Sliding mode-based adaptive tube model predictive control for robotic manipulators with model uncertainty and state constraints

In this paper, the optimal tracking control for robotic manipulatorswith state constraints and uncertain dynamics is investigated, and a sliding mode-based adaptive tube model predictive control method is proposed. First, utilizing the high-order fully actuated system approach, the nominal model of the robotic manipulator is constructed as the predictive model. Based on the nominal model, a nominal model predictive controller with the sliding mode is designed, which relaxes the terminal constraints, and realizes the accurate and stable tracking of the desired trajectory by the nominal system. Then, an auxiliary controller based on the node-adaptive neural networks is constructed to dynamically compensate nonlinear uncertain dynamics of the robotic manipulator. Furthermore, the estimation deviation between the nominal and actual states is limited to the tube invariant sets. At the same time, the recursive feasibility of nominal model predictive control is verified, and the ultimately uniformly boundedness of all variables is proved according to the Lyapunov theorem. Finally, experiments show that the robotic manipulator can achieve fast and efficient trajectory tracking under the action of the proposed method.     

Predicting the output error of the suboptimal state estimator to improve the performance of the MPC-based artificial pancreas

The error of single step-ahead output prediction is the information traditionally used to correct the state estimate while exploiting the new measurement of the system output. However, its dynamics and statistical properties can be further studied and exploited in other ways. It is known that in the case of suboptimal state estimation, this output prediction error forms a correlated sequence, hence it can be effectively predicted in real time. Such a suboptimal scenario is typical in applications where the process noise model is not known or it is uncertain. Therefore, the paper deals with the problems of analytical and empirical modeling, identification, and prediction of the output error of the suboptimal state estimator for the sake of improving the output prediction accuracy and ultimately the performance of the model predictive control. The improvements are validated on an empirical model of type 1 diabetes within an in-silico experiment focused on glycemia prediction and implementation of the MPC-based artificial pancreas.     

Observer design and interval estimation of time-delay discrete-time linear systems with external disturbance and measurement noise

For a class of time-delay discrete-time linear systems with external disturbance and measurement noise, the interval estimation problems of state and measurement noise are investigated in this paper. First, the system state together with the time-delay term and measurement noise is augmented as a new state, and a singular system is then constructed. Subsequently, a kind of decoupling technique is employed to eliminate the effect of external disturbance, and an observer is designed to simultaneously estimate the system state and measurement noise. Based on the estimated state and measurement noise, the interval estimations of system state and measurement noise are obtained by reachability analysis technique. Finally, the effectiveness of the proposed method is verified by a four-tank liquid level system.     

Adaptive feedback control for nonlinear triangular systems subject to uncertain asymmetric dead-zone input

In this paper, an adaptive control strategy is proposed to investigate the issue of uncertain dead-zone input for nonlinear triangular systems with unknown nonlinearities. The considered system has no precise priori knowledge about the dead-zone feature and growth rate of nonlinearity. Firstly, a dynamic gain is introduced to deal with the unknown growth rate, and the dead-zone characteristic is processed by the adaptive estimation approach without constructing the dead-zone inverse. Then, by virtue of hyperbolic functions and sign functions, a new adaptive state feedback controller is proposed to guarantee the global boundedness of all signals in the closed-loop system. Moreover, the uncertain dead-zone input problem for nonlinear upper-triangular systems is solved by the similar control strategy. Finally, two simulation examples are given to verify the effectiveness of the control scheme.     

Consistent Kalman filters for nonlinear uncertain systems over sensor networks

In this paper, we study how to design filters for nonlinear uncertain systems over sensor networks. We introduce two Kalman-type nonlinear filters in centralized and distributed frameworks. Moreover, the tuning method for the parameters of the filters is established to ensure the consistency, i.e., the mean square error is upper bounded by a known parameter matrix at each time. We apply the consistent filters to the track-to-track association analysis of multi-targets with uncertain dynamics. A novel track-to-track association algorithm is proposed to identify whether two tracks are from the same target. It is proven that the resulting probability of mis-association is lower than the desired threshold. Numerical simulations on track-to-track association are given to show the effectiveness of the methods.     

