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This paper proposes a new robust output-feedback adaptive event-triggered control (AETC) method for linear systems with parametric uncertainties. The proposed event-triggered mechanism (ETM) is obtained based on the L 2 stability condition. In this paper, two design approaches are presented, the emulation approach (pre-designed control gain) and the co-design approach. In the latter, the event-triggering law and the output-feedback controller are designed simultaneously to have a more efficient control system. The proposed adaptive event-triggered mechanism (AETM) in both approaches leads to an increase in the average of inter-event times based on linear matrix inequalities (LMIs). Consequently, in the proposed methods, the stability of the event-based system is ensured, the Zeno phenomenon is avoided, the feasibility margin and the quality of the response are well maintained, and the number of samplings is reduced, considerably. Finally, to indicate the capability of the proposed methods, two numerical simulations are presented. [ABSTRACT FROM AUTHOR]

Handling the uncertainties in the utility grid and uncertainties in renewable energy sources is a main challenge to accomplish the modern grid code requirements. This article proposes a new control strategy based on interval type‐2 fuzzy sets for controlling the grid‐connected dispersed generation (DG) system tied to the distorted electric grid. The proposed control technique can easily model and handle the uncertainties in the system parameters and renewable energy sources. The existence of three‐dimensional membership functions of type‐2 fuzzy sets offers an additional degree of freedom to counter the uncertainties in the system. The proposed strategy is effective in improving the dynamic response during system uncertainties such as distortions in grid voltage, variations in grid frequency, variations in renewable energy sources and due to presence of non‐linear and unbalanced loads. Also, it improves the quality of the current being injected to the grid during uncertainties. The proposed control strategy is applied to control the dc side capacitor voltage as well as to control the current loop of the grid connected inverter. The proposed system is simulated in MATLAB Simulink environment and the performance is compared with traditional controllers to show the effectiveness of the proposed control strategy during system abnormalities. [ABSTRACT FROM AUTHOR]

The problem of global asymptotic stability (GAS) of fixed-point state-delayed uncertain discrete-time systems combined with a saturation operator in state-space is investigated in this paper. The uncertainties in the system are presumed to be norm-bounded, which has been frequently employed in robust control for uncertain systems. This paper proposes a new GAS criterion for the considered system. The saturation nonlinearities associated with the system, which operate exclusively in the linear region, are identified using a unique methodology. Such identification leads to an improved characterization of saturation nonlinearities involved in the system. The proposed criterion utilizes an upper bound of parameter uncertainties, an asymptotic bound on the system's states, and a precise characterization of saturation nonlinearities involving system parameters. The merit of the criterion is also exemplified through examples along with simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system. [ABSTRACT FROM AUTHOR]

In this article, we are dedicated to coping with the control design for underactuated mechanical system (UMS) with system uncertainties, which is also subject to a set of servo constraints. For the nominal system without any initial condition deviations, this article provides a general model-based servo control with the idea of second-order constraints, which can be derived from both holonomic and nonholonomic ones. For the uncertain system, with the uncertainties being separated into matched portions and mismatched portions, this article provides an adaptive robust control scheme to guarantee the UMS to attain the deterministic performance on the basis of nominal control. The leakage-type adaptive law is to size up the unknown uncertainty bounds. The cart-pole system and the rotational-translational actuator system are used to verify the availability of the proposed adaptive robust control. [ABSTRACT FROM AUTHOR]

This article employs a recently proposed high frequency, continuous‐time periodic controller to compensate single‐input‐single‐output linear plants with norm‐bounded time‐varying uncertainties. To this end, the design of periodic controller is converted into designing a linear time‐invariant (LTI) controller for a single‐input‐two‐output equivalent uncertain system, following averaging technique. To represent this equivalent uncertain system into a standard form of linear uncertain systems, where uncertainties appear in system matrix A and input matrix B, the observer canonical form description of the original uncertain plant is exploited. Using the relationship between quadratic stability and ℋ∞‐norm minimization result available in literature, it is proved that the presence of virtual output with the periodic feedback introduces a feedforward action on the disturbance input of the generalized plant, unlike an LTI one. By virtue of this, the proposed periodic controller can tolerate more uncertainty bound in the input matrix B than its LTI counterpart, while keeping the bound on system matrix A the same. Finally, a linear matrix inequality‐based method is used to design the periodic controller to achieve quadratic stability along with robust linear quadratic performance. Suitable examples are considered to show the superiority of the periodic control as compared to LTI ones. [ABSTRACT FROM AUTHOR]

In a feedback control loop, when there exists a delay in processing the control signal (often called computational delay), it is difficult to stabilize the system, particularly when the system exhibits uncertainty. To solve this problem, we proposed a new robust proportional integral control strategy for a class of uncertain systems exhibiting parametric uncertainty. A two-stage scheme is proposed in which the first stage identifies the worst plant that has the highest chance of facing instability; and in the second stage, based on the worst plant, the tuning parameters of the proportional integral controller are determined using the stability boundary locus approach under the desired closed-loop specifications of gain and phase margins. The efficiency of the proposed scheme is verified for servo and regulatory control problems. [ABSTRACT FROM AUTHOR]

