Showing papers in "International Journal of Systems Science in 2016"

Distributed robust finite-time nonlinear consensus protocols for multi-agent systems

Abstract: This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.

Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems

Abstract: As a variation of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete and inconsistent information that exists in the real world. Simplified neutrosophic sets SNSs have been proposed for the main purpose of addressing issues with a set of specific numbers. However, there are certain problems regarding the existing operations of SNSs, as well as their aggregation operators and the comparison methods. Therefore, this paper defines the novel operations of simplified neutrosophic numbers SNNs and develops a comparison method based on the related research of intuitionistic fuzzy numbers. On the basis of these operations and the comparison method, some SNN aggregation operators are proposed. Additionally, an approach for multi-criteria group decision-making MCGDM problems is explored by applying these aggregation operators. Finally, an example to illustrate the applicability of the proposed method is provided and a comparison with some other methods is made.

UAV path planning using artificial potential field method updated by optimal control theory

Abstract: The unmanned aerial vehicle UAV path planning problem is an important assignment in the UAV mission planning. Based on the artificial potential field APF UAV path planning method, it is reconstructed into the constrained optimisation problem by introducing an additional control force. The constrained optimisation problem is translated into the unconstrained optimisation problem with the help of slack variables in this paper. The functional optimisation method is applied to reform this problem into an optimal control problem. The whole transformation process is deduced in detail, based on a discrete UAV dynamic model. Then, the path planning problem is solved with the help of the optimal control method. The path following process based on the six degrees of freedom simulation model of the quadrotor helicopters is introduced to verify the practicability of this method. Finally, the simulation results show that the improved method is more effective in planning path. In the planning space, the length of the calculated path is shorter and smoother than that using traditional APF method. In addition, the improved method can solve the dead point problem effectively.

Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets

Abstract: In this paper, two optimisation models are established to determine the criterion weights in multi-criteria decision-making situations where knowledge regarding the weight information is incomplete and the criterion values are interval neutrosophic numbers. The proposed approach combines interval neutrosophic sets and TOPSIS, and the closeness coefficients are expressed as interval numbers. Furthermore, the relative likelihood-based comparison relations are constructed to determine the ranking of alternatives. A fuzzy cross-entropy approach is proposed to calculate the discrimination measure between alternatives and the absolute ideal solutions, after a transformation operator has been developed to convert interval neutrosophic numbers into simplified neutrosophic numbers. Finally, an illustrative example is provided, and a comparative analysis is conducted between the approach developed in this paper and other existing methods, to verify the feasibility and effectiveness of the proposed approach.

Multirate parallel distributed compensation of a cluster in wireless sensor and actor networks

Abstract: The stabilisation problem for one of the clusters with bounded multiple random time delays and packet dropouts in wireless sensor and actor networks is investigated in this paper. A new multirate switching model is constructed to describe the feature of this single input multiple output linear system. According to the difficulty of controller design under multi-constraints in multirate switching model, this model can be converted to a Takagi–Sugeno fuzzy model. By designing a multirate parallel distributed compensation, a sufficient condition is established to ensure this closed-loop fuzzy control system to be globally exponentially stable. The solution of the multirate parallel distributed compensation gains can be obtained by solving an auxiliary convex optimisation problem. Finally, two numerical examples are given to show, compared with solving switching controller, multirate parallel distributed compensation can be obtained easily. Furthermore, it has stronger robust stability than arbitrary switching controller and single-rate parallel distributed compensation under the same conditions.

Pricing, manufacturing and inventory policies for raw material in a three-level supply chain

Abstract: We studied a decentralised three-layer supply chain including a supplier, a producer and some retailers. All the retailers order their demands to the producer and the producer order his demands to the supplier. We assumed that the demand is price sensitive and shortage is not permitted. The goal of the paper is to optimise the total cost of the supply chain network by coordinating decision-making policy using Stackelberg–Nash equilibrium. The decision variables of our model are the supplier's price, the producer's price and the number of shipments received by the supplier and producer, respectively. To illustrate the applicability of the proposed model numerical examples are presented.

Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay

Abstract: This paper is concerned with the problems of finite-time stability FTS and finite-time stabilisation for a class of nonlinear systems with time-varying delay, which can be represented by Takagi–Sugeno fuzzy system Some new delay-dependent FTS conditions are provided and applied to the design problem of finite-time fuzzy controllers First, based on an integral inequality and a fuzzy Lyapunov–Krasovskii functional, a delay-dependent FTS criterion is proposed for open-loop fuzzy system by introducing some free fuzzy weighting matrices, which are less conservative than other existing ones Then, the parallel distributed compensation controller is designed to ensure FTS of the time-delay fuzzy system Finally, an example is given to illustrate the effectiveness of the proposed design approach

Neural network-based adaptive consensus tracking control for multi-agent systems under actuator faults

Abstract: In this paper, a distributed output feedback consensus tracking control scheme is proposed for second-order multi-agent systems in the presence of uncertain nonlinear dynamics, external disturbances, input constraints, and partial loss of control effectiveness. The proposed controllers incorporate reduced-order filters to account for the unmeasured states, and the neural networks technique is implemented to approximate the uncertain nonlinear dynamics in the synthesis of control algorithms. In order to compensate the partial loss of actuator effectiveness faults, fault-tolerant parts are included in controllers. Using the Lyapunov approach and graph theory, it is proved that the controllers guarantee a group of agents that simultaneously track a common time-varying state of leader, even when the state of leader is available only to a subset of the members of a group. Simulation results are provided to demonstrate the effectiveness of the proposed consensus tracking method.

Reaching a consensus in networks of high-order integral agents under switching directed topologies

Abstract: Consensus problem of high-order integral multi-agent systems under switching directed topology is considered in this study. Depending on whether the agent’s full state is available or not, two distributed protocols are proposed to ensure that states of all agents can be convergent to a same stationary value. In the proposed protocols, the gain vector associated with the agent’s estimated state and the gain vector associated with the relative estimated states between agents are designed in a sophisticated way. By this particular design, the high-order integral multi-agent system can be transformed into a first-order integral multi-agent system. Also, the convergence of the transformed first-order integral agent’s state indicates the convergence of the original high-order integral agent’s state, if and only if all roots of the polynomial, whose coefficients are the entries of the gain vector associated with the relative estimated states between agents, are in the open left-half complex plane. Therefore, many analysis techniques in the first-order integral multi-agent system can be directly borrowed to solve the problems in the high-order integral multi-agent system. Due to this property, it is proved that to reach a consensus, the switching directed topology of multi-agent system is only required to be ‘uniformly jointly quasi-strongly connected’, which seems the mildest connectivity condition in the literature. In addition, the consensus problem of discrete-time high-order integral multi-agent systems is studied. The corresponding consensus protocol and performance analysis are presented. Finally, three simulation examples are provided to show the effectiveness of the proposed approach.

Lévy flight artificial bee colony algorithm

Abstract: Artificial bee colony ABC optimisation algorithm is a relatively simple and recent population-based probabilistic approach for global optimisation. The solution search equation of ABC is significantly influenced by a random quantity which helps in exploration at the cost of exploitation of the search space. In the ABC, there is a high chance to skip the true solution due to its large step sizes. In order to balance between diversity and convergence in the ABC, a Levy flight inspired search strategy is proposed and integrated with ABC. The proposed strategy is named as Levy Flight ABC LFABC has both the local and global search capability simultaneously and can be achieved by tuning the Levy flight parameters and thus automatically tuning the step sizes. In the LFABC, new solutions are generated around the best solution and it helps to enhance the exploitation capability of ABC. Furthermore, to improve the exploration capability, the numbers of scout bees are increased. The experiments on 20 test problems of different complexities and five real-world engineering optimisation problems show that the proposed strategy outperforms the basic ABC and recent variants of ABC, namely, Gbest-guided ABC, best-so-far ABC and modified ABC in most of the experiments.

