Gain Matrix Research Articles

Collaborative-prediction-based recursive filtering for nonlinear systems with sensor saturation under duty cycle scheduling

In this paper, a recursive filtering problem is analyzed for nonlinear systems with sensor saturation under duty cycle scheduling (DCS). The sensor saturation is taken into account to describe practical engineering better. The DCS is introduced to conserve energy by alternating sensor nodes between active and dormant states. The considered problem aims to design a collaboration-prediction-based recursive filtering algorithm for nonlinear systems with sensor saturation such that, under the sparse measurements due to DCS, satisfactory filtering performance is guaranteed. By solving a set of matrix difference equations, the upper bound on the filtering error covariance is first obtained, and then the gain matrix of the filter that minimizes the upper limit is calculated. In addition, the boundedness of the upper bound of the filtering error covariance is analyzed. Finally, the effectiveness of the proposed collaboration-prediction-based recursive filtering algorithm is verified by the simulation example.

A plantwide control proposal for ethylbenzene production

In the present article, a plantwide control structure is proposed for the benzene alkylation process. The mathematical model used in the simulations developed in scilab free software, version 6.1, was based on previous studies. Initially, operational restrictions were evaluated and possible controlled variables were chosen based on operational objectives and tested by performing step disorders to validate the criteria. The choice of the best pairs was made through the RGA (Relative Gain Array) relative gain matrix. The structural decisions adopted and the results obtained through computational simulation indicated that although there are interactions between the control loops, the possible pairs, T1-FR2 and T4-Q4, minimize the system interactions. The adjusted parameters of the controller were effective in controlling the disturbance, presenting little or no overshoot with satisfactory ascent and response times. The control structure adopted with the PID controller is just one of the fundamental steps within the plantwide control methodology and shows the controller’s ability to meet the proposed structural objectives.

Positivity and decentralized [formula omitted] control of nonlinear interconnected switched positive systems under MDDT constraint

The article is focused on the problems of positivity and decentralized L1 control for nonlinear interconnected switched positive systems(NISPSs) under mode-dependent dwell time(MDDT) constraint, which includes mode-dependent constant dwell time(MDCDT), mode-dependent minimum dwell time(MDMDT) and mode-dependent ranged dwell time(MDRDT) constraints. Both nonlinear subsystems and nonlinear interconnections are included in the considered NISPSs. First, a sufficient and necessary condition of positivity is presented for NISPSs. Next, by applying a novel discretized linear copositive Lyapunov function method, a sufficient condition of exponential stability with L1-gain performance is provided for NISPSs under MDCDT, MDMDT and MDRDT constraints, respectively. Further, by applying the matrix decomposition technology to the decentralized controller gain matrix, an effective mode-dependent piece-wise design scheme of decentralized L1 controller in the solvable linear programming(LP) form is proposed for NISPSs under MDCDT, MDMDT and MDRDT constraints, respectively. The proposed decentralized L1 controller design scheme for NISPSs under MDDT constraint can be degenerated into the one in mode-independent constraint case accordingly. At last, four examples with comparisons are given to illustrate the importance and effectiveness of the obtained results.

Distributed fixed-time and prescribed-time average consensus for multi-agent systems with energy constraints

This paper is devoted to the investigation of the fixed-time and prescribed-time average consensus problem for multi-agent systems (MASs) with energy constraints. For the purpose of the fixed-time and prescribed-time average consensus of MASs, two control algorithms are firstly developed in this paper on the basis of the fixed-time technique and the prescribed-time technique. Then, the time integral of the quadratic function is constructed to calculate the energy consumption by the error between each agent and the reference state. And the sufficient conditions for the stability of the Lyapunov function are provided by designing the parameters and the gain matrix. Ultimately, the theoretical results are effectively and correctly verified by utilizing simulations.

Adaptive event-triggered path following control for networked autonomous vehicles under aperiodic denial-of-service attacks

ABSTRACT This paper studies the adaptive event-triggered (AET)-based path following control problem for networked autonomous vehicles subject to aperiodic denial-of-service (DoS) attacks. Firstly, considering the strong dependence between scheduling parameters, a polytopic linear parameter varying system is established to represent the nonlinear path following system. Secondly, to save limited communication bandwidth and guarantee a desired path following control performance effectively, a novel AET mechanism with nonmonotonic characteristics is designed, and a compensation strategy is presented to tackle the effect of packet losses caused by DoS attacks on the system. Thirdly, sufficient conditions are developed for the output feedback controller gain matrix and the AET mechanism weighting matrix such that the closed-loop system is guaranteed to be stable and an performance is satisfied. Finally, simulation results verify the proposed control strategy.