This paper addresses the control of a continuous-time system with possibly large uncertainty of unknown internal dynamics or external disturbance. A novel control scheme is proposed to estimate and cancel the system uncertainty effectively so as to enhance disturbance rejection (DR) performance. Unlike asymptotic analysis with infinite gain in the literature, the estimation transient analysis is carried out for the proposed scheme with a finite estimator gain and the precise error formulas are derived, based on a classical low-order plant description. The control performance associated with a realizable gain is quantified by tight bounds with respect to the ideal case, which enables easy parameter tuning. The necessary and sufficient condition for the internal stability of the control system is established, along with a D-decomposition method for determining the complete set of the gain intervals that could internally stabilize the plant. In the presence of measurement noise, a low-pass filter is introduced to attenuate its adverse effect. Simulations and semi-realistic experiments are performed to demonstrate the effectiveness of the proposed scheme, which shows evident improvement on DR performance over the well-known active DR control. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive robust boundary controller is designed for an unstable heat equation with external disturbance flowing into the control end. The disturbance and uncertainty effect is cancelled out in the closed-loop system by using on-line approximation of disturbance upper-bound provided as an output of adaptive robust update law. The asymptotic stability of the controlled system in the presence of unknown disturbance and/or parametric uncertainties is proved utilising the Lyapunov theorem. Unlike previous researches, the control implementation does not require prior knowledge of unknown disturbance. Moreover, the controller does not require measuring the system states or estimating the system states by an observer. The adaptive robust controller can be regarded as a combination of the best qualities of the adaptive controller and the robust controller with no prior knowledge of system uncertainty, and asymptotic tracking error performance. Numerical simulations and comparisons are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article studies the control problem for nonlinear uncertain systems with measurement uncertainty. By seizing the equivalent total effect of multiple uncertainties in both dynamics and measurement, an active disturbance rejection control design is proposed. By timely estimating and compensating for the total effect of various uncertainties, the highly consistent transient performance of tracking is theoretically revealed. Moreover, the relationship between the tracking error and the controller parameters is qualitatively shown. Finally, the simulation and experimental results illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In the robust performance design, the celebrated $\mu$ -synthesis provides a reputed tool for systems with norm-bounded uncertainty. However, such small-gain methods inevitably limit the achievable robust performance when the dynamic uncertainty is not characterized by its gain bound. To achieve a high robust performance for systems with positive real (PR) uncertainty, an output strict passivity (OSP) approach is proposed recently which makes use of the positive realness and the maximum gain information of the uncertainty. Aiming at an even higher robust performance, this article proposes a novel model for PR uncertainties which captures the frequency-dependent gain bound, and establishes the corresponding design theory to actively utilize both gain and phase bounds of the uncertainty in the robust performance design. A case study reveals that the new uncertainty model alone yields a substantial improvement over the OSP method in performance even under the same design setup. Moreover, the best tuned controller outperforms the OSP controller. [ABSTRACT FROM AUTHOR]

A non-fragile robust model predictive control (RMPC) is designed in the uncertain systems under bounded control signals. To this aim, a class of the nonlinear systems with additive uncertainty is considered in its general form. The RMPC synthesis could lead to the proper selection of the controller's gains. Thus, the non-fragile RMPC design is translated into a minimization problem subjected to some constraints in terms of linear matrix inequality (LMI). Hence, the controller's gains are computed by solving such a minimization problem. In some numerical examples, the suggested non-fragile RMPC is compared with the other methods. The simulation results demonstrate the effectiveness of the proposed RMPC in comparison with similar techniques. • An uncertain system is described via the general form of the additive uncertainty. • The controller constraints and fragility are simultaneously concerned in RMPC design. • Non-fragile RMPC is translated into a minimization problem subjected to some LMIs. • The examples show effectiveness of the proposed method over the similar techniques. [ABSTRACT FROM AUTHOR]

This study focuses in the output feedback stabilisation of constrained linear systems affected by uncertainties and noisy output measurements. The system states are restricted inside a given polytope and a classical Luenberger observer is used to reconstruct the unmeasurable states from output observations. Based on the observed states, a state feedback is proposed as the control input. The stability analysis and the control design are done using an extended version of the attractive ellipsoid method (AEM) approach. To avoid the violation of state constraints, this work proposes a barrier Lyapunov function (BLF) based analysis. The control parameters are obtained throughout the solution of some optimisation problems such that the BLF ensures an approximation of the constraints by a maximal ellipsoidal set and the AEM provides the characterisation of a minimal ultimately bounded set for the closed-loop system solutions. Numerical simulations show the advantages using the BFL-AEM methodology against classical sub-optimal controllers in academic second order and third order examples. Then, the proposed control strategy is applied over a Buck DC-DC converter. In all the cases, the method proposed here prevails over the other controllers. [ABSTRACT FROM AUTHOR]