Resilient control of cyber-physical systems against intelligent attacker: a hierarchal stackelberg game approach

Abstract: This paper is concerned with the resilient control under denial-of-service attack launched by the intelligent attacker. The resilient control system is modelled as a multi-stage hierarchical game with a corresponding hierarchy of decisions made at cyber and physical layer, respectively. Specifically, the interaction in the cyber layer between different security agents is modelled as a static infinite Stackelberg game, while in the underlying physical layer the full-information H∞ minimax control with package drops is modelled as a different Stackelberg game. Both games are solved sequentially, which is consistent with the actual situations. Finally, the proposed method is applied to the load frequency control of the power system, which demonstrates its effectiveness.

Linguistic hesitant fuzzy multi-criteria decision-making method based on evidential reasoning

Abstract: Linguistic hesitant fuzzy sets LHFSs, which can be used to represent decision-makers’ qualitative preferences as well as reflect their hesitancy and inconsistency, have attracted a great deal of attention due to their flexibility and efficiency. This paper focuses on a multi-criteria decision-making approach that combines LHFSs with the evidential reasoning ER method. After reviewing existing studies of LHFSs, a new order relationship and Hamming distance between LHFSs are introduced and some linguistic scale functions are applied. Then, the ER algorithm is used to aggregate the distributed assessment of each alternative. Subsequently, the set of aggregated alternatives on criteria are further aggregated to get the overall value of each alternative. Furthermore, a nonlinear programming model is developed and genetic algorithms are used to obtain the optimal weights of the criteria. Finally, two illustrative examples are provided to show the feasibility and usability of the method, and comparison analysis with the existing method is made.

Hybrid feature selection algorithm using symmetrical uncertainty and a harmony search algorithm

Abstract: Microarray technology can be used as an efficient diagnostic system to recognise diseases such as tumours or to discriminate between different types of cancers in normal tissues. This technology has received increasing attention from the bioinformatics community because of its potential in designing powerful decision-making tools for cancer diagnosis. However, the presence of thousands or tens of thousands of genes affects the predictive accuracy of this technology from the perspective of classification. Thus, a key issue in microarray data is identifying or selecting the smallest possible set of genes from the input data that can achieve good predictive accuracy for classification. In this work, we propose a two-stage selection algorithm for gene selection problems in microarray data-sets called the symmetrical uncertainty filter and harmony search algorithm wrapper SU-HSA. Experimental results show that the SU-HSA is better than HSA in isolation for all data-sets in terms of the accuracy and achieves a lower number of genes on 6 out of 10 instances. Furthermore, the comparison with state-of-the-art methods shows that our proposed approach is able to obtain 5 out of 10 new best results in terms of the number of selected genes and competitive results in terms of the classification accuracy.

A consensus reaching model for 2-tuple linguistic multiple attribute group decision making with incomplete weight information

Abstract: The aim of this paper is to put forward a consensus reaching method for multi-attribute group decision-making MAGDM problems with linguistic information, in which the weight information of experts and attributes is unknown. First, some basic concepts and operational laws of 2-tuple linguistic label are introduced. Then, a grey relational analysis method and a maximising deviation method are proposed to calculate the incomplete weight information of experts and attributes respectively. To eliminate the conflict in the group, a weight-updating model is employed to derive the weights of experts based on their contribution to the consensus reaching process. After conflict elimination, the final group preference can be obtained which will give the ranking of the alternatives. The model can effectively avoid information distortion which is occurred regularly in the linguistic information processing. Finally, an illustrative example is given to illustrate the application of the proposed method and comparative analysis with the existing methods are offered to show the advantages of the proposed method.

Consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations

Abstract: Due to the uncertainty of the decision environment and the lack of knowledge, decision-makers may use uncertain linguistic preference relations to express their preferences over alternatives and criteria. For group decision-making problems with preference relations, it is important to consider the individual consistency and the group consensus before aggregating the preference information. In this paper, consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations U2TLPRs are investigated. First of all, a formula which can construct a consistent U2TLPR from the original preference relation is presented. Based on the consistent preference relation, the individual consistency index for a U2TLPR is defined. An iterative algorithm is then developed to improve the individual consistency of a U2TLPR. To help decision-makers reach consensus in group decision-making under uncertain linguistic environment, the individual consensus and group consensus indices for group decision-making with U2TLPRs are defined. Based on the two indices, an algorithm for consensus reaching in group decision-making with U2TLPRs is also developed. Finally, two examples are provided to illustrate the effectiveness of the proposed algorithms.

Robust unknown input observer for state and fault estimation in discrete-time Takagi–Sugeno systems

Abstract: In this paper, a robust unknown input observer UIO for the joint state and fault estimation in discrete-time Takagi–Sugeno TS systems is presented. The proposed robust UIO, by applying the framework, leads to a less restrictive design procedure with respect to recent results found in the literature. The resulting design procedure aims at achieving a prescribed attenuation level with respect to the exogenous disturbances, while obtaining at the same time the convergence of the observer with a desired bound on the decay rate. An extension to the case of unmeasurable premise variables is also provided. Since the design conditions reduce to a set of linear matrix inequalities that can be solved efficiently using the available software, an evident advantage of the proposed approach is its simplicity. The final part of the paper presents an academic example and a real application to a multi-tank system, which exhibit clearly the performance and effectiveness of the proposed strategy.

Hesitant fuzzy information measures and their applications in multi-criteria decision making

Abstract: Hesitant fuzzy set HFS is a powerful decision tool to express uncertain information more flexibly and comprehensively. The aim of this paper is to propose more reasonable information measures for HFSs in comparison with the existing ones. First, a series of distance measures is suggested for hesitant fuzzy element and hesitant fuzzy sets. These measures are directly calculated from hesitant fuzzy elements without judging the decision-makers’ risk preference and adding any values into the hesitant fuzzy element with the smaller number of elements. Then, some similarity and entropy measures are proposed based on the transforming relationship among the information measures. Additionally, based on the proposed information measures, a TOPSIS method for hesitant fuzzy information is provided. Finally, some numerical examples are used in order to illustrate the proposed decision method and a comparative analysis is made to demonstrate that the suggested measures are more objective and feasible in certain cases.

Adaptive synchronised tracking control for multiple robotic manipulators with uncertain kinematics and dynamics

Abstract: In this study, a new adaptive synchronised tracking control approach is developed for the operation of multiple robotic manipulators in the presence of uncertain kinematics and dynamics. In terms of the system synchronisation and adaptive control, the proposed approach can stabilise position tracking of each robotic manipulator while coordinating its motion with the other robotic manipulators. On the other hand, the developed approach can cope with kinematic and dynamic uncertainties. The corresponding stability analysis is presented to lay a foundation for theoretical understanding of the underlying issues as well as an assurance for safely operating real systems. Illustrative examples are bench tested to validate the effectiveness of the proposed approach. In addition, to face the challenging issues, this study provides an exemplary showcase with effectively to integrate several cross boundary theoretical results to formulate an interdisciplinary solution.

Adaptive ILC algorithms of nonlinear continuous systems with non-parametric uncertainties for non-repetitive trajectory tracking

Abstract: In this article, two adaptive iterative learning control ILC algorithms are presented for nonlinear continuous systems with non-parametric uncertainties. Unlike general ILC techniques, the proposed adaptive ILC algorithms allow that both the initial error at each iteration and the reference trajectory are iteration-varying in the ILC process, and can achieve non-repetitive trajectory tracking beyond a small initial time interval. Compared to the neural network or fuzzy system-based adaptive ILC schemes and the classical ILC methods, in which the number of iterative variables is generally larger than or equal to the number of control inputs, the first adaptive ILC algorithm proposed in this paper uses just two iterative variables, while the second even uses a single iterative variable provided that some bound information on system dynamics is known. As a result, the memory space in real-time ILC implementations is greatly reduced.

