Admissible Uncertainties Research Articles

Robust sequential fusion Kalman estimators with asymptotic equivalence and stability for networked uncertain sensor systems

For networked uncertain sensor systems (NUSSs) with an improved unified sensor model with “hard” and “soft” sensors including five uncertainties plus two-step random measurement delays and colored measurement noises, applying the block matrix inversion formula, a new sequential inverse covariance fusion (SICF) approach is presented. It can sequentially compute the global inverse covariance according to the time order of the received data, but need not wait until all data are received. The corresponding minimax robust time-varying and steady-state sequential fusion (SF) Kalman estimators (predictor, filter, and smoother) are presented in the sense that their actual error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. They have lower computation complexities and higher accuracies equivalent to ones of the robust optimal batch-fusion (BF) Kalman estimators, and are suitable for real-time applications. Their asymptotic equivalence, absolute asymptotic stability, and accuracy relations are proved. Their strict complexity analysis is given. They constitute a novel universal robust SF estimation, convergence and stability theory for NUSSs. One simulation example applied to the uncertain ARMA signal processing verifies the effectiveness of the proposed approach and theory.

Robust fractional order singular Kalman filter

AbstractIn this article, the state estimation problem of linear fractional order singular (FOS) systems subject to matrix uncertainties is investigated where a recursive robust algorithm is derived. Considering an uncertain discrete‐time linear FOS system with added process and measurement noises, we aim to design a robust Kalman‐type state estimation algorithm based on an optimal data fitting approach with a given sequence of observations. As a substitute for the stochastic formulation, this general filter is obtained by minimizing a completely deterministic regularized residual norm in its worst‐possible form at each step over admissible uncertainties. Analysis of the algorithm shows that not only does the proposed robust filter cover the traditional robust Kalman filters (KFs), but it also represents an extension of the nominal fractional singular KF (FSKF) when the system is not subject to uncertainties. Furthermore, besides giving a sufficient condition for the existence of the robust filter, we derive conditions for the asymptotic properties of the filter, where we demonstrate that the filter and the Riccati equation are stable and converge when an equivalent system is detectable and stabilizable. A numerical example is included to demonstrate the performance of the introduced filter.

Robust Optimal Control for Discrete-Time LTI Systems Over Multiple Additive White Gaussian Noise Channels

Unlike the traditional point-to-point control structure, control system design through network media introduces additional constraints due to limited capacities of the used communication channels. In this paper, we address the optimal performance control problem for linear uncertain discrete-time systems over multiple additive white Gaussian noise (AWGN) channels, where mean power constraints are imposed on the actuator side. The desired controller is aimed to robustly stabilize the plant, to minimize the linear quadratic (LQ) cost, and to satisfy diverse pre-specified mean power limits associated with individual elements of the control law, simultaneously. Within the framework of system level synthesis, the performance objective and power constraints, together with relevant upper bounds, over all admissible uncertainties are characterized in terms of system responses of the closed-loop system and statistics of the communication channels. Based on this characterization, numerically tractable algorithms are proposed for controller synthesis. The counterpart for deterministic systems is also discussed as a special case with corresponding algorithms being provided. Moreover, the relative performance loss incurred by the size of model uncertainties and the finite truncation is explicitly established. An example is also included to show the effectiveness of the present results.

Robust weighted fusion Kalman estimators for systems with uncertain noise variances, multiplicative noises, missing measurements, packets dropouts and two‐step random measurement delays

AbstractFor multisensor networked systems with uncertain noise variances, multiplicative noises and multiple networked‐induced uncertainties including missing measurements, packets dropouts and two‐step random measurement delays, the robust weighted fusion estimation problem is addressed in this article. More precisely, the system noise variances are assumed to be uncertain but bounded, the other four uncertainties are compensated into fictitious white noise by the proposed model transformation method, which includes the augmented method and extended fictitious noise technique. Then local multi‐model system is obtained, for which robust local Kalman estimator is obtained based on the minimax robust estimation principle and unified estimation method. Based on this, the six robust weighted fusion time‐varying Kalman estimators are presented in a unified form, which include robust weighted fusers weighted by matrices, diagonal, scalars, and a robust covariance intersection (CI) fuser and two fast CI (FCI) fusers. The robustness proving method, including the extended Lyapunov equation approach with two kinds of generalized Lyapunov equations, non‐negative matrix factorization and elementary transformation of matrix, is presented to prove that the actual estimation error variances are guaranteed to have minimal upper bounds for all admissible uncertainties. The accuracy relations are proved. Further, the robust local and fused steady‐state Kalman estimators are presented. Finally, a simulation example applied to Internet‐based three tank water system is given to demonstrate effectiveness of the proposed results.

