set of unknown parameters. In the present paper, the adaptive stabilization problem is considered for a subclass of parameter-affine minimum-phase systems. The solution of the problem is based on new recurrent objective inequalities enabling to estimate and validate the closed loop system online and to formulate a simple projection-type parameter estimation algorithm instead of the brute-force search used in Huang and Guo (2012). The computational tractability of the proposed finite-memory stabilizing feedback is illustrated via simulations. [ABSTRACT FROM AUTHOR]

This paper addresses a design method of controller networks, i.e., networked controllers which cooperatively determine the control inputs by exchanging the information with their neighbors. The problem considered here is to design the controllers stabilizing the resulting feedback system for an unknown network topology. As a solution to the problem, we propose controllers such that the entire network acts as a state feedback controller through a consensus protocol, and derive gain conditions to stabilize the resulting feedback system. This enables us to obtain a controller network that is robust against uncertainties of the network topology. [ABSTRACT FROM AUTHOR]

In this paper a robust and optimal attitude control design that uses the minimal kinematic parameters and angular velocities feedback is presented for the three-axis attitude stabilization of spacecraft with inertia uncertainties. After proposing a new class of robust attitude control laws for the three-axis attitude stabilization of spacecraft with inertia uncertainties, it is shown that the proposed robust attitude control laws are optimal with respect to performance indices. A numerical example is given to illustrate the theoretical results presented in this paper. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the use of polar logarithmic quantization (PLQ) for multi-input systems, and the corresponding design issues for the underlying networked control system (NCS). It is shown that the PLQ induces sector bounded nonlinear uncertainties in multiplicative and relative forms for vector-valued analog signals, similar to those in the scalar case. For the two-input NCS, optimal quantization is obtained through minimization of the quantization error that is quantified explicitly. The results are extended to more than two-input NCSs with an upper bound derived for the quantization error. Feedback stabilization and control of the NCS are also investigated under the PLQ at the plant input under state feedback. The coarsest quantization density (CQD) is studied and obtained. Results in this paper are illustrated by a numerical example. [Copyright &y& Elsevier]

Abstract: In this paper, a new method is introduced to enhance feedback robustness against communication gain uncertainties. The method employs a fundamental property in stochastic differential equations to add a scaled stochastic dither under which tolerable gain uncertainties can be much enlarged, beyond the traditional deterministic optimal gain margin. Algorithms, stability, convergence, and robustness are presented for first-order systems. Extension to higher-dimensional systems is further discussed. Simulation results are used to illustrate the merits of this methodology. [Copyright &y& Elsevier]

Abstract: This paper reports a new fractional-order four-dimensional (4D) smooth autonomous system which is special since it can generate a four-wing hyperchaotic attractor but has only one zero equilibrium. The issue of robust control for the fractional-order hyperchaotic system with uncertainties and interference is considered. On the basis of the fractional Lyapunov stability theorem, a linear state feedback controller is derived to guarantee robust Mittag–Leffler stability of the fractional-order hyperchaotic system. The control strength matrix is obtained by solving the linear matrix inequality (LMI). The effectiveness and robustness of the proposed scheme is verified via numerical simulation. [Copyright &y& Elsevier]

Abstract: This paper presents an off-line approach to the dynamic output feedback robust model predictive control (OFRMPC) for a system with both polytopic uncertainty and bounded disturbance. For the off-line optimization, a sequence of controller parameters and the corresponding regions of attraction are calculated for all combinations of the pre-specified estimated states and estimation error sets (EESs). These controller parameters and the corresponding regions of attraction are stored in a look-up table. On-line, the controller parameters are searched in this look-up table corresponding to real-time EES, and to the region of attraction with the closest containment of real-time estimated state. This method considerably reduces the on-line computational burden. Two numerical examples are given to illustrate the effectiveness of the approach. [Copyright &y& Elsevier]

Abstract: This work concerns robust static output feedback controller (SOFC) design for uncertain and disturbed Takagi–Sugeno (TS) systems using an H-infinity criterion. The main result is based on a descriptor formulation of the closed-loop dynamics. The proposed approach allows avoiding appearance of crossing terms between the controller’s and the TS system’s input matrices leading to easier LMI formulation than existing studies in the literature. Moreover, the proposed SOFC design conditions do not require any restrictions on the output equation and allow dealing with unmeasurable premise variables. Indeed, taking advantage of the uncertain TS modeling, nonlinearities associated to unmeasurable premises variables can be reported from the nominal part to the uncertainties. To provide LMIs of less conservatism, the results are conducted in the non-quadratic framework. Finally, two numerical examples and a benchmark of a crane system are proposed to illustrate the efficiency of the SOFC design methodology. [Copyright &y& Elsevier]