This paper presents a robust neural network with an extended state observer control methodology for a piezoelectric-actuator-based surgical device. This control methodology is proposed for tracking of desired motion trajectories in the presence of unknown or uncertain system parameters, nonlinearities including friction, hysteresis, and disturbances in the motion system. In particular, the radial basis function neural network, which serves as a function approximator, aims to create a model for an unknown function to find a relationship between input and output data. An extended state observer is utilized to assist in canceling disturbances and uncertainties of the system dynamically. The stability of the control approach is analyzed. The convergence of position and velocity tracking errors is proven theoretically. Experiments are conducted to demonstrate that the performance with an improved accuracy can be attained by the proposed control scheme. With the motion tracking capability, the control methodology helps the novel surgical device achieve higher success rate in operation, which is also suitable for similar piezoelectric ultrasonic actuator applications. [ABSTRACT FROM AUTHOR]

This note investigates the dynamic positioning control problem of full-actuated marine vehicles in the presence of system uncertainties and input constraints. In the control algorithm, the ship model uncertainty is approximated by the radial-basis-function neural networks. The effect of input saturation is analyzed by the auxiliary system, states of the auxiliary system are employed to develop the control scheme. By virtue of the dynamic surface control technique, the inherent problem of "explosion of complexity" problem occurred during conventional Backstepping design framework is avoided. The semi-global uniformly ultimately bounded stability of the closed-loop is guaranteed by Lyapunov theory. Since the minimal learning parameterization based adaptive law is derived, the number of parameters updated online is reduced to 6. Consider the servo-system uncertainty, the control inputs of interest are achieved as the measurable propeller pitch whose characteristics would facilitate the implementation of the algorithm in the practical engineering. Finally, by employing a supply vessel as the plant, comparison simulations are conducted to demonstrate the effectiveness and robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• Systematically dealing with mismatch between a process model and the true plant. • Ensuring recursive feasibility and stability of SMPC when the process operating point is changed, for example, due to economic considerations. • Guaranteeing offset-free tracking for all operating points. This paper presents a stochastic-tube model predictive control (MPC) strategy that systematically handles plant-model mismatch, guarantees stability in the presence of changing operating conditions, and ensures offset-free tracking for all reachable operating conditions. The key notion of this work is to separate the system uncertainty into two distinct sources of additive bounded state error. The first source is a non-random uncertainty that represents mismatch between the linear model of the controller and the true plant (as well as other types of persistent disturbances). The second source represents random fluctuations due to either the intrinsic stochastic variability of the system, or exogenous disturbances. Recursive feasibility and stability of the stochastic-tube MPC strategy is guaranteed by defining the terminal invariant set to include the effect of changes in the steady-state operating conditions. Offset-free tracking is achieved with a disturbance estimator that can be tuned independently of the controller. To reduce the conservatism inherent to robust control performance, a new filter model for deterministic disturbances is proposed that predicts uncertainty in the future evolution of the disturbances based on a bound on how quickly the plant-model mismatch can vary. The stochastic-tube MPC strategy is demonstrated on two simulation case studies—a benchmark DC-DC converter and an industrially-motivated fluidized-bed catalytic cracking unit. [ABSTRACT FROM AUTHOR]

This paper investigates a class of uncertain linear discrete-time systems subject to input rate saturation. A predictive sliding mode control approach is proposed which guarantees the control inputs remain bounded in the input rate saturation. Furthermore, the disturbance observer is developed to compensate for the system uncertainty and disturbance. Finally, the simulations demonstrate the effectiveness of the proposed predictive sliding mode control scheme. [ABSTRACT FROM AUTHOR]

• Dynamic formulation of a deployable cable-driven robot considering the actuator models was derived. • A novel control topology based on a cascade structure was proposed. • Stability of the system as a whole was analyzed via Lyapunov direct method. • The novel method was implemented on a deployable cable-driven robot called ARASCAM. • Results showed that our controller achieved a suitable tracking performance. In this paper, we derive the dynamic formulation of a deployable cable-driven robot that considers models of the actuator and power transmission systems, and we investigate the challenges of structural uncertainty. To accommodate the inherent uncertainty of the system, we propose a proper control topology based on a cascade structure. The inner loop of the structure controls the cable forces, and the outer loop tracks the precise position of the robot's end-effector. For the design of the outer loop controller, we propose a robust sliding mode controller with a stability analysis that is based on the Lyapunov direct method. The main contribution of this paper is to analyze the stability of the system as a whole considering both the inner and outer loop controllers. Finally, in order to illustrate the performance of the proposed controller, we present the results of an experiment on a deployable suspended cable-driven robot, which shows the effectiveness of the proposed controller in the presence of the inherent uncertainties of the system. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we consider the design of robust quadratic regulators for linear systems with probabilistic uncertainty in system parameters. The synthesis algorithms are presented in a convex optimization framework, which optimize with respect to an integral cost. The optimization problem is formulated as a lower‐bound maximization problem and developed in the polynomial chaos framework. Two approaches are considered here. In the first approach, an exact optimization problem is formulated in the infinite‐dimensional space, which is solved approximately using polynomial‐chaos expansions. In the second approach, an approximate problem is formulated using a reduced‐order model and solved exactly. The robustness of the controllers from these two approaches are compared using a realistic flight control problem based on an F16 aircraft model. Linear and nonlinear simulations reveal that the first approach results in a more robust controller. [ABSTRACT FROM AUTHOR]