Identifying Admissible Uncertainty Bounds for the Input of Planning Algorithms

Identifying Admissible Uncertainty Bounds for the Input of Planning Algorithms

Non-fragile robust model predictive controller design for uncertain time-delay systems with input constraints

ABSTRACT This paper addresses a non-fragile robust model predictive control design for a class of continuous-time uncertain systems with multiple state-delay and constrained control signals. The parameters of the system and the control gain are assumed to have perturbation in the additive form. The Lyapunov–Krasovskii functional approach is employed to derive sufficient conditions for determining a non-fragile robust state-feedback controller for all admissible uncertainties by minimising the upper bound of the defined quadratic cost function with respect to some linear matrix inequalities (LMIs). An additional inequality condition is imposed to address the constraint associated with the control signals. Numerical simulations are provided to assess the performance of the proposed controller.

Robust Optimal Control With Inexact State Measurements and Adjustable Uncertainty Sets

The efficacy of robust optimal control with adjustable uncertainty sets is verified in several domains under the perfect state information setting. This paper investigates constrained robust optimal control for linear systems with linear cost functions subject to uncertain disturbances and state measurement errors that are both residing in adjustable uncertainty sets. We first show that the class of affine feedback policies of state measurements are equivalent to the class of affine feedback policies of estimated disturbances in terms of their conservativeness. Then, we formulate and solve a robust optimal control problem with adjustable uncertainty sets by considering the disturbance feedback policies. In contrast to the conventional robust optimal control, where uncertainty sets are fixed and known a priori, the uncertainty sets themselves are regarded as decision variables in our design. In particular, given the metrics for evaluating the optimal size/shape of the polyhedral uncertainty sets, a bilinear optimization problem is formulated to decide the optimal size/shape of uncertainty sets and a corresponding optimal control policy to robustly guarantee that the system will respect its constraints for all admissible uncertainties. In addition, we introduce a convex approximation for the proposed scheme to provide a computationally efficient inner approximation of the original problem. The proposed scheme is illustrated by numerical simulation of a building temperature control problem to demonstrate its effectiveness.

Attitude tracking control for reentry vehicles using centralised robust model predictive control

In this work, a centralised robust model predictive control (CRMPC) algorithm is proposed for reentry vehicles to track reference attitude trajectories subject to state/input constraints and uncertainties. In contrast to most designs that apply a cascade control structure for the two-timescale attitude dynamical systems, the proposed control scheme utilises a centralised structure to avoid additional controller development and parameter turning. By designing a nonlinear feedback law and tightening the system constraints, robust constraint satisfaction can be ensured for all admissible uncertainties. In addition, to guarantee the recursive feasibility and closed-loop stability of the proposed CRMPC, a terminal controller, along with a terminal region, is introduced. The validity of using the proposed approach to solve the considered problem is confirmed by executing several experimental studies, which were compared against two other established methods.

Robust control of uncertain time-delay Markovian jump quaternion-valued neural networks subject to partially known transition probabilities: direct quaternion method.

This paper addresses the issue of robust stochastic stabilization and control of uncertain time-delay Markovian jump quaternion-valued neural networks (MJQVNNs) subject to partially known transition probabilities. First, the direct quaternion method is proposed to analyse the MJQVNNs, which is different from some conventional methods in that the former is without any decomposition for systems. After that, in order to estimate the upper bound of the derivative of the constructed Lyapunov-Krasovskii functional(LKF) more accurately, the real-valued convex inequality is extended to quaternion domain. Then, by designed the mode-dependent state feedback controllers, the robust stochastic stabilization conditions of MJQVNNs are given for the admissible uncertainties, and reduce the influence of input disturbance on the controlled output to a specified performance level. Lastly, two numerical examples are given to illustrate the effectiveness of the proposed method.

Sequential Covariance Intersection Fusion Robust Time-Varying Kalman Filters with Uncertainties of Noise Variances for Advanced Manufacturing.

This paper addresses the robust Kalman filtering problem for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, the robust local time-varying Kalman filters are presented. Further, the batch covariance intersection (BCI) fusion and a fast sequential covariance intersection (SCI) fusion robust time-varying Kalman filters are presented. They have the robustness that the actual filtering error variances or their traces are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved based on the proposed Lyapunov equations approach. The concepts of the robust and actual accuracies are presented, and the robust accuracy relations are proved. It is also proved that the robust accuracies of the BCI and SCI fusers are higher than that of each local Kalman filter, the robust accuracy of the BCI fuser is higher than that of the SCI fuser, and the actual accuracies of each robust Kalman filter are higher than its robust accuracy for all admissible uncertainties of noise variances. The corresponding steady-state robust local and fused Kalman filters are also presented for multisensor time-invariant systems, and the convergence in a realization between the local and fused time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and the correctness of the robust accuracy relations.