Set-Membership Adaptive Robot Control With Deterministically Bounded Learning Gains

As a powerful set-membership adaptive identification algorithm, the optimal bounded ellipsoid (OBE) enables fast convergence speeds because it exploits <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information about system dynamics by estimating sets of feasible solutions rather than single-point solutions. However, its learning gain matrix suffers from vanishing or unbounded growth, which seriously limits its practical performance. In this paper, a novel OBE algorithm is proposed to ensure that the learning gain matrix is constrained by upper and lower bounds, which are unaffected by the hardly predictable excitation levels and can be determined before implementing the algorithm. Thus, the system robustness and tracking capability for time-varying dynamics can be improved. In light of the proposed OBE identification algorithm, an adaptive robot control strategy is further proposed, where the robot dynamics are reconstructed through neural networks. The practical partial asymptotic stability of the closed-loop system is demonstrated using the Lyapunov method. Furthermore, noisy acceleration signals and the inversion of the inertial matrix are eliminated with the proposed control strategy. Experimental results on a robot manipulator validate the effectiveness of the proposed approach.

An Adaptive Torque Observer Based on Fuzzy Inference for Flexible Joint Application

Torque observation techniques have been widely employed to estimate the load torque of flexible joints driven by a permanent magnet synchronous machine (PMSM). However, the performance of the observer degrades significantly when the position and orientation of the robot continuously changes, resulting in substantial irregular load variations. In this paper, an adaptive torque observer based on fuzzy inference is proposed to overcome this issue. Instead of relying on theoretical or numerical derivation, the relationship between the load inertia and the closed-loop poles of the torque observer is expressed by fuzzy inference. This approach enables the flexible configuration of the poles based on the load inertia, allowing for automatic tuning of the gain matrix. Consequently, the observer can ensure robustness and maintain superior performance under varying load conditions. The effectiveness of the proposed observer is validated through simulation and experimental results. It shows that compared to the classical Luenberger observer, the proposed adaptive torque observer can achieve more accurate observation results and exhibits a more dynamic response in the presence of varying load inertia.

Asynchronous Switching Control of Discrete Time Delay Linear Switched Systems Based on MDADT

Ideally, switching between subsystems and controllers occurs synchronously. In other words, whenever a subsystem requires switching, its corresponding sub-controller will be promptly activated. However, in reality, due to network delays, system detection, etc., the activation of candidate controllers frequently lags, which causes issues with asynchronous switching between controllers and subsystems. This asynchronous switching problem may affect system performance and even make the system unstable because the state between the subsystem and the controller may be inconsistent, resulting in the controller not being able to control the subsystem correctly. To keep the system stable while using asynchronous switching, this work suggests an asynchronous control technique for a class of discrete linear switching systems with time delay based on the mode-dependent average dwell time (MDADT). First, we construct a state feedback controller and establish a closed-loop system. In the asynchronous and synchronous intervals of subsystems and controllers, different Lyapunov functions are selected, and sufficient conditions for exponential stability and the H∞ performance of the closed-loop system under asynchronous switching are obtained. In addition, using the MDADT switching strategy, the relevant parameters of each subsystem are designed and the corresponding state–feedback controller gain matrix can be obtained. Finally, a switching system with three subsystems is shown. The approach is confirmed by simulating it using the average dwell time (ADT) switching strategy and the MDADT switching strategy separately.

Event-triggered finite-time [formula omitted] control for positive Markov jump systems with partly known transition probability

The article studies the event-triggered finite-time L1 control design for positive Markov jump systems(PMJSs) with partly known transition probability. Firstly, with regard to the unique positive characteristic, a novel 1-norm based event-triggering condition is proposed for PMJSs. Then, sufficient conditions of positivity and finite-time L1 boundedness are provided for the closed-loop system under the constructed even-triggered control law. Based on this, by applying the matrix decomposition technology to the event-triggered controller gain matrix, an effective mode-dependent event-triggered finite-time L1 control scheme in the solvable linear programming(LP) form is presented for PMJSs while preserving the positivity and finite-time L1 boundedness in closed-loop. Further, an effective LP-based event-triggered finite-time L1 control scheme is also obtained for PMJSs with completely known transition probability and completely unknown transition probability, respectively. Finally, two examples are presented to verify the validity of the obtained results.