The control problem for a ship steering system with speed loss is discussed in this paper. Two methods are proposed to deal with the unknown bounded disturbance for a sliding mode controller applied to a nonlinear surface vessel heading control system. The system uncertainties caused by speed changes are taken as internal disturbances, while the wave moments are considered as external disturbances. A feedback linearization method is adopted to simplify the nonlinear system. An adaptive method and a Nonlinear Disturbance Observer (NDO) are proposed for course keeping manoeuvres and speed keeping in vessel steering and provide robust performance for time varying wave disturbance and actuator dynamics. Furthermore, the overall stability conditions of the proposed controllers are analysed by Lyapunov's direct method. Finally, simulation results using the characteristics of a naval vessel illustrate the effectiveness of the presented control algorithms. [ABSTRACT FROM AUTHOR]

Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future experiments. Merging mathematical theory with empirical measurements in a statistically coherent way is critical and challenges abound, e.g., ill-posedness of the parameter estimation problem, proper regularization and incorporation of prior knowledge, and computational limitations. To address these issues, we propose a new method for learning parameterized dynamical systems from data. We first customize and fit a surrogate stochastic process directly to observational data, front-loading with statistical learning to respect prior knowledge (e.g., smoothness), cope with challenging data features like heteroskedasticity, heavy tails, and censoring. Then, samples of the stochastic process are used as "surrogate data" and point estimates are computed via ordinary point estimation methods in a modular fashion. Attractive features of this two-step approach include modularity and trivial parallelizability. We demonstrate its advantages on a predator-prey simulation study and on a real-world application involving within-host influenza virus infection data paired with a viral kinetic model, with comparisons to a more conventional Markov chain Monte Carlo (MCMC) based Bayesian approach. [ABSTRACT FROM AUTHOR]

Robust control of under-actuated mechanical systems (UMSs) with model uncertainty is still a challenging problem. For UMSs, the model parametric uncertainties make it difficult to precisely calculate the isolated equilibrium point corresponding to a fixed input. Without an accurate destination state, many set-point control methods cannot eliminate the positioning errors. An improved sliding mode control (ISMC) method is proposed to solve the robust control problem for a class of UMSs with model uncertainty and input disturbance. A balance variable is introduced in the sliding surface design to compensate for the disturbance caused by the inaccurate destination state, and the ISMC method is proposed to make the system state reach the sliding surface in finite time. Linear matrix inequality approach and particle swarm optimisation algorithm are applied to design the sliding mode surface parameters. The simulation results on an UMS are presented to show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Autonomous underwater vehicles (AUVs) are highly nonlinear underactuated systems with uncertain dynamics and a challenging control problem. The main focus of this paper is to present a control law that shows desirable performance in the presence of modeling uncertainties. In this study, uncertainties are considered to be bounded and the AUV mathematical model is obtained in the presence of such uncertainties. Forces and torques applied to the AUV are also designed using a nonlinear dynamic controller. Appropriate adaptive rules are also presented to overcome system uncertainties and external disturbances. The adaptive nonlinear dynamic controller is designed based on upper bounds of system uncertainties and its stability is proven using the Lyapunov theory. In this article, the performance of the proposed control algorithm for tracking reference trajectories in an obstacle-rich environment is investigated. Therefore, the control algorithm is combined with potential fields for obstacle avoidance. Obtained results show the efficiency of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, we consider both one-period and multi-period distributionally robust mean-CVaR portfolio selection problems. We adopt an uncertainty set which considers the uncertainties in terms of both the distribution and the first two order moments. We use the parametric method and the dynamic programming technique to come up with the closed-form optimal solutions for both the one-period and the multi-period robust portfolio selection problems. Finally, we show that our approaches are efficient when compared with both normal based portfolio selection models, and robust approaches based on known moments. [ABSTRACT FROM AUTHOR]

