Bounded Input Disturbances Research Articles

Reachable Set Estimation for Memristive Complex-Valued Neural Networks With Disturbances.

This brief focuses on reachable set estimation for memristive complex-valued neural networks (MCVNNs) with disturbances. Based on algebraic calculation and Gronwall-Bellman inequality, the states of MCVNNs with bounded input disturbances converge within a sphere. From this, the convergence speed is also obtained. In addition, an observer for MCVNNs is designed. Two illustrative simulations are also given to show the effectiveness of the obtained conclusions.

Fixed-Time Cooperative Tracking Control for Double-Integrator Multiagent Systems: A Time-Based Generator Approach.

In this article, both the fixed-time distributed consensus tracking and the fixed-time distributed average tracking problems for double-integrator-type multiagent systems with bounded input disturbances are studied. First, a new practical robust fixed-time sliding-mode control method based on the time-based generator is proposed. Second, two fixed-time distributed consensus tracking observers for double-integrator-type multiagent systems are designed to estimate the state disagreement between the leader and the followers under undirected and directed communication, respectively. Third, a fixed-time distributed average tracking observer for double-integrator-type multiagent systems is designed to measure the average value of multiple reference signals under undirected communication. Note that all the proposed observers are constructed with time-based generators and can be trivially extended to that for high-order integrator-type multiagent systems. Furthermore, by combining the proposed fixed-time sliding-mode control method with the information provided by the fixed-time observers, the fixed-time controllers are designed to solve the fixed-time distributed consensus tracking and the distributed average tracking problems. Finally, a few numerical simulations are shown to verify the results.

Disturbance Observer-Based Robust Take-Off Control for a Semi-Submersible Permeable Slender Hybrid Unmanned Aerial Underwater Quadrotor

The development of hybrid unmanned aerial underwater vehicles (HAUVs) compatible with the advantages of the aerial vehicles and the underwater vehicles is of great significance. This paper presents the first study on a new HAUV layout using four rotors to realize the medium crossing motion of a transverse slender body similar to the fuselage of a missile or a submarine, that is, the hybrid aerial underwater quadrotor (HAUQ). Then, a robust control strategy is proposed for the take-off HAUQ on the water in the presence of unknown disturbances and complex model dynamic uncertainties. As a semi-submersible HAUQ rises straight from the water, the inside of the slender fuselage placed horizontally is filled with water. The center of the mass, the moment of inertia, and the arm of the force of the HAUQ will change rapidly in the take-off phase from the water because of the rapid nonuniform change in mass caused by the passive fast drainage. It is difficult to establish an accurate mathematical model of the complex dynamic changes caused by the multi-media dynamics, the fast changing buoyancy, and the added mass crossing the air–water surface. Therefore, an uncertain kinematic and dynamic model is established through the passive, fast, nonuniform change and the complex dynamics are considered as the unknown terms, and the external disturbances of gust and other factors are assumed as the bounded disturbance input. A robust design approach is introduced to deal with the fast time-varying mass disturbance based on the input-to-state stability (ISS) theorem. The complex dynamics are estimated using the basis function and the unknown weight parameters, and the adaptive laws are adopted for the on-line estimation of the unknown weight parameters. Considering the residual disturbance of the uncertain nonlinear system as a total disturbance term, a disturbance observer is introduced for disturbance observation. The numerical simulation shows the feasibility and robustness of the proposed algorithm.

Semi-active fuzzy cooperative control of vehicle suspension with a magnetorheological damper

This study attempts to improve the vibration isolation performance of a vehicle suspension system with a magnetorheological damper (MRD) under complex driving conditions. Structure parameter uncertainty, disturbance of the driving process, and response time delay of MRD are all addressed. Firstly, experiments of MRD were carried out in a damping force testing machine to identify the parameters of the MRD adjustable Sigmoid model by the Levenberg-Marquardt optimization algorithm. Then, the parameter identification is verified by comparing experimental and simulation data. Secondly, the state space equations of the suspension system are derived by Newton’s second law. The transfer function from the bounded disturbance input to the control output is obtained based on H∞ control theory. To make the Infinite norm of the system transfer function less than a certain value, three control strategies are proposed: variable structure control (VSC), disturbance rejection control (DRC), and delay tolerance control (DTC). Thirdly, considering these issues together to weaken the effect of disturbances on vehicle driving conditions, a fuzzy cooperative control (FCC) strategy is proposed based on the linear matrix inequality (LMI) theory. Simulation results demonstrate that FCC semi-active vehicle suspension systems conduct effective vibration isolation performance while responding to multiple external disturbances.

On reachable set problem for impulse switched singular systems with mixed delays

AbstractThis paper focuses on the reachable set problem for impulse switched singular (ISS) systems with mixed time‐varying delays via the Lyapunov theory. To solve the state boundary of system, a real‐bounded lemma is developed by analyzing the impulse switching point under bounded disturbance input and initial function. Based on real‐bounded lemma and integral inequality technology, a sufficient condition for reachable set of ISS system is established in the form of linear matrix inequalities (LMIs) to ensure that the reachable state of system is limited to a closed bounded set. Simulation results are given to verify the validity of the obtained theoretical results for the reachable state criterion.