Behavior learning based distributed tracking control for human-in-the-loop multi-agent systems

In this study, the distributed tracking problem for human-in-the-loop multi-agent systems (HiTL MASs) has been investigated. First, we construct an HiTL MAS model with a non-autonomous leader which can receive the control signal from a human operator and generate the desired trajectory. The human control signal is assumed to be generated by a leader’s state feedback control law with an unknown gain matrix that represents the control behavior of the human operator. Then, we propose a fully distributed adaptive control method that enables all followers to simultaneously track the human-controlled leader and online learn the unknown human operator’s feedback gain matrix. Furthermore, the parameter estimation error is also discussed, and all followers will learn the true value of the human operator’s feedback gain matrix when the state of the leader satisfies the persistent excitation (PE) condition. Moreover, a novel distributed adaptive control law is developed for each follower to remove the PE condition by utilizing the concurrent learning (CL) technique. Finally, simulated examples demonstrating the effectiveness of the proposed methodologies are presented.

Event‐triggered nonfragile state estimation for delayed neural networks with additive and multiplicative gain variations

AbstractThis article aims to design a nonfragile state estimator for neural networks with time‐varying delay under the event‐triggered mechanism. This paper addresses the two most common issues that exist in large‐scale networks: gain variations in the estimator design and lack of network resources. Based on the nonfragile paradigm and an event‐triggered mechanism, an estimator is being developed to address this issue, considering both the additive and multiplicative structured gain variations. Through the Lyapunov–Krasovskii functional method and linear matrix inequality technique, sufficient conditions are derived to guarantee the existence of the proposed state estimator by employing the generalized free‐weighting matrix inequality and improved reciprocally convex inequality. Moreover, the obtained linear matrix inequalities provide an explicit expression of the estimator gain matrix and triggering matrix. Eventually, two numerical examples are provided to authenticate the proposed findings.

Designing multivariable PI controller with multi-response optimization for a pilot plant binary distillation column: a robust design approach

Purpose The purpose of this paper is to propose and validate a robust industrial control system. The aim is to design a Multivariable Proportional Integral controller that accommodates multiple responses while considering the process's control and noise parameters. In addition, this paper intended to develop a multidisciplinary approach by combining computational science, control engineering and statistical methodologies to ensure a resilient process with the best use of available resources. Design/methodology/approach Taguchi's robust design methodology and multi-response optimisation approaches are adopted to meet the research aims. Two-Input-Two-Output transfer function model of the distillation column system is investigated. In designing the control system, the Steady State Gain Matrix and process factors such as time constant (t) and time delay (?) are also used. The unique methodology is implemented and validated using the pilot plant's distillation column. To determine the robustness of the proposed control system, a simulation study, statistical analysis and real-time experimentation are conducted. In addition, the outcomes are compared to different control algorithms. Findings Research indicates that integral control parameters (Ki) affect outputs substantially more than proportional control parameters (Kp). The results of this paper show that control and noise parameters must be considered to make the control system robust. In addition, Taguchi's approach, in conjunction with multi-response optimisation, ensures robust controller design with optimal use of resources. Eventually, this research shows that the best outcomes for all the performance indices are achieved when Kp11 = 1.6859, Kp12 = −2.061, Kp21 = 3.1846, Kp22 = −1.2176, Ki11 = 1.0628, Ki12 = −1.2989, Ki21 = 2.454 and Ki22 = −0.7676. Originality/value This paper provides a step-by-step strategy for designing and validating a multi-response control system that accommodates controllable and uncontrollable parameters (noise parameters). The methodology can be used in any industrial Multi-Input-Multi-Output system to ensure process robustness. In addition, this paper proposes a multidisciplinary approach to industrial controller design that academics and industry can refine and improve.

The detection mechanism for false data injection attack via the ellipsoidal set‐membership approach

AbstractThe false data injection (FDI) attack detection problem in cyber‐physical systems (CPSs) is investigated in this paper. A novel attack detection algorithm is proposed based on the ellipsoidal set‐membership approach. In comparison to the existing FDI attack detection methods, the developed attack detection approach in this paper neither requires predefined thresholds nor specific statistical characteristics of the attacks. In order to guarantee that the estimation ellipsoid contains normal states despite the unknown but bounded (UBB) process and measurement noises, the one‐step ellipsoidal set‐membership estimation method is put forward. In addition, a convex optimization algorithm is introduced to calculate the gain matrix of the observer recursively. Moreover, with the help of the state estimation ellipsoid, the residual ellipsoid can be obtained for attack detection. Whether a detector can detect the FDI attack depends on the relationship between the residual value and residual ellipsoidal set. Finally, the effectiveness of the proposed method is demonstrated by a numerical simulation example.