This paper presents a new theoretical framework that, by integrating robust statistics and robust control theory, allows us to develop a robust dynamic state estimator of a cyber-physical system. This state estimator combines the generalized maximum-likelihood-type (GM) estimator, the unscented Kalman filter (UKF), and the H-infinity filter into a robust H-infinity UKF filter in the Krein space, which is able to handle large system uncertainties as well as suppress outliers while achieving a good statistical efficiency under Gaussian and non-Gaussian process and observation noises. Specifically, we first use the statistical linearization approach to build a linearlike regression model in the Krein space. Then, we show that the H-infinity UKF is just the Krein space Kalman filter that exhibits a bounded estimation error in presence of system uncertainties while minimizing the least squares criterion; consequently, it suffers from a lack of robustness to outliers and non-Gaussian noise. Because the GM estimator is able to handle outliers, but it may yield large estimation errors in the presence of system uncertainties, we propose to combine it with the H-infinity UKF in a robust H-infinity UKF. We carry out a theoretical analysis to demonstrate the connections that our filter has with the H-infinity UKF and the GM-UKF. The good performance of the new filter is demonstrated via extensive simulation performed on the IEEE 39-bus power system. [ABSTRACT FROM AUTHOR]

Abstract Robust constrained control of linear systems with parametric uncertainty and additive disturbance is addressed. The main contribution is the introduction of a mathematically rigorous and computationally tractable framework for stabilizing model predictive control with online parameter estimation to improve performance and reduce conservatism. Requirements for closed-loop stability and provable constraint satisfaction are considered separately, resulting in the use of online set-membership system identification combined with homothetic prediction tubes for robust constraint satisfaction, and an H ∞ optimal point estimate of the unknown parameters to achieve a finite closed-loop gain from the disturbance to the state. Extensions to time-varying parameters and persistently exciting inputs to guarantee parameter convergence are presented. A numerical example illustrates the proven properties and efficacy of the approach. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we address the vibration abatement problem of a flexible riser system preceded by nonlinear input saturation characteristic and uncertainties of the system. By virtue of Lyapunov theory, auxiliary system and robust control strategy, a boundary robust adaptive anti-saturation control is developed to restrain the vibration, remove the nonlinear input saturation effects and compensate for the uncertainties of system parameters and boundary disturbance. Applying the rigorous analysis without simplifying or discretizing the partial differential equation dynamics, the controlled system is ensured to be uniformly bounded stable with the designed control law. In the end, simulation results are presented for control performance verification. Highlights • A boundary robust adaptive anti-saturation control is presented to suppress the riser's vibration. • The online updating laws are developed to compensate the uncertainties of system. • The auxiliary system is introduced to handle the input saturation. • The σ-modification is exploited to adjust the robustness of the system. • The stability of the closed-loop system is proved via rigorous Lyapunov analysis. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the robust H ∞ filtering of polytopic uncertain stochastic systems is designed under quantized sampled outputs. An novel parameters-dependent time-scheduled Lyapunov functional is constructed using segmentation technology and linear interpolation. Based on this new Lyapunov functional and convex combination method, sufficient stochastic exponential stability criteria of the filtering error dynamics are proposed and a prescribed H ∞ performance level can be guaranteed by designing the stochastically stable filter. The better H ∞ performance can be obtained with a larger interval dividing parameter. A numerical example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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]

We aim to control the differential mobile robot system to follow a class of pre-specified constraints sufficiently closely in the presence of system uncertainties. The mass and the moment of inertia of the differential mobile robot are considered as the uncertain parameters, which are (possibly) fast time-varying. In the first step, based on Udwadia and Kalaba's approach, an adaptive robust control scheme is proposed to deal with the system uncertainties. The adaptive law is of leakage type, which can adjust itself based on the tracking error. Using this adaptive robust control scheme, we can obtain the desired armature currents of the two direct current (DC) motors, which are not the real control inputs. In the second step, taking the motor dynamics into account, a Lyapunov Minimax approach for the required actual control inputs (i.e., the input voltages of the two DC motors) is proposed to generate the desired armature currents. This two-step control methodology guarantees uniform boundedness and uniform ultimate boundedness, and renders the system to follow a class of pre-specified constraints approximately. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic output feedback robust model predictive control for system with polytopic model uncertainty. Earlier researches on this topic utilise iterative methods to solve the non-convex optimisation problem which are computationally demanding. In order to reduce the computational burden, we explore a new approach in this paper, where, by utilising some proper matrix transformations, a computationally more efficient but conservative convex optimisation problem is formulated which can be solved in terms of linear matrix inequalities. Furthermore, we try to reduce the conservativeness by introducing a nonsingular matrix as a degree of freedom. The recursive feasibility and the convergence of the augmented state to the equilibrium point are guaranteed. The effectiveness of the proposed approach is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the robust control issues of nonlinear multiplayer systems by utilizing adaptive dynamic programming (ADP) methods and fills a gap in the ADP field, where actuator uncertainties for multiplayer systems are still not addressed. Two types of actuator uncertainties including bounded nonlinear perturbation and unknown constant actuator fault are taken into consideration. First, a data-driven reinforcement learning (RL) approach is derived to learn the optimal solutions of multiplayer nonzero-sum games. Then, based on the obtained optimal control policies, two robust control schemes are developed to handle these two different types of uncertainties, respectively, and the associated stability analysis is also provided. To implement the proposed iterative RL approach, a single neural network (NN) architecture with least-square-based updating law is given, which reduces the computation burden compared with the traditional dual NN architecture. Finally, two numerical examples are shown to test the feasibility of our proposed schemes. [ABSTRACT FROM AUTHOR]