Data‑driven disturbance observer‑based control: an active disturbance rejection approach

In this paper, a data-driven method for disturbance estimation and rejection is presented. The proposed approach is divided into two stages: an inner stabilization loop, to set the desired reference model, together with an outer loop for disturbance estimation and compensation. Inspired by the active disturbance rejection control framework, the exogenous and endogenous disturbances are lumped into a total disturbance signal. This signal is estimated using an on-line algorithm based on a datadriven predictor scheme, whose parameters are chosen to satisfy high robustness-performance criteria. The above process is presented as a novel enhancement to design a disturbance observer, which constitutes the main contribution of the paper. In addition, the control strategy is completely presented in discrete time, avoiding the use of discretization methods for its digital implementation. As a case study, the voltage control of a DC-DC synchronous buck converter afected by disturbances in the input voltage and the load is considered. Finally, experimental results that validate the proposed strategy and some comparisons with the classical disturbance observer-based control are presented.     

Bipartite consensus for nonlinear time-delay multiagent systems via time-varying gain control method

The bipartite consensus problem is addressed for a class of nonlinear time-delay multiagent systems in this paper. Therein, the uncertain nonlinear dynamics of all agents satisfy a Lipschitz growth condition with unknown constants, and part of the state information cannot be measured. In this case, a time-varying gain compensator is constructed, which only utilizes the output information of the follower and its neighbors. Subsequently, a distributed output feedback control protocol is proposed on the basis of the compensator. According to Lyapunov stability theory, it is proved that the bipartite consensus can be guaranteed by means of the designed control protocol. Different from the existing literature, this paper studies the leader–follower consensus problem under a weaker connectivity condition, i.e., the signed directed graph is structurally balanced and contains a directed spanning tree. Two simulation examples are carried out to show the feasibility of the proposed control strategy     

Suppression of high order disturbances and tracking for nonchaotic systems: A time-delayed state feedback approach

Time-delayed state feedback is an easy realizable control method that generates control force by differencing the current and the delayed versions of the system states. In this paper, a new form of the time-delayed state feedback structure is introduced. Based on the proposed time-delayed state feedback method, a new robust tracking system is designed. This tracking system improves the conventional state feedback with integral action disturbance rejection characteristics in the presence of the disturbance signals imposed on the system dynamics or on the sensors that measure the system states. Also, the proposed tracking system tracks the ramp-shaped reference input signal, which is not achievable through conventional state feedback. Moreover, since the proposed method adds delays to the closed-loop system dynamics, the ordinary differential equation of the system changes to a delay differential equation with an infinite number of characteristic roots. Thus, conventional pole placement techniques cannot be used to design the time-delayed state feedback controller parameters. In this paper, the simulated annealing algorithm is used to determine the proposed control system parameters and move the unstable roots of the delay differential equation to the left half-plane. Finally, the efficiency of the proposed reference input tracker is demonstrated by presenting two numerical examples.     

Model variables identification of a gas turbine using a subspace approach based on input/output data measurements

This paper deals with a state model identification of a gas turbine used for gas transport, using a subspace approach of the state space model. This method provides a reliable and robust state representation of the model, taking advantage of its benefits in the control, monitoring, and supervision of this machine. The model for each variable is set so that the state matrices associated with the gas turbine model are determined from their real input/output data. The comparison of the obtained identification results with those of the actual turbine operation serves to validate the proposed model in this work. This numerical algorithm of the subspace identification method is full of information and more accurate in terms of residual modeling error, and expresses a very high level of confidence in the identified turbine system dynamics. Hence, the controllability and observability tests of turbine operation for different input/output variables allowed to validate the real-time operating stability of the turbine.     

On extended state Kalman filter-based identification algorithm for aerodynamic parameters

In this paper, the problem of time-varying aerodynamic parameters identification under measurement noises is studied. By analyzing the key aerodynamic parameters that affect the aircraft control system, a system model with extended states for identifying equivalent aerodynamic parameters is established, and error parameters are extended to the system state, avoiding the difficulty caused by the unknown dynamic in the system. Furthermore, an identification algorithm based on extended state Kalman filter is designed, and it is proved that the algorithm has quasi-consistency, thus, the estimation error can be evaluated in real time. Finally, the simulation results under typical flight scenarios show that the designed algorithm can accurately identify aerodynamic parameters, and has desired convergence speed and convergence precision.     