STABILIZATION OF DISCRETE-TIME SYSTEMS WITH STATE-DELAYS AND SATURATING CONTROL INPUTS

Context. The presence of time delays occurs in many complex dynamical systems, particularly in the areas of modern communication and information technologies, such as the problem of stabilizing networked control systems and high-speed communication networks. In many cases, time-delays lead to a decrease in the efficiency of such systems and even to the loss of stability. In the last decade, many interesting solutions using the Lyapunov-Krasovskii functional have been proposed for stability analysis and synthesis of a stabilizing regulator for discrete-time dynamic systems with unknown but bounded state-delays. The presence of nonlinear constraints on the amplitude of controls such as saturation further complicates this problem and requires the development of new approaches and methods.&#x0D; Objective. The purpose of this study is to develop a procedure for calculating the control gain matrix of state feedback that ensures the asymptotic stability of the analyzed system, as well as a procedure for calculating the maximum permissible value of the state-delay under which the stability of the closed-loop system can be ensured for a given set of admissible initial conditions.&#x0D; Method. The paper uses the method of descriptor transformation of the model of a closed-loop system and extends the invariant ellipsoids method to systems with unknown but bounded state-delays. The application of the Lyapunov-Krasovskii functional and the technique of linear matrix inequalities made it possible to reduce the problem of calculating the control gain matrix to the problem of semi-definite programming, which can be solved numerically. An iterative algorithm for solving the bilinear matrix inequality is proposed for calculating the maximum permissible value of the time-delay.&#x0D; Results. The results of numerical modeling confirm the effectiveness of the proposed approach in the problems of stabilizing discrete-time systems under the conditions of state-delays and nonlinear constraints on controls, which allows to recommend the proposed method for practical use for the problem of stability analysis and synthesis of stabilizing regulator, as well as for calculating the maximum permissible value of time-delay.&#x0D; Conclusions. An approach is proposed that allows extending the invariant ellipsoids method to discrete-time dynamic systems with unknown but bounded state-delays for solving the problem of system stabilization using static state feedback based on the application of the Lyapunov-Krasovskii functional. The results of numerical modeling confirm the effectiveness of the proposed approach in the presence of the saturation type nonlinear constraints on the control signals.

A Low Complexity Proportionate Generlized Correntropy-Based Diffusion LMS Algorithm With Closed-Form Gain Coefficients

This brief proposes a correntropy-based proportionate diffusion algorithm with low computational complexity. The proportionate diffusion algorithms in the literature suffer from a high computational complexity due to the complicated calculation process of the coefficients of the gain matrix, i.e., by solving an optimization problem or solving a linear system of equations via a matrix inversion. In this brief, by defining a proper correntropy kernel function and suitably assuming a wise constraint, the gain matrix coefficients are derived in a closed-form formula. In fact, the correntropy kernel function is used to determine the gain coefficients. This closed-form formula significantly reduces the computational complexity of the proposed algorithm. Moreover, a condition of uniform convergence for the distributed estimation algorithm at each time instant is obtained analytically. Simulation results show the lower steady-state Normalized Mean Square Deviation (NMSD) and lower computational complexity of the proposed algorithm compared to some other competing algorithms.

Observer‐based sliding mode fault tolerant control for nonlinear descriptor systems

AbstractIn this article, the design and analysis of fault tolerant control (FTC) are investigated for stochastic nonlinear descriptor systems by using the sliding mode approach. First, an integral sliding mode‐based descriptor observer (ISM‐DO) is constructed to estimate the state and fault. The proposed ISM‐DO retains the basic characteristics of descriptor systems, meanwhile, it is not only suitable for dual normalized descriptor systems, but also for non‐dual normalized descriptor systems. It is more universal than the existing sliding mode fault tolerant control (SMFTC) methods. In the sequel, a novel restricted equivalent form based algorithm is developed to solve the sliding parameters. The proposed method provides a general algorithm, and it does not impose additional rank constraints. Further, a new adaptive sliding mode fault tolerant controller is constructed to stabilize the fault system, the assumption related to the diffusion matrix is removed. Based on these ingredients, the asymptotically mean square admissibility of the closed‐loop fault system and the observer gain matrix are got by a sufficient linear matrix inequality condition. The effectiveness of the proposed method is verified by simulations.