Output feedback based robust iterative learning control via a heuristic approach for batch processes with time-varying state delays and uncertainties

This paper proposes an output feedback (OF) based PD-type robust iterative learning control (ILC) scheme for a class of discrete batch processes with time-varying delays and uncertainties in the absence of accurate state measurements, which is convenient for practical applications. Based on a repetitive process model and Lyapunov–Krasovskii theory, sufficient conditions are established in terms of linear matrix inequalities (LMIs) to ensure the robust stability along the trial for all admissible uncertainties. A two-stage heuristic approach is developed to iteratively calculate the feasible ILC gains based on a pre-designed state feedback (SF) controller, which circumvents the non-convex stability conditions expressed in bilinear matrix inequalities caused by OF. In addition, the conditions can be extended to the case of non-repetitive uncertainties in the system and meet the prescribed H∞ performance level. Finally, a simulation of injection molding process is given to demonstrate the effectiveness of the proposed method.

On designing the hybrid-triggered dynamic output feedback guaranteed cost control for uncertain T-S fuzzy networked control systems with cyber attack and actuator saturation

In this paper, we study the hybrid-triggered dynamic output feedback-based guaranteed cost control issue for uncertain Takagi-Sugeno (T-S) fuzzy networked control systems (NCSs) with cyber attack and actuator saturation. The hybrid-triggered mechanism comprising of time-triggered mechanism (TTM) and event-triggered mechanism (ETM) is provided to adjust the trigger strategy due to the variety in network resource utilization. Both the switching between two trigger mechanisms and the cyber attack phenomenon in communication network are respectively represented by two Bernoulli distributions. The data quantization is characterized by the sector bound technique and actuator saturation is addressed by invoking an auxiliary matrix. The stability of closed-loop NCSs with bounded disturbance and cyber attack is expressed by the methodology of quadratic boundedness (QB). The existence criteria and design strategies for minimizing the upper bound of performance in view of dynamic output feedback controller are constructed for any admissible uncertainties. Subsequently, in the light of the cone complementarity linearization (CCL) algorithm, the controller design issue is cast into the convex optimization issue which is capable of solving by the technique about linear matrix inequalities (LMIs). Finally, simulation example is employed to demonstrate the validity of designed controller.

Casing Wear Log Using a Prewear Ellipse Shape from Ultrasonic Logging Data

Summary The inspection of casing integrity is an important field of study regarding well safety assessment. In casing design, casing wear prediction is usually performed with a torque and drag model calibrated with laboratory simulation results. The availability of ultrasonic logging data makes it possible to calibrate these models, correlating actual conditions with similar equipment, operations, and trajectory. This work presents an accurate methodology that quantifies casing wear under a certain uncertainty level using data from ultrasonic logging tools. An ellipse equation is adopted to estimate the prewear condition of the cross section, and then it is applied to calculate wear. Also, a methodology to generate synthetic tube cross sections with prescribed ovality, eccentricity, and groove wear, with any intensities and locations, is presented. A model error analysis is carried out to compare the accuracy of the proposed strategy with others found in the literature. A statistical error analysis shows how the measurement noise is related to the estimated wear. This provides the level of uncertainty of the response, which can improve the right interpretation of data. Results demonstrate that the strategy successfully achieves an adequate quantification and can be applied to estimate casing wear profiles, under an admissible uncertainty tolerance.

Robust dynamic output‐feedback ℋ∞ control for uncertain Takagi–Sugeno time‐delay systems

This work deals with the problem of robust output‐feedback control for a class of uncertain Takagi–Sugeno (T‐S) fuzzy systems with state time‐varying delays. The system is described by a state‐space T‐S fuzzy model with time‐varying delays and norm‐bounded parameter uncertainties. A robust control strategy via Lyapunov–Krasovskii functionals for stability and performance conditions is derived. The T‐S fuzzy‐model‐based framework is employed in analysis, and formulations are performed based on the solution of a set of delay‐dependent linear matrix inequalities (LMIs). By solving the derived LMI conditions via a convex programming toolbox, a full‐order robust dynamic output‐feedback controller is designed. The obtained robust output‐feedback controller guarantees asymptotic stability of the closed‐loop system and provides an norm, that is, disturbance attenuation level, for all admissible uncertainties. In this sequel, three examples are given to reveal the effectiveness and merits of the proposed approaches.