Automatic modeling algorithm of stochastic error for inertial sensors

This paper proposes an automatic algorithm to determine the properties of stochastic processes and their parameters for inertial error. The proposed approach is based on a recently developed method called the generalized method of wavelet moments (GMWM), whose estimator was proven to be consistent and asymptotically normally distributed. This algorithm is suitable mainly (but not only) for the combination of several stochastic processes, where the model identification and parameter estimation are quite difficult for the traditional methods, such as the Allan variance and the power spectral density analysis. This algorithm further explores the complete stochastic error models and the candidate model ranking criterion to realize automatic model identification and determination. The best model is selected by making the trade-off between the model accuracy and the model complexity. The validation of this approach is verified by practical examples of model selection for MEMS-IMUs (micro-electro-mechanical system inertial measurement units) in varying dynamic conditions.     

Design of tracking observers for locally jointly observable systems

This paper considers distributed state estimation of continuous-time linear system monitored by a network of multiple sensors. Each sensor can only access locally partial measurement output of the system and effectively communicates with its neighbors to cooperatively achieve the asymptotic estimation of the target full system state. For a constructive design, we shall incorporate the concept of system immersions and propose a class of distributed tracking observers for the problem under a reasonable condition of the locally joint observability. Moreover, as a direct application of the proposed observer design, we further present an interesting leader-following consensus design for multi-agent system.     

A novel suboptimal algorithm for state estimation of Markov jump linear systems

This paper is concerned with state estimation problem for Markov jump linear systems where the disturbances involved in the systems equations and measurement equations are assumed to be Gaussian noise sequences.Based on two properties of conditional expectation,orthogonal projective theorem is applied to the state estimation problem of the considered systems so that a novel suboptimal algorithm is obtained.The novelty of the algorithm lies in using orthogonal projective theorem instead of Kalman filters to estimate the state.A numerical comparison of the algorithm with the interacting multiple model algorithm is given to illustrate the effectiveness of the proposed algorithm.     

Iterative learning control for nonlinear systems with uncertain state delay and arbitrary initial error

Most of the existing iterative learning control algorithms proposed for time-delay systems are based on the condition that the time-delay is precisely available, and the initial state is reset to the desired one or a fixed value at the start of each operation, which makes great limitation on the practical application of corresponding results. In this paper, a new iterative learning control algorithm is studied for a class of nonlinear system with uncertain state delay and arbitrary initial error. This algorithm needs to know only the boundary estimation of the state delay, and the initial state is updated, while the convergence of the system is guaranteed. Without state disturbance and output measurement noise, the system output will strictly track the desired trajectory after successive iteration. Furthermore, in the presence of state disturbance and measurement noise, the tracking error will be bounded uniformly. The convergence is strictly proved mathematically, and sufficient conditions are obtained. A numerical example is shown to demonstrate the effectiveness of the proposed approach.     

Maximum correntropy-based pseudolinear Kalman filter for passive bearings-only target tracking

This paper proposes a new approach for solving the bearings-only target tracking (BoT) problem by introducing a maximum correntropy criterion to the pseudolinear Kalman filter (PLKF). PLKF has been a popular choice for solving BoT problems owing to the reduced computational complexity. However, the coupling between the measurement vector and pseudolinear noise causes bias in PLKF. To address this issue, a bias-compensated PLKF (BC-PLKF) under the assumption of Gaussian noisewas formulated. However, this assumptionmay not be valid in most practical cases. Therefore, a bias-compensated PLKF with maximum correntropy criterion is introduced, resulting in two new filters: maximum correntropy pseudolinear Kalman filter (MC-PLKF) and maximum correntropy bias-compensated pseudolinear Kalman filter (MC-BC-PLKF). To demonstrate the performance of the proposed estimators, a comparative analysis assuming large outliers in the process and measurement model of 2D BoT is conducted. These large outliers are modeled as non-Gaussian noises with diverse noise distributions that combine Gaussian and Laplacian noises. The simulation results are validated using root mean square error (RMSE), average RMSE (ARMSE), percentage of track loss and bias norm. Compared to PLKF and BC-PLKF, all the proposed maximum correntropy-based filters (MC-PLKF and MC-BC-PLKF) performed with superior estimation accuracy.     