Abstract The augmented state robust regularized least-squares filter (ASRRLSF) and two-stage robust regularized least-squares filter (TSRRLSF) are proposed for discrete time-varying nonlinear systems with unknown inputs and norm-bounded uncertainties. Unknown inputs affect both state-space model and measurements equation of the system. Combining system states and unknown inputs as an augmented state, the ASRRLSF is developed by converting a deterministic min–max optimization problem to a robust regularized least-squares problem. If dimension of the augmented state increases, the performance of the proposed ASRRLSF will reduce and the computational cost will increase rapidly. Therefore, in the following, the TSRRLSF is proposed by decoupling the ASRRLSF to lower order filters as system states filter and unknown inputs filter using T transformation. Finally, two numerical examples are given in order to illustrate the performance of the proposed filtering approaches. [ABSTRACT FROM AUTHOR]

This paper establishes a general analytical framework for continuous-time stochastic control problems for an ambiguity-averse agent (AAA) with time-inconsistent preference, where the control problems do not satisfy Bellman’s principle of optimality. The AAA is concerned about model uncertainty in the sense that she is not completely confident in the reference model of the controlled Markov state process and rather considers some similar alternative models. The problems of interest are studied within a set of dominated models and the AAA seeks for an optimal decision that is robust with respect to model risks. We adopt a game-theoretic framework and the concept of subgame perfect Nash equilibrium to derive an extended dynamic programming equation and extended Hamilton–Jacobi–Bellman–Isaacs equations for characterizing the robust dynamically optimal control of the problem. We also prove a verification theorem to theoretically support our construction of robust control. To illustrate the tractability of the proposed framework, we study an example of robust dynamic mean–variance portfolio selection under two cases: 1. constant risk aversion; and 2. state-dependent risk aversion. [ABSTRACT FROM AUTHOR]

With increasing renewable distributed energy resources integrated into a microgrid (MG), it is difficult to realize its optimal operation due to various uncertainties, e.g., power outputs of wind turbines and photovoltaic cells. This paper presents a flexible scheduling model for the optimal operation of an MG in which the expectation of operational cost and the robustness of scheduling solutions are considered, simultaneously. To balance the tradeoff between minimizing the expectation of operational cost and enhancing robustness, the proposed flexible scheduling model of MG is formulated as a multiobjective optimization problem by introducing a robustness preference parameter. In this way, the relationship between the expected operational cost and the robustness of scheduling solution is investigated, and the fuzzy decision making method is used for selecting a suitable solution. Finally, a modified MG is used for case study, and simulation results verify the applicability and effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

The brushless doubly fed induction machine (BDFM) has great potential in the wind energy generation system because it offers the advantages of higher reliability and maintenance-free operation. In this paper, a mathematical model in the power windings stator flux orientation frame is discussed by taking the rotor flux as the disturbance. Consequently, the control of the BDFM system is implemented by generating suitable control winding currents. Moreover, in order to eliminate the speed error and compensate the system uncertainties caused by the rotor flux and parameter perturbations, an integral sliding mode variable structure controller for the rotor speed is developed, and the reactive power is adjusted by a proportional-integral (PI) controller in the outer-loop. Furthermore, the control winding currents are regulated by the PI control scheme in the inner-loop. The proposed control frame achieves a good static and satisfactory dynamic control performance. Finally, simulation and experimental results are used to verify the correctness and feasibility of the proposed method. [ABSTRACT FROM PUBLISHER]

The problem of robust output regulation is studied for a class of parameter uncertain systems under unity output feedback control. The objective is tracking of the desired reference trajectory in the presence of the disturbance, both generated by a common exosystem. Because of the anti-stability of the exosystem and potentially unbounded reference trajectory, the output tracking error is employed as the measurement signal and used as the input to the feedback controller. The method of p-copy of the internal model is utilised to augment the plant dynamics. Assuming that the output regulation condition is satisfied for all the parameter uncertainties, it is shown that the problem of robust output regulation is equivalent to the problem of robust output stabilisation. Furthermore, for quadratically bounded parameter uncertainties, an application of the notion of the quadratic stability leads to ℋ∞-based robust control, and the maximum allowable uncertainty bound can be computed, below which the robust output regulation can be achieved. [ABSTRACT FROM AUTHOR]