Synchronisation of a fractional-order chaotic system using finite-time input-to-state stability

Abstract: The issue of synchronisation for a fractional-order chaotic system with uncertainties and disturbance is studied in this paper. The finite-time input-to-state stable theory of fractional-order dynamical system is presented for the first time. A linear feedback controller is proposed to achieve synchronisation of this fractional-order system and guarantee the bounded state error for any bounded interference in finite time. Since the chaotic system displays special dynamical behaviours as invariable Lyapunov exponent spectrums and controllable signal amplitude, one can achieve complete synchronisation and projective synchronisation by only adjusting the system parameter. Numerical simulations are shown to verify the feasibility of the presented synchronisation scheme.

Epidemic spreading model of complex dynamical network with the heterogeneity of nodes

Abstract: In this paper, we model epidemic spreading by considering the mobility of nodes in complex dynamical network based on mean field theory using differential equations. Moreover, a resistance factor which can characterise the impact of individual's difference on the propagation dynamics in complex dynamical network is proposed by considering the influence of total number of connections and the continuous time to remain in contact. The effect of heterogeneity on the evolution process of propagation dynamics is explored by simulation. Extensive simulations are conducted to study the key influence parameters and the influence of them on the spreading dynamics, which are helpful to the understanding of epidemic spreading mechanism and the designing of effective control strategies.

Passivity and robust synchronisation of switched interval coupled neural networks with time delay

Abstract: This paper is concerned with passivity and robust synchronisation of switched coupled neural networks with uncertain parameters. First, the mathematical model of switched coupled neural networks with interval uncertain parameters is established, which consists of L modes and switches from one mode to another according to the switching rule. Second, by employing passivity theory and linear matrix inequality techniques, delay-independent and delay-dependent conditions are derived to guarantee the passivity of switched interval coupled neural networks. Moreover, based on the proposed passivity results, global synchronisation criteria can be obtained for switched coupled neural networks with or without uncertain parameters. Finally, an illustrative example is provided to demonstrate the effectiveness of the obtained results.

Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand

Abstract: An inventory system for perishable items with limited replenishment capacity is introduced in this paper. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realise profit maximisation, an optimisation problem is addressed to seek for the optimal joint dynamic pricing and replenishment policy which is obtained by solving the optimisation problem with Pontryagin’s maximum principle. A joint mixed policy, in which the sales price is a static decision variable and the replenishment rate remains to be a dynamic decision variable, is presented to compare with the joint dynamic policy. Numerical results demonstrate the advantages of the joint dynamic one, and further show the effects of different system parameters on the optimal joint dynamic policy and the maximal total profit.

A new approach to handle additive and multiplicative uncertainties in the measurement for LPV filtering

Abstract: This paper presents a general framework to cope with full-order linear parameter-varying LPV filter design subject to inexactly measured parameters. The main novelty is the ability of handling additive and multiplicative uncertainties in the measurements, for both continuous and discrete-time LPV systems, in a unified approach. By conveniently modelling scheduling parameters and uncertainties affecting the measurements, the filter design problem can be expressed in terms of robust matrix inequalities that become linear when two scalar parameters are fixed. Therefore, the proposed conditions can be efficiently solved through linear matrix inequality relaxations based on polynomial solutions. Numerical examples are presented to illustrate the improved efficiency of the proposed approach when compared to other methods and, more important, its capability to deal with scenarios where the available strategies in the literature cannot be used.

Economic production quantity EPQ models under an imperfect production process with shortages backordered

Abstract: In this paper, we develop economic production quantity EPQ models to determine the optimal production lot size and backorder quantity for a manufacturer under an imperfect production process. The imperfect production process is characterised by the fraction of defective items at the time of production γ. The paper considers different cases of the EPQ model depending on 1 whether γ is known with certainty or is a random variable, and 2 whether imperfect items are drawn from inventory a as they are detected, b at the end of each production period or c at the end of each production cycle. Straightforward convexity results are shown and closed-form solutions are provided for the optimal order and backorder quantities for each of the cases we considered. We provide two numerical examples: one in which the defective probability follows a uniform distribution and the second which we assume follows a beta distribution, to illustrate the effects of yield variability and timing of the withdrawal of defectives on the optimal solutions. We obtain similar results for both numerical examples, which show that both the yield variability and the withdrawal timing are not critical factors.