Input-to-State Constrained Safety Zeroing Control Barrier Function and Its Application to Time-varying Obstacle Avoidance for Electric Wheelchair

The safety guarantee of a control system under input disturbances is challenging. In this paper, we introduce an input-to-state constrained safety zeroing control barrier function (ISCSf-ZCBF) and propose an ISCSf-ZCBF-based human assist controller to ensure the safety of a human-operated system with unknown bounded input disturbances. The proposed human assist controller ensures not only safety but continuity and minimal intervention, which are suitable properties for human assist control. Then, we employ an ISCSf-ZCBF to achieve time-varying obstacle avoidance for an electric wheelchair by regarding an estimation error of obstacle velocity as an input disturbance. Finally, we experimentally confirm the effectiveness of the proposed controller.

Reachable set estimation and aperiodic sampled‐data controller design for Markovian jump systems

AbstractIn this article, the problem of reachable set estimation (RSE) and aperiodic sampled‐data controller design are considered for Markovian jump systems (MJSs) with unit‐energy bounded disturbance and unit‐peak bounded disturbance inputs. First, by constructing mode‐dependent loop‐based Lyapunov functional, the linear matrix inequalities method is used to derive sufficient conditions for all states of MJSs under zero initial conditions to be bounded by ellipsoids. Second, RSE is considered in the process of designing the aperiodic sampled‐data controller. The objective is that the resulting ellipsoid comprises the reachable set of the closed‐loop system. Finally, the effectiveness of these methods is illustrated by the actual aircraft model and simulation results in this article. Furthermore, compared with other articles through numerical comparison, the method provided in this article can obtain less conservative results.

Reachable set estimation for discrete‐time systems with hybrid time‐delays

AbstractThis article investigates the problem of reachable set estimation for linear discrete‐time systems (LDSs) with both discrete and distributed delays as well as bounded disturbance inputs. The purpose is to determine a bounded set in which all the LDSs states are in the set. By exploiting Wirtinger‐based summation inequality and linear matrix inequalities techniques, a sufficient criterion is established which guarantees the states of LDSs are bounded by the ellipsoid. An improved Lyapunov–Krasovskii (L‐K) functional is addressed and the L‐K functional matrices are not required all to be positive definite. Finally, the effectiveness and superiority of the proposed methods are substantiated by two numerical examples.

State bounding for fuzzy memristive neural networks with bounded input disturbances

This paper investigates the state bounding problem of fuzzy memristive neural networks (FMNNs) with bounded input disturbances. By using the characters of Metzler, Hurwitz and nonnegative matrices, this paper obtains the exact delay-independent and delay-dependent boundary ranges of the solution, which have less conservatism than the results in existing literatures. The validity of the results is verified by two numerical examples.

Practical Sliding Mode Using State Depended Intermittent Control

This brief introduces a practical sliding mode using state depended intermittent control strategy. Robust stabilization of the linear time-invariant system is achieved by rejecting the effect of matched and bounded input disturbances using the proposed state dependent intermittent sliding mode control (SDI-SMC). The system trajectories are driven to a predesigned practical sliding mode band by the proposed control to establish a practical sliding mode. The salient feature of the proposed control strategy is that the control is turned off whenever it is not necessary, which will result in a considerable saving in the control effort and other resources. The proposed SDI-SMC is simulated on the model of an industrial plant emulator and a detailed comparison is done with sliding mode control (SMC), event-triggered sliding mode control (ET-SMC) and adaptive sliding mode control (Adp-SMC).

Event-based Finite-time Boundedness of Discrete-time Network Systems

This paper deals with the event-based finite-time H∞ control problem of discrete-time network control systems with norm bounded input disturbances and nonlinear stochastic functions. A network-induced delay stochastic model is first constructed by event-triggered approach. Utilizing stochastic analysis and event-triggered schemes, conditions on stochastic finite-time (FT) boundedness and stochastic H∞ FT boundedness are then derived for the network model. Subsequently, an event-based finite-time controller and an event-triggered matrix are co-designed to ensure that the stochastic model is stochastically FT bounded or stochastically H∞ FT bounded by utilizing matrix decomposition scheme. All derived criteria can be solved in terms of convex optimal method, and numerical examples demonstrate the validity of obtained results as well.

SYNCHRONIZATION OF UNCERTAIN FRACTIONAL ORDER CHAOTIC SPROTT CIRCUIT USING SLIDING MODE CONTROLLER

In this paper, fractional order sliding mode controller is used to synchronize Sprott fractional order chaotic electric circuits with fractional dynamic in the presence of uncertainty and bounded input disturbance.

Fixed-Time Estimators of Derivatives of Unknown Maps

A systematic and generalized asymptotic derivative estimator design method is first presented for unknown maps by adding a sinusoidal excitation signal to the argument of the map. Then, based on the proposed asymptotic derivative estimator approach and based on the existing design methods for both finite-time and fixed-time state observers, finite-time and fixed-time derivative estimators are designed. The sufficient conditions for finite-time and fixed-time input-to-state stable of the finite-time and fixed-time derivative estimators are given respectively when a bounded disturbance input exists.