Neural-Network-Based Secure State Estimation Under Energy-Constrained Denial-of-Service Attacks: An Encoding-Decoding Scheme

This paper is concerned with the secure state estimation issue for a class of networked nonlinear systems under energy-constrained denial-of-service (EC-DoS) cyber-attacks and encoding-decoding scheme (EDS). The information transmissions between sensors and the estimator are executed via a bandwidth-limited communication network, on which the EDS is deployed to convert transmitted signals into finite-length codewords for the purpose of improving transmission efficiency. The EC-DoS attacks, whose intention is to jeopardize the network-based signal transmissions by overloading the communication resource, are assumed to occur in an intermittent way with bounded occurrence frequency/durations owing to the inherent energy constraints on the attackers. Considering the worst case of such EC-DoS attacks, a neural-network (NN)-based state estimator is constructed to generate the desired state estimates for the underlying networked nonlinear system. By employing the Lyapunov stability theory, the estimation error dynamics of the system state and the neural-network weight are jointly analyzed within a unified framework. Subsequently, sufficient conditions are obtained for the existence of the desired NN-based state estimator, and then both the desired estimator gain matrix and the NN tuning parameters are characterized. Finally, the validity of our estimation approach is confirmed by an example.

Ellipsoidal tube‐based output feedback robust MPC for linear systems with bounded disturbances and noises

AbstractThis paper designs an ellipsoidal tube‐based output feedback robust model predictive control approach for linear systems with bounded disturbances and noises subject to physical constraints. The ellipsoidal tube‐based output feedback robust model predictive control approach combines the off‐line optimization to compute controller parameters and deal with system uncertainties, and the on‐line optimization to stabilize the nominal system with time‐varying tightened constraints. In the off‐line optimization, the state observer gain, ancillary feedback controller gain, and tightened constraint sets on the nominal system are synthesized in one optimization. Then, an ellipsoidal terminal constraint set with terminal controller gain and terminal cost matrix, and tightened constraint sets related to different sizes of estimation error bounds are computed. In the on‐line model predictive control optimization with time‐varying tightened constraints, a sequence of nominal control inputs is receding horizon optimized to steer the nominal system state to the ellipsoidal terminal constraint set. When the current nominal system state is bounded within the ellipsoidal terminal constraint set, the nominal control inputs are switched to the feedbacks on the closed‐loop nominal system states. Recursive feasibility of the proposed algorithm and robust stability of the controlled system are guaranteed.

Approximate Kalman filtering by both M-robustified dynamic stochastic approximation and statistical linearization methods

The problem of designing a robustified Kalman filtering technique, insensitive to spiky observations, or outliers, contaminating the Gaussian observations has been presented in the paper. Firstly, a class of M-robustified dynamic stochastic approximation algorithms is derived by minimizing at each stage a specific time-varying M-robust performance index, that is, general for a family of algorithms to be considered. The gain matrix of a particular algorithm is calculated at each stage by minimizing an additional criterion of the approximate minimum variance type, with the aid of the statistical linearization method. By combining the proposed M-robust estimator with the one-stage optimal prediction, in the minimum mean-square error sense, a new statistically linearized M-robustified Kalman filtering technique has been derived. Two simple practical versions of the proposed M-robustified state estimator are derived by approximating the mean-square optimal statistical linearization coefficient with the fixed and the time-varying factors. The feasibility of the approaches has been analysed by the simulations, using a manoeuvring target radar tracking example, and the real data, related to an object video tracking using short-wave infrared camera.

H∞ observer-based sliding mode control for uncertain discrete-time singularly perturbed systems

This paper studies the sliding mode control (SMC) problem of discrete-time singularly perturbed systems (DTSPSs) with external perturbations and nonlinear inputs. First, to estimate the state of the original system, a novel state observer is constructed. Under this condition, the observer error system is ensured to be input-to-state stable (ISS) and satisfies the given H∞ performance index. Then, an appropriate sliding mode control law is proposed to satisfy the reachability condition. On this basis, the ISS criterion for the sliding mode dynamics (SMDs) is given, and the controller gain matrix is also obtained. In addition, a feasible algorithm is given to compute the upper bound for the small parameter. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.