Random gradient-free method for online distributed optimization with strongly pseudoconvex cost functions

This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state information with its current neighbors through a time-varying digraph. In addition, the agents do not have access to the information about the current cost functions until decisions are made. Different from most existing works on online distributed optimization, here we consider the case where the cost functions are strongly pseudoconvex and real gradients of the cost functions are not available. To handle this problem, a random gradient-free online distributed algorithm involving the multi-point gradient estimator is proposed. Of particular interest is that under the proposed algorithm, each agent only uses the estimation information of gradients instead of the real gradient information to make decisions. The dynamic regret is employed to measure the proposed algorithm. We prove that if the cumulative deviation of the minimizer sequence grows within a certain rate, then the expectation of dynamic regret increases sublinearly. Finally, a simulation example is given to corroborate the validity of our results.     

Krein-space approach to robust filtering for uncertain systems with time-varying bias

In this paper, a novel Krein space approach to robust estimation for uncertain systems with accumulated bias is proposed. The bias is impacted by system uncertainties and exists in both state transition and observer matrices. Initial conditions and cross-correlated uncertainty inputs are described by the sum quadratic constraint （SQC）. Without modifying the SQC, the minimal state of the SQC is obtained through Krein space method. The inertia condition for a minimum of a deterministic quadratic form is derived when the coefficient of observer uncertainty input is non-unit matrix. Recursions of Krein space state filtering and bias filtering are developed respectively. Since the cross correlation between uncertainties is considered, a cross correlation gain is introduced into the posteriori estimator. Finally, a numerical example illustrates the performance of the proposed filter.     

Analysis of quantization noise and state estimation with quantized measurements

The approximate correction of the additive white noise model in quantized Kalman filter is investigated under certain conditions. The probability density function of the error of quantized measurements is analyzed theoretically and experimentally. The analysis is based on the probability theory and nonparametric density estimation technique, respectively. The approximator of probability density function of quantized measurement noise is given. The numerical results of nonparametric density estimation algorithm demonstrate that the theoretical conclusion is reasonable. Based on the analysis of quantization noise, a novel algorithm for state estimation with quantized measurements also is proposed. The algorithm is based on the least-squares estimator and unscented transform. By least-squares estimator, the effective information is extracted from the quantized measurements. Also, using the information to update the estimated state can give a better estimation under the influence of quantization. The root mean square error (RMSE) of the proposed algorithm is compared with the RMSE of the existing methods for a typical tracking scenario in wireless sensor networks systems. Simulations provide a strong evidence that this tracking algorithm could indeed give us a more precise estimated result.     

Active disturbance rejection control of nonlinear SISO Lagrangian systems via endogenous injections and exogenous feedback for trajectory tracking

This article deals with a linear classical approach for the robust output reference trajectory tracking control of nonlinear SISO Lagrangian systems with a controllable (fat) tangent linearization around an operating equilibrium point. An endogenous injections and exogenous feedback (EIEF) approach is proposed, which is naturally equivalent to the generalized proportional integral control method and to a robust classical compensation network. It is shown that the EIEF controller is also equivalent, within a frequency domain setting demanding respect for the separation principle, to the reduced order observer based active disturbance rejection control approach. The proposed linear control approach is robust with respect to total disturbances and, thus, it is efective for the linear control of the nonlinear Lagrangian system. An illustrative nonlinear rotary crane Lagrangian system example, which is non-feedback linearizable, is presented along with digital computer simulations.     

Secure state estimation for cyber-physical systems with unknown input sliding mode observer

In recent years, cyber attacks have posed great challenges to the development of cyber-physical systems. It is of great significance to study secure state estimation methods to ensure the safe and stable operation of the system. This paper proposes a secure state estimation for multi-input and multi-output continuous-time linear cyber-physical systems with sparse actuator and sensor attacks. First, for sparse sensor attacks, we propose an adaptive switching mechanism to mitigate the impact of sparse sensor attacks by filtering out their attack modes. Second, an unknown input sliding mode observer is designed to not only observe the system states, sensor attack signals, and measurement noise present in the system but also counteract the effects of sparse actuator attacks through an unknown input matrix. Finally, for the design of an unknown input sliding mode state observer, the feasibility of the observing system is demonstrated by means of Lyapunov functions. Additionally, simulation experiments are conducted to show the effectiveness of this method.