Adaptive control of uncertain time-delay chaotic systems

This work investigates adaptive control of a large class of uncertain time-delay chaotic systems （UTCSs） with unknown general perturbation terms bounded by a polynomial （unknown gains）, Associated with the different cases of known and unknowl system matrices, two corresponding adaptive controllers are proposed to stabilize unstable fixed points of the systems by means of Lyapunov stability theory and linear matrix inequafities （LMI） which can be solved easily by convex optimization algorithms, Two examples are used for examining the effectiveness of the proposed methods.

Observer-based adaptive control of uncertain time-delay switched systems with stuck actuator faults

This paper concerns the observer-based adaptive control problem of uncertain time-delay switched systems with stuck actuator faults. Under the case where the original controller cannot stabilize the faulty system, multiple adaptive controllers are designed and a suitable switching logic is incorporated to ensure the closed-loop system stability and state tracking. New delay-independent sufficient conditions for asymptotic stability are obtained in terms of linear matrix inequalities based on piecewise Lyapunov stability theory. On the other hand, adaptive laws for on-line updating of some of the controller parameters are also designed to compensate the effect of stuck failures. Finally, simulation results for reference [1] model show that the design is feasible and efficient.

Nonfragile guaranteed cost control for Delta operator-formulated uncertain time-delay systems

With consideration that the controller parameters may vary from the designed value when the controller is realized, based on Lyapunov stability theory, a design method of nonfragile guaranteed cost control for a class of Delta operator-formulated uncertain time-delay systems is studied. A sufficient condition for the existence of the nonfragile guaranteed cost controller is given. A numeric example is then given to illustrate the effectiveness and the feasibility of the designed method. The results show that even if the parameters of the designed controller are of variations, the closed-loop system is still asymptotically stable and the super value of the cost function can also be obtained, while the closed-loop system will be unstable if the variations of the controller parameters are not considered when the controller is designed. The nonfragile guaranteed cost controller derived from the traditional shift operator method may cause the closed-loop system to be unstable, while the nonfragile guaranteed cost controller based on Delta operator method can avoid the unstable problem of the closed-loop system.

PASSIVE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY SYSTEMS

This paper focuses on the passive control for a class of linear time delay system with norm bounded time varying parameter uncertainties by using a linear matrix inequality (LMI) approach. A sufficient condition under which the uncertain time delay system is quadratically stable and strictly passive for all admissible uncertainties was derived. It is shown that the solvability of problem of the robust passive controller design is implied by the feasibility of a linear matrix inequality.

Design of variable structure controller for uncertain time-delay singular system

To study the approximation theory of real sliding mode and the design of variable structure controller for time-invariant linear uncertain time-delay singular system,the approximation theory of real sliding mode was developed to provide foundation for obtaining sliding mode by equivalent control,and switching functions with integral dynamic compensators and variable structure controllers were designed respectively under two circumstances that the system without uncertain part was stabilized by delay-dependent and delay-independent linear state feedback. The design guarantees the asymptotical stablity of switching manifolds,and the variable structure controllers can force solution trajectory of the system to arrive at the switching manifolds in limited time. A numerical example is given to demonstrate the feasibility and simplicity of the design method.

Adaptive Consensus of Uncertain Multi-Agent Systems With Unified Prescribed Performance

Dear Editor,An adaptive consensus control algorithm for uncertain multi-agent systems(MAS),capable of guaranteeing unified prescribed performance,is presented in this letter.Unlike many existing prescribed performance related works,the developed control exhibits some features.Firstly,a distributed prescribed time observer is introduced so that not only each follower is able to estimate the leader’s signal within a predetermined time,but also the control design for each agent is independent with its neighbors.

Hepatic perivascular epithelioid cell tumors:Benign,malignant,and uncertain malignant potential

In 2013,the World Health Organization defined perivascular epithelioid cell tumor(PEComa)as“a mesenchymal tumor which shows a local association with vessel walls and usually expresses melanocyte and smooth muscle markers.”This generic definition seems to better fit the PEComa family,which includes angiomyolipoma,clear cell sugar tumor of the lung,lymphangioleiomyomatosis,and a group of histologically and immunophenotypically similar tumors that include primary extrapulmonary sugar tumor and clear cell myomelanocytic tumor.Clear cell tumors with this immunophenotypic pattern have also had their malignant variants described.When localizing to the liver,preoperative radiological diagnosis has proven to be very difficult,and most patients have been diagnosed with hepatocellular carcinoma,focal nodular hyperplasia,hemangioma,or hepatic adenoma based on imaging findings.Examples of a malignant variant of the liver have been described.Finally,reports of malignant variants of these lesions have increased in recent years.Therefore,we support the use of the Folpe criteria,which in 2005 established the criteria for categorizing a PEComa as benign,malignant,or of uncertain malignant potential.Although they are not considered ideal,they currently seem to be the best approach and could be used for the categorization of liver tumors.

Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking

This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a large class of engineering systems,such as vehicular systems,robot manipulators and satellites.All these systems are often characterized by highly nonlinear characteristics,heavy modeling uncertainties and unknown perturbations,therefore,accurate-model-based nonlinear control approaches become unavailable.Motivated by the challenge,a reinforcement learning(RL)adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics.The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error(RISE)control approach.Different from a classical RISE control law,a tanh(·)function is utilized instead of a sign(·)function to acquire a more smooth control signal.The developed controller requires very little prior knowledge of the dynamic model,is robust to unknown dynamics and exogenous disturbances,and can achieve asymptotic output tracking.Eventually,co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom(3-DOF)manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach.