Reachable set bounding for a class of memristive complex-valued neural networks with disturbances

This study focus on reachable set bounding for memristive complex-valued neural networks (MCVNNs) with bounded input disturbances. In order to find the region such that all the solutions of MCVNNs with bounded input disturbances converge within it, we utilize a approach based on Lyapunov–Krasovskii functional (LKF). From this, we derive some improved conditions to get the bounding ellipsoid in accordance with linear matrix inequalities (LMIs), the stability criteria are also obtained. At last, two illustrative simulations are also provided to show the availability and validity of obtained conclusions.

Distributed Robust Global Containment Control of Second-Order Multiagent Systems With Input Saturation

In this paper, we study the robust global containment control problem for second-order multiagent systems with bounded input disturbances subject to input saturation under general directed communication graphs. Two types of distributed controllers based on novel sliding mode control ideas are respectively proposed to solve the globally asymptotic containment problem for multiagent systems with static leaders and the practical containment problem for the case with dynamic leaders subject to unknown control inputs. One distinctive feature of the proposed controllers is that only local velocity measurements, relative position, and velocity measurements are involved in designing the controllers, which thus effectively reduces the information transmission burden among the agents for real-time implementation. Another favorable property of the designed controllers is that the global information such as the spectrum of the graph Laplacian matrix is not required in designing these controllers under general directed communication graphs. Simulations on containment control of multiple quadrotors are performed to illustrate the effectiveness of the proposed containment controllers.

Using SOS and Sublevel Set Volume Minimization for Estimation of Forward Reachable Sets

In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equations (ODE’s) with either (or both) L2 or point-wise bounded input disturbances. To make our approximations tight we seek to minimize the volume of our approximation set. Our approach to volume minimization is based on the use of a convex determinant-like objective function. We provide several numerical examples including the Lorenz system and the Van der Pol oscillator.

Reachable set estimation and dissipativity for discrete-time T–S fuzzy singular systems with time-varying delays

This paper studies the problems of reachable set estimation and dissipativity analysis for a class of nonlinear singular system with time-varying delays and bounded input disturbances. The nonlinear singular system is modeled by Takagi–Sugeno (T–S) fuzzy singular delay system. Firstly, based on new Lyapunov–Krasovskii functional, in which the difference of triple-summable terms and both the upper and the lower bound of time-varying delays are considered, and by using the free-weighting matrix technique, reciprocally convex combination approach, a new delay-dependent reachable set estimation and dissipativity condition is obtained. Furthermore, the derived condition can be converted into linear matrix inequalities (LMIs), and it can guarantee the reachable set to be bounded by the intersection of ellipsoids and the T–S fuzzy singular delay system is strictly (G1,G2,G3)−δ̃−dissipative. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained results in this paper.

Reachable set estimation for discrete-time bilinear systems with time-varying delays

The problem of reachable set estimation is studied for discrete-time bilinear system in this paper. Time-varying delays and bounded input disturbances are both considered in bilinear system. The aim is to find reachable set that converges from all the states of system with initial conditions. By constructing Lyapunov–Krasovskii functional, sufficient delay-dependent less conservative stable conditions of reachable set estimation are obtained for bilinear delay system via the reciprocally convex combination and delay partition approaches. The derived theorem can guarantee that all the states of system with initial conditions from some domain are bounded in an ellipsoid and all the states from other domain are converged exponentially within a ball. One simulation example is presented to illustrate the correctness of the derived result in this paper.

Reachable set bounding for a class of bidirectional associative memory NNSs with Markov jump switching parameters

This paper studies the problem how to estimate the reachable set for a class of delayed bidirectional associative memory neural network systems (NNSs), which have Markov switching parameters and unit-energy or unit-peak bounded disturbance inputs. The feature of the Markov jump bidirectional associative memory NNSs shows in the following twofold: the time delay is time varying; the transition rates is time varying. Moreover, the time-varying transition rates is piecewise constant. Using the Lyapunov functional method, delay-partitioning and linear matrix inequalities techniques, the estimate problem of the reachable set depending on time delay is solved. The effectiveness of the given results is illustrated by the proposed numerical examples.

Further Results on Reachable Set Bounding for Discrete-Time System with Time-Varying Delay and Bounded Disturbance Inputs

This paper investigates the problem of reachable set bounding for discrete-time system with time-varying delay and bounded disturbance inputs. Together with a new Lyapunov-Krasovskii functional, discrete Wirtinger-based inequality, and reciprocally convex approach, sufficient conditions are derived to find an ellipsoid to bound the reachable sets of discrete-time delayed system. The main advantage of this paper lies in two aspects: first, the initial state vectors are not necessarily zero; second, the obtained criteria in this paper do not really require all the symmetric matrices involved in the employed Lyapunov-Krasovskii functional to be positive definite. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.