Abstract: Task-space feedback information such as visual feedback is used in many modern robot control systems as it improves robustness to model uncertainty. However, existing task-space feedback control schemes are only valid locally in a finite task space within a limited sensing zone where the singularity of the Jacobian matrix can be avoided. The global stability problem of a task-space control system has not been systemically solved. In this paper, we introduce a novel regional feedback method for robot task-space control. Each feedback information is employed in a local region, and the combination of regional information ensures the global convergence of robot motion. The transition from one feedback information to another is embedded in the controllers without using any hard or discontinuous switching. Using the regional feedback, a new task-space control method is proposed, which consists of a reaching task variable that drives the robot from one task space to another and a desired task variable to move the robot to the desired position at the ending stage. We shall show that the proposed regional feedback control method is a united formulation to address various open issues in task-space control problems such as singularity problem and limited sensing zone. This is the first result in task-space control that the global dynamic stability can be guaranteed with the consideration of singularity issues and limited sensing zones. [Copyright &y& Elsevier]

Abstract: In this paper, a robust adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large-scale stochastic nonlinear systems with unknown nonlinear functions, dynamical uncertainties and without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. To solve the problem of the dynamical uncertainties, the changing supply function technique is incorporated into the backstepping recursive design technique, and a new robust adaptive fuzzy decentralized output feedback control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: The robust delay-dependent control for an uncertain switched system with sampled-data input is investigated in this paper. The design of the sampled-data state feedback control technique is based on a computer digital control theory and used instead of analog elements. Hence designing a practical and useful feedback control strategy is a very important work in implementation. The time-varying delay approach is used to deal the sampled-data state feedback input problem. The upper bound for the sampled time of state is estimated from the proposed LMI optimization approach. A numerical example is illustrated to show the use of the main results. [Copyright &y& Elsevier]

Abstract: We propose robust controller designs to synchronize networks with uncertainties in their node dynamics and their connections. We consider two situations: in the first, we assume that the effect of uncertainties vanishes as synchronization is achieved. In the second, disturbances are assume nonvanishing but bounded. To achieve robust synchronization on these situations, we design local feedback controllers, which are smooth in the first case, and discontinuous in the latter. These designs allow us to establish synchronization criteria for this class of uncertain dynamical networks. We use numerical experiments to illustrate our results. [Copyright &y& Elsevier]

Abstract: Unstable time-delay systems and recycling systems are challenging problems for control analysis and design. When an unstable time-delay system has a recycle, its control problem becomes even more difficult. A control methodology for this class of systems is proposed in this paper. The considered strategy is based on the fact that if some internal system signals are available for measurement, then it will be possible to decouple the backward dynamics of the system and then a feedback controller could be designed for the forward dynamics. The key point for this strategy to be carried out is an asymptotic observer–predictor proposed to estimate these required internal signals. Necessary and sufficient conditions to assure convergence of this observer are given. After proving that the proposed control scheme tracks a step input signal and at the same time reject step disturbances, a procedure summarizing the methodology is provided. Robustness with respect to delay uncertainty and model parameters are also analyzed. [Copyright &y& Elsevier]

Abstract: It is well-known that robustness refers to the ability dealing with unknown uncertainties or unmodeled dynamics of the model-based control theory. However, this kind of robustness no longer has any significance for model free or data-driven control theory because the controller is designed only using I/O data of the controlled plant. In this paper, a novel robustness of the model free control or data-driven control is presented when the system is controlled by the model free adaptive control (MFAC) scheme. It is assumed that an MFAC scheme is implemented via a network control system and that data dropout occurs due to a failing sensor, actuator or network failure, resulting in what it is called intermittent MFAC. The stability of such a MFAC scheme is analyzed by the statistical approach. It is shown that the MFAC system is still stable when data dropout occurs, and the data dropout impacts the convergence speed. [Copyright &y& Elsevier]