Delay-dependent Robust Control for Uncertain Linear Systems with Distributed and Multiple Delays

This paper considers robust control of uncertain linear neutral systems with multiple state and state derivative delays. With equivalent descriptor representation, the stabilization problem is extended to more general class of neutral-type uncertain linear systems with discrete and distributed delays. The parametric uncertainties are time varying and unknown but norm bounded. Two delay-dependent/independent approaches are proposed to design robust controllers for a class of uncertain linear neutral systems with parametric uncertainty, discrete and distributed multiple delays. Using a presented descriptor model and an appropriate Lyapunov functional, sufficient conditions for closed loop stability are given in terms of linear matrix inequalities (LMIs). Solving the LMI problems, a robust memoryless state feedback is designed for all admissible uncertainties. The results depend on the size and varying rate of the delays. Two examples are provided to show the effectiveness of the proposed strategy.

Robust time‐varying estimator for descriptor system with random one‐step measurement delay

AbstractFor the linear stochastic descriptor system with random one‐step measurement delay and uncertain‐variance correlated noises, the robust estimation problem is addressed. Applying the singular value decomposition method, augmented state approach and fictitious noise approach, the original descriptor system is transformed to new standard system only with uncertain‐variance fictitious noises. Based on Kalman filtering and the minimax robust estimation principle, the actual Kalman estimator for the proposed standard system with actual measurement and the upper bounds of the variances is presented, including the Kalman predictor, filter, smoother and white noise deconvolution estimator. According to the relation of the new standard system and the original system, the actual estimator of original state of descriptor system and actual estimation error variance are presented. Further, the robustness of the actual estimator is proved by the Lyapunov equation approach, that is, the actual estimation error variance is guaranteed to have minimal upper bound for all admissible uncertainties. A simulation example about circuits system verifies the correctness and effectiveness of the proposed results.

Application of Magnetic Sensor for Magnetic Profile (1D) and Surface (2D) Measurement of Automotive Wheels.

This paper shows a report of over three years of intensive work on application of a 3-axis anisotropic magnetoresistive sensor with I2C interface for measurement of magnetic flux density distribution of automotive wheels. The work was undertaken to answer the question of whether is a possibility to effectively apply low-cost magnetic sensors with serial interface to measure the magnetic field surrounding the automotive wheel or tire. Two measurement techniques were discussed: Magnetic profile (1D) and magnetic surface measurement (2D) over tread, and also gear associated with the sensor, as well as its design, layout, operation, and control technique during (1D) and (2D) measurements. Three experiments were performed to asses accuracy and repeatability concerning component and resultant magnetic circumferential profiles and also magnetic surface. Differences between measurement outcomes in experiment were assessed. The results show that accuracy and repeatability lays below maximum admissible uncertainty declared by the producer. This proves directly that there is no measurable influence of motors, gear, operation, or measurement procedure on results obtained by magnetic sensors, and indirectly, that the assumed requirements regarding gear design and parameters are correct, and measurement of magnetic flux density distribution of automotive wheels and tires using (1D) and (2D) techniques is possible using a 3-axis anisotropic magnetoresistive sensor with I2C interface.

Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration

In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.

Finite-time reliable filtering for Takagi–Sugeno fuzzy semi-Markovian jump systems

In this study, we concentrate on the problem of a finite-time reliable filter design for discrete-time Takagi–Sugeno fuzzy semi-Markovian jump systems with time-varying delay, sensor faults and randomly occurring uncertainties. To be precise, the time-varying transition probability matrices for the considered system are described by a semi-Markov process. Specifically, the objective is to design a reliable filter ensuring the strict dissipativity performance of the augmented filtering error system in the presence of sensor failures. Further, the stochastic variables describing the random nature of the parameter uncertainties are assumed to follow the Bernoulli distribution. A new finite-time stochastic stability criterion based on reciprocally convex approach and Lyapunov–Krasovskii stability theory is established in terms of linear matrix inequalities for the considered Takagi–Sugeno fuzzy semi-Markovian jump systems. Moreover, the delay-dependent conditions are established to guarantee the augmented filtering error system to be stochastically finite-time bounded and to achieve a prescribed strict dissipativity performance level for all admissible uncertainties and sensor faults. Finally, a numerical example is provided to show the correctness and effectiveness of the proposed method.

Resilient Observer-Based H ∞ Control of Uncertain Nonlinear Networked Control Systems

This paper considers the resilient H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> dynamic control of nonlinear uncertain systems over a network assuming random communication packet dropouts, a subject which is seldom considered in the current literature for such uncertain systems. The uncertainties in the system and the controller are real, time-varying and norm bounded. Bernoulli distribution with white sequence is used to model the random packet losses with assumed conditions on the probability distribution. The resilient controller designed is an observer-based dynamic. The resulted closed-loop system is exponentially mean square stable and the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance is less than a prescribed level γ for all admissible uncertainties. New sufficient conditions for the existence of such a controller are presented and proved based on the linear matrix inequalities (LMIs) approach. A numerical example is presented to demonstrate and show the effectiveness of the developed theory.