Many transportation systems for routing flows between several origin-destination pairs of demand nodes have been widely designed as hub-and-spoke networks. To improve the provided service level of these networks, service time requirements are here considered during modeling, giving rise to a multiple allocation incomplete hub location problem with service time requirements. The problem consists of designing a hub and spoke network by locating hubs, establishing inter-hub arcs, and routing origin-destination demand flows at minimal cost while meeting some service time requirements. As travel times are usually uncertain for most real cases, the problem is approached via a binary linear programming robust optimization model, which is solved by two specialized Benders decomposition algorithms. The devised Benders decomposition framework outperforms a general purpose optimization solver on solving benchmark instances of the hub location literature. The achieved results also show how the probability of violating the travel time requirements decreases with the prescribed protection level, at the expense of the higher costs of the optimal solution for the robust optimization model. [ABSTRACT FROM AUTHOR]

This paper focuses on the robust control problem for a class of linear uncertain systems by using frequency techniques. The controller/observer dynamics are analyzed using Lyapunov techniques, in terms of the state and state estimation error, for an uncertainty constrained over a specified range. A Popov-type criterion, a "circle criterion," defined as the Popov frequency condition and the uncertainty circle, is formulated. It is proved that the closed-loop system is robustly stable if the Popov condition holds at all frequencies. The proposed method is validated against a robust controller for a balancing robot (BR). [ABSTRACT FROM AUTHOR]

The problem of the attitude stabilization of a quadrotor unmanned aerial vehicle is considered in simulation. An uncertain-like Takagi–Sugeno model of the quadrotor, where the nonlinear entries which depend on the input motor voltages are reported in uncertainties, is proposed to avoid closed-loop algebraic loops. The design of a Parallel Distributed Compensation (PDC) control law is considered with D -stability constraints in order to improve the closed-loop transient response. In this context, new generic and relaxed Linear Matrix Inequality (LMI) conditions are proposed. These new PDC controller design conditions constitute an alternative to previously proposed D -stabilizing non-PDC controller ones. Indeed, non-PDC controllers require online inversions of time-varying matrices, which is a major drawback for embedded applications with low computational capabilities. The conservatism of the proposed LMI conditions with respect to previous results is illustrated through an academic example. Then, simulations of the quadrotor with usual prescribed LMI regions are proposed to show the effectiveness of the proposed conditions. [ABSTRACT FROM AUTHOR]

In this paper the following selection problem is discussed. A set of n items is given and we wish to choose a subset of exactly p items of the minimum total cost. This problem is a special case of 0–1 knapsack in which all the item weights are equal to 1. Its deterministic version has an O ( n ) -time algorithm, which consists in choosing p items of the smallest costs. In this paper it is assumed that the item costs are uncertain. Two robust models, namely two-stage and recoverable ones, under discrete and interval uncertainty representations, are discussed. Several positive and negative complexity results for both of them are provided. [ABSTRACT FROM AUTHOR]

In our study, we integrate the data uncertainty of real-world models into our regulatory systems and robustify them. We newly introduce and analyse robust time-discrete target–environment regulatory systems under polyhedral uncertainty through robust optimization. Robust optimization has reached a great importance as a modelling framework for immunizing against parametric uncertainties and the integration of uncertain data is of considerable importance for the model’s reliability of a highly interconnected system. Then, we present a numerical example to demonstrate the efficiency of our new robust regression method for regulatory networks. The results indicate that our approach can successfully approximate the target–environment interaction, based on the expression values of all targets and environmental factors. [ABSTRACT FROM AUTHOR]

Demand forecasting is an important factor in production planning, but future demand is not easy to forecast in practice. We consider a multiperiod, multiproduct production planning problem under demand uncertainty with constrains for raw materials, manufacturing capacity, and inventory. Under the assumption that probability distribution of demand is not available, two types of robust optimization models are proposed. First, a robust counterpart is developed to determine the here-and-now decision. Next, an affinely adjustable robust counterpart is developed to determine the wait-and-see decisions by approximating a robust solution with a linear decision rule. The robust models find an optimal solution that is always feasible and less sensitive against all realized demand within a given uncertainty set, in order to minimize production, procurement, inventory, and lost sales costs even in the worst case. Numerical studies demonstrated that, without knowing probability distribution of future demand, the affinely adjustable robust counterpart approach could outperform the robust counterpart and deterministic model in terms of the average cost, the standard deviation of the realized cost, and the worst-case scenario cost. The proposed method is much better than the others, especially when penalty cost due to lost sales is high and unknown demand is left skewed. [ABSTRACT FROM PUBLISHER]

Rotor speed control of wind turbines is a key factor in achieving the maximum power of wind. It is known that a high-performance controller can significantly increase the amount of energy that can be captured from this source. The main problem regarding this issue is the lack of information about the correct dynamic model of the system. This uncertainty of the model is generally associated with unknown parameters (structured uncertainty) and/or external disturbances (unstructured uncertainty). Some adaptive and robust control approaches are developed in the literature in order to deal respectively with structured and unstructured uncertainties. In this paper, to compensate for both types of uncertainty, a robust controller, which includes an adaptive feedforward term, is proposed to track the optimal speed. In addition to considering the uncertainties, another advantage of the presented approach is that, using a smooth control effort, it provides global asymptotic tracking. A complete stability proof of the system is presented, and simulation results illustrate the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