Guaranteed Cost Attitude Tracking Control for Uncertain Quadrotor Unmanned Aerial Vehicle Under Safety Constraints

In this paper,guaranteed cost attitude tracking con-trol for uncertain quadrotor unmanned aerial vehicle(QUAV)under safety constraints is studied.First,an augmented system is constructed by the tracking error system and reference system.This transformation aims to convert the tracking control prob-lem into a stabilization control problem.Then,control barrier function and disturbance attenuation function are designed to characterize the violations of safety constraints and tolerance of uncertain disturbances,and they are incorporated into the reward function as penalty items.Based on the modified reward function,the problem is simplified as the optimal regulation problem of the nominal augmented system,and a new Hamilton-Jacobi-Bellman equation is developed.Finally,critic-only rein-forcement learning algorithm with a concurrent learning tech-nique is employed to solve the Hamilton-Jacobi-Bellman equa-tion and obtain the optimal controller.The proposed algorithm can not only ensure the reward function within an upper bound in the presence of uncertain disturbances,but also enforce safety constraints.The performance of the algorithm is evaluated by the numerical simulation.

Practical prescribed-time fuzzy tracking control for uncertain nonlinear systems with time-varying actuators faults

The paper investigates the practical prescribed-time fuzzy tracking control problem for a category of nonlinear system subject to time-varying actuator faults.The presence of unknown nonlinear dynamics and actuator faults makes achieving tracking control within a prescribed-time challenging.To tackle this issue,we propose a novel practical prescribed-time fuzzy tracking control strategy,which is independent of the initial state of the system and does not rely on precise modeling of the system and actuators.We apply the approximation capabilities of fuzzy logic systems to handle the unknown nonlinear functions and unidentified actuator faults in the system.The piecewise controller and adaptive law constructed based on piecewise prescribed time-varying function and backstepping technique method establish the theoretical framework of practical prescribed-time tracking control,and extend the range of prescribed-time tracking control to infinity.Regardless of the initial conditions,the proposed control strategy can guarantee that all signals remain uniformly bounded within the practical prescribed time in the presence of unknown nonlinear item and time-varying actuator faults.Simulation example is presented to demonstrate the effectiveness of the proposed control strategy.

Integral sliding mode control of time-delay systems with mismatching uncertainties

A linear matrix inequality （LMI）-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system under consideration may have mis- matching norm bounded uncertainties in the state matrix as well as the input matrix, A sufficient condition for the existence of a sliding surface is given to guarantee asymptotic stability of the full order slJdJng mode dynamics. An LMI characterization of the slid- ing surface is given, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Finally, a simulation is given to show the effectiveness of the proposed method.

ROBUST STABILITY FOR A TYPE OF UNCERTAIN TIME-DELAY SYSTEMS

Some new results for stability of uncertain time-delay systems are derived and the stability degree is also discussed. Some previous results for stability and robust stability of time-delay systems are improved. Lastly, examples are included to illustrate our results.

Decentralized robust guaranteed cost control for a class of interconnected singular large-scale systems with time-delay and parameter uncertainty

The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality （LMI） via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.

Stability analysis and design of time-delay uncertain systems using robust reliability method

A robust reliability method for stability analysis and reliability-based stabilization of time-delay dynamic systems with uncertain but bounded parameters is presented by treating the uncertain parameters as interval variables.The performance function used for robust reliability analysis is defined by a delayindependent stability criterion.The design of robust controllers is carried out by solving a reliability-based optimization problem in which the control cost satisfying design requirements is minimized.This kind of treatment makes it possible to achieve a balance between the reliability and control cost in the design of controller when uncertainties must be taken into account.By the method,a robust reliability measure of the degree of stability of a time-delay uncertain system can be provided,and the maximum robustness bounds of uncertain parameters such that the time-delay system to be stable can be obtained.All the procedures are based on the linear matrix inequality approach and therefore can be carried out conveniently.The effectiveness and feasibility of the proposed method are demonstrated with two practical examples.It is shown by numerical simulations and comparison that it is meaningful to take the robust reliability into account in the control design of uncertain systems.

An Improved Approach to Delay-dependent Robust Stabilization for Uncertain Singular Time-delay Systems

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality （LMI）. Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.

Observer-based robust predictive control of singular systems with time-delay and parameter uncertainties

The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.

Adaptive Fuzzy Observer Backstepping Control for a Class of Uncertain Nonlinear Systems with Unknown Time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Robust reliable guaranteed cost control for uncertain singular systems with time-delay

The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.

Design of performance robustness for uncertain nonlinear time-delay systems via neural network

Performance robustness problems via the state feedback controller are investigated for a class of uncertain nonlinear systems with time-delay in both state and control, in which the neural networks are used to model the nonlinearities. By using an appropriate uncertainty description and the linear difference inclusion technique, sufficient conditions for existence of such controller are derived based on the linear matrix inequalities （LMIs）. Using solutions of LMIs, a state feedback control law is proposed to stabilize the perturbed system and guarantee an upper bound of system performance, which is applicable to arbitrary time-delays.