Joint optimisation of price, warranty and recovery planning in remanufacturing of used products under linear and non-linear demand, return and cost functions

Abstract: We investigate joint optimisation of remanufacturing, pricing and warranty decision-making for end-of-life products. A novel mathematical–statistical model is proposed where decisions involve pricing of returned used products cores, degree of their remanufacturing, selling price and the warranty period for the final remanufactured products. The virtual age reliability improvement approach is chosen to model the upgrading of the cores to higher quality levels. We consider price-and warranty-dependent demand, price-and age-dependent return, and age-dependent remanufacturing cost in the model development. Both linear and non-linear forms of these functions are investigated. First, under some restrictive conditions of upgrade level and age distribution of received cores, special cases of the problem, which can be solved using a recently developed non-linear optimisation solver, are presented. We also implement a particle swarm optimisation algorithm for the solution of the original problem when all the restrictive assumptions are dropped. Finally, numerical experiments and sensitivity analysis are presented to address different aspects of the model and the solution approaches.

A general U-block model-based design procedure for nonlinear polynomial control systems

Abstract: The proposition of U-model concept in terms of ‘providing concise and applicable solutions for complex problems’ and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared not rigorously defined for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems in brief, linear polynomial approaches → nonlinear polynomial plants. This paper represents the next milestone work – using linear state-space approaches to design nonlinear polynomial control systems in brief, linear state-space approaches → nonlinear polynomial plants. The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Consensus with a reference state for fractional-order multi-agent systems

Abstract: This paper investigates consensus of fractional-order multi-agent systems MASs with a reference state. First, a consensus control law with a constant reference state is given using graph theory and stability analysis of fractional-order. Then, a general control law and a particular one for consensus of fractional-order MASs with a time-varying reference state are proposed. Next, the above control laws are extended to solve formation tracking problem. Finally, several simulations are presented to verify the effectiveness of the obtained results.

On fractional order composite model reference adaptive control

Abstract: This paper presents a novel composite model reference adaptive control approach for a class of fractional order linear systems with unknown constant parameters. The method is extended from the model reference adaptive control. The parameter estimation error of our method depends on both the tracking error and the prediction error, whereas the existing method only depends on the tracking error, which makes our method has better transient performance in the sense of generating smooth system output. By the aid of the continuous frequency distributed model, stability of the proposed approach is established in the Lyapunov sense. Furthermore, the convergence property of the model parameters estimation is presented, on the premise that the closed-loop control system is stable. Finally, numerical simulation examples are given to demonstrate the effectiveness of the proposed schemes.

Dynamic design, numerical solution and effective verification of acceleration-level obstacle-avoidance scheme for robot manipulators

Abstract: For avoiding obstacles and joint physical constraints of robot manipulators, this paper proposes and investigates a novel obstacle avoidance scheme termed the acceleration-level obstacle-avoidance scheme. The scheme is based on a new obstacle-avoidance criterion that is designed by using the gradient neural network approach for the first time. In addition, joint physical constraints such as joint-angle limits, joint-velocity limits and joint-acceleration limits are incorporated into such a scheme, which is further reformulated as a quadratic programming QP. Two important ‘bridge’ theorems are established so that such a QP can be converted equivalently to a linear variational inequality and then equivalently to a piecewise-linear projection equation PLPE. A numerical algorithm based on a PLPE is thus developed and applied for an online solution of the resultant QP. Four path-tracking tasks based on the PA10 robot in the presence of point and window-shaped obstacles demonstrate and verify the effectiveness and accuracy of the acceleration-level obstacle-avoidance scheme. Besides, the comparisons between the non-obstacle-avoidance and obstacle-avoidance results further validate the superiority of the proposed scheme.