Abstract: In this work the input amplitude saturation problem is analysed in the Quantitative Feedback Theory (QFT) framework. This paper reviews previous works in the literature dealing with the input amplitude saturation problem in the presence of an uncertain plant in the frequency domain using QFT. The objective of this paper is to compare the different available approaches and summarize the design process for each case so that this paper can be used as a tutorial; there are six main approaches to this problem. Two of these approaches use the classical two degrees of freedom control scheme for QFT; in both of these, the design constraints of a linear QFT compensator are added in the loop shaping stage: they are added in the first approach to avoid excitation of the actuator saturation and in the second one to guarantee global stability. The other three techniques are considered as anti-windup (AW) approaches. Starting from a base design in QFT with two degrees of freedom, the first AW approach introduces a third degree of freedom that guarantees the stability of the system, allowing for base designs for high performance. The other two AW approaches also introduce a third degree of freedom, but they take simple stability considerations into account and focus on the performance of the system. The last solution consists of using a reference governor technique, which guarantees the computation of a reference signal for an inner control loop that is shaped using QFT in such a way that robust stability will be guaranteed. The reference governor technique is a time domain approach that implies the resolution of an optimization problem. The rest of the approaches are frequency domain techniques based on a loop shaping method in the traditional QFT sense. [Copyright &y& Elsevier]

Abstract: In this paper, fuzzy threshold values, instead of crisp threshold values, have been used for optimal reliability-based multi-objective Pareto design of robust state feedback controllers for a single inverted pendulum having parameters with probabilistic uncertainties. The objective functions that have been considered are, namely, the normalized summation of rising time and overshoot of cart (S RO–C) and the normalized summation of rising time and overshoot of pendulum (S RO–P) in the deterministic approach. Accordingly, the probabilities of failure of those objective functions are also considered in the reliability-based design optimization (RBDO) approach. A new multi-objective uniform-diversity genetic algorithm (MUGA) is presented and used for Pareto optimum design of linear state feedback controllers for single inverted pendulum problem. In this way, Pareto front of optimum controllers is first obtained for the nominal deterministic single inverted pendulum using the conflicting objective functions in time domain. Such Pareto front is then obtained for single inverted pendulum having probabilistic uncertainties in its parameters using the statistical moments of those objective functions through a Monte Carlo simulation (MCS) approach. It is shown that multi-objective reliability-based Pareto optimization of the robust state feedback controllers using MUGA with fuzzy threshold values includes those that may be obtained by various crisp threshold values of probability of failures and, thus, remove the difficulty of selecting suitable crisp values. Besides, the multi-objective Pareto optimization of such robust feedback controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust state feedback controllers can be compromisingly chosen from the Pareto frontiers. [Copyright &y& Elsevier]

Abstract: In this paper, adaptive control is studied for a class of single-input–single-output (SISO) nonlinear discrete-time systems in strict-feedback form with nonparametric nonlinear uncertainties of the Lipschitz type. To eliminate the effect of the nonparametric uncertainties in an unmatched manner, a novel future states prediction is designed using states information at previous steps to compensate for the effect of uncertainties at the current step. Utilizing the predicted future states, constructive adaptive control is developed to compensate for the effects of both parametric and nonparametric uncertainties such that global stability and asymptotical output tracking is achieved. The effectiveness of the proposed control law is demonstrated in the simulation. [Copyright &y& Elsevier]

Abstract: Due to time spent in computation and transfer, control input is usually subject to delays. Problems of deterministic systems with input delay have received considerable attention. However, relatively few works are concerned with problems of stochastic system with input delay. This paper studies delayed-feedback stabilization of uncertain stochastic systems. Based on a new delay-dependent stability criterion established in this paper, a robust delayed-state-feedback controller that exponentially stabilizes the uncertain stochastic systems is proposed. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper provides an overview of computationally efficient approaches for quantifying the influence of parameter uncertainties on the states and outputs of nonlinear dynamical systems with finite-time control trajectories, focusing primarily on computing probability distributions. The advantages and disadvantages of various uncertainty analysis approaches, which use approximate representations of the full nonlinear model using power series or polynomial chaos expansions, are discussed in terms of computational cost and accuracy in computing the shape and tails of the state and output distributions. Application of the uncertainty analysis methods to a simulation study is used to provide advice as to which uncertainty analysis methods to select for a particular application. In particular, the results indicate that first-order series analysis can be accurate enough for the design of real-time robust feedback controllers for batch processes, although it is cautioned that the accuracy of such analysis should be confirmed a posteriori using a more accurate uncertainty analysis method. The polynomial chaos expansion is well suited to robust design and control when the objectives are strongly dependent on the shape or tails of the distributions of product quality or economic objectives. [Copyright &y& Elsevier]