This paper proposes a discrete-time sliding mode control (DT-SMC) algorithm for uncertain linear systems with time-varying delay on the state. The parameter uncertainties and the external disturbances are assumed to be unknown but norm-bounded. The sliding mode existence depends on that of the stable linear sliding surface, which is ensured by a sufficient condition that depends on the delay bounds and is derived using LMI. A numerical example as well as an application to the Two-Area Four-Machine power system has been presented to illustrate and confirm the usefulness and the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Uncertainty is frequently present in logistics and transportation, where vehicle routing problems play a crucial role. However, due to the complexity inherent in dealing with uncertainty, most research has been devoted to deterministic problems. This paper considers a robust version of the vehicle routing problem with hard time windows, in which travel times are uncertain. A budget polytope uncertainty set describes the travel times, to limit the maximum number of sailing legs that can be delayed. This makes sure that improbable scenarios are not considered, while making sure that solutions are immune to delays on a given number of sailing legs. Existing exact methods are only able to solve small instances of the problem and can be computationally demanding. With the aim of solving large instances with reduced running times, this paper proposes an efficient heuristic based on adaptive large neighborhood search. The computational study performed on instances with different uncertainty levels compares and analyzes the performance of four versions of the heuristic and shows how good quality solutions can be obtained within short computational times. [ABSTRACT FROM AUTHOR]

This work studies interpolation techniques that can be employed on off-line robust constrained model predictive control (MPC) for a discrete time-varying system with polytopic parametric uncertainty. A sequence of feedback gains is determined by solving off-line a series of optimal control optimization problems. A sequence of nested corresponding polyhedral invariant set is then constructed. At each sampling time, the smallest invariant set containing the current state is determined. If the current invariant set is the innermost set, the pre-computed gain associated with the innermost set is applied. If otherwise, a feedback gain is variable and determined by a linear interpolation of the pre-computed gains. Two interpolation algorithms are investigated. The proposed algorithms are illustrated with case studies of a two-tank system and a four-tank system. The simulation results showed that the proposed interpolation techniques can improve control performance of off-line robust MPC while on-line computation is still tractable. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive smooth second-order sliding mode control law for a class of uncertain non-linear systems. The key point of this control law is ensuring a smooth control signal considering parametric uncertainty and disturbances with unknown bounds. The proposed control method is obtained by introducing a continuous function under the integral and using adaptive gains. The switching function and its derivative are forced to zero in finite time. This is achieved using a smooth control command and without the prior knowledge of upper bound parameters of uncertainties. The finite-time stability is proved based on a quadratic Lyapunov approach and the reaching time is estimated. This structure is used to create a homing guidance law and the efficiency is evaluated via simulations. [ABSTRACT FROM AUTHOR]

Output containment problem for high-order nonlinear time-invariant multi-agent systems in directed networks is investigated in this paper. The output is related with the observation matrix. The dimensions of observation matrix are extended so that it is non-singular. Then the containment problem is transformed into stability problem. The model of each agent is constructed by a nominal system combined with uncertainties. A robust controller, which includes a nominal controller and a robust compensator, is proposed to achieve output containment and restrain external uncertainties. The nominal controller is based on the output feedback and the nominal system constructed by the nominal controller contains desired containment properties. The robust compensator design is based on robust signal compensation technology for restraining the effects of external disturbances. A sufficient condition on the output containment is proposed and the containment errors can be made as small as desired with the expected convergence rate. Finally, numerical simulation is presented to demonstrate the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the robust stabilsation of uncertain delayed Markovian jump systems. Given a Markovian jump system with time delay and Brownian motion simultaneously, we allow the uncertainty added in the form of additive perturbations and existing in the drift and diffusion sections at the same time. A sufficient condition on the mean square stability of system in the face of such disturbances is obtained, which is similar to small-gain theorem. A kind of partially delay-dependent controller stabilising the resulting closed-loop system is firstly designed to relate to the probability distribution of delay, whose key idea is applied to construct a delayed controller with disordering phenomenon. It is seen that the existence conditions established here could be solved easily. Based on the proposed results, some applications on robust synchronisation of uncertain delayed multi-agent systems with Markovian switching are considered. It is shown that the robust synchronisation of such an uncertain multi-agent network could be achieved by a protocol that each controller being partially delay-dependent or disordering could robustly stabilise a given single Markovian jump system. As for these cases, the proposed protocols could be obtained by solving certain algebraic Riccati equations and inequalities, which also involve weighting factors and depend on the eigenvalues of the Laplacian graph. [ABSTRACT FROM AUTHOR]