Sequential Inverse Optimal Control of Discrete-Time Systems

This paper presents a novel sequential inverse optimal control(SIOC)method for discrete-time systems,which calculates the unknown weight vectors of the cost function in real time using the input and output of an optimally controlled discrete-time system.The proposed method overcomes the limitations of previous approaches by eliminating the need for the invertible Jacobian assumption.It calculates the possible-solution spaces and their intersections sequentially until the dimension of the intersection space decreases to one.The remaining one-dimensional vector of the possible-solution space’s intersection represents the SIOC solution.The paper presents clear conditions for convergence and addresses the issue of noisy data by clarifying the conditions for the singular values of the matrices that relate to the possible-solution space.The effectiveness of the proposed method is demonstrated through simulation results.

A Note on the Inverse Connected p-Median Problem on Block Graphs

Recently, the inverse connected p-median problem on block graphs G(V,E,w) under various cost functions, say rectilinear norm, Chebyshev norm, and bottleneck Hamming distance. Their contributions include finding a necessary and sufficient condition for the connected p-median problem on block graphs, developing algorithms and showing that these problems can be solved in O(n log n) time, where n is the number of vertices in the underlying block graph. Using similar technique, we show that some results are incorrect by a counter-example. Then we redefine some notations, reprove Theorem 1 and redescribe Theorem 2, Theorem 3 and Theorem 4.

A Path Planning Algorithm Based on Improved RRT Sampling Region

For the problem of slow search and tortuous paths in the Rapidly Exploring Random Tree(RRT)algorithm,a feedback-biased sampling RRT,called FS-RRT,is proposedbasedon RRT.Firstly,toimprove the samplingefficiency of RRT to shorten the search time,the search area of the randomtree is restricted to improve the sampling efficiency.Secondly,to obtain better information about obstacles to shorten the path length,a feedback-biased sampling strategy is used instead of the traditional random sampling,the collision of the expanding node with an obstacle generates feedback information so that the next expanding node avoids expanding within a specific angle range.Thirdly,this paper proposes using the inverse optimization strategy to remove redundancy points from the initial path,making the path shorter and more accurate.Finally,to satisfy the smooth operation of the robot in practice,auxiliary points are used to optimize the cubic Bezier curve to avoid path-crossing obstacles when using the Bezier curve optimization.The experimental results demonstrate that,compared to the traditional RRT algorithm,the proposed FS-RRT algorithm performs favorably against mainstream algorithms regarding running time,number of search iterations,and path length.Moreover,the improved algorithm also performs well in a narrow obstacle environment,and its effectiveness is further confirmed by experimental verification.

Identification of Unknown Groundwater Pollution Sources and Determination of Optimal Well Locations Using ANN-GA Based Simulation-Optimization Model

The linked simulation-optimization model can be used for solving a complex groundwater pollution source identification problem. Advanced simulators have been developed and successfully linked with numerous optimization algorithms for identification of groundwater pollution sources. However, the identification of pollution sources in a groundwater aquifer using linked simulation-optimization model has proven to be computationally expensive. To overcome this computational burden, an approximate simulator, the artificial neural network (ANN) model can be used as a surrogate model to replace the complex time-consuming numerical simulation model. However, for large-scale aquifer system, the performance of the ANN-based surrogate model is not satisfactory when a single ANN model is used to predict the concentration at different observation locations. In such a situation, the model efficiency can be enhanced by developing separate ANN model for each of the observation locations. The number of ANN models is equal to the number of observation wells in the aquifer. As a result, the complexity of the ANN-based simulation-optimization model will be related to the number of observation wells. Thus, this study used a modified formulation to find out the optimal numbers of observation wells which will eventually reduce the computational time of the model. The performance of the ANN-based simulation-optimization model is evaluated by identifying the groundwater pollutant sources of a hypothetical study area. The limited evaluation shows that the model has the potential for field application.

Parameter optimization of gravity density inversion based on correlation searching and the golden section algorithm

For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized. we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.

Seismic Vulnerability Assessment from Earthquake Damages Historical Data Using Constrained Optimization Technique

This present work falls within the context of efforts that have been made over the past many years, aimed in improving the seismic vulnerability modelling of structures when using historical data. The historical data describe the intensity and the damages, but do not give information about the vulnerability, since only in the ’90 the concept of vulnerability classes was introduced through the EMS92 and EMS98 scales. Considering EMS98 definitions, RISK-UE project derived a method for physical damage estimation. It introduced an analytical equation as a function of an only one parameter (Vulnerability Index), which correlates the seismic input, in term of Macroseismic Intensity, with the physical damage. In this study, we propose a methodology that uses optimization algorithms allowing a combination of theoretical-based with expert opinion-based assessment data. The objective of this combination is to estimate the optimal Vulnerability Index that fits the historical data, and hence, to give the minimum error in a seismic risk scenario. We apply the proposed methodology to the El Asnam earthquake (1980), but this approach remains general and can be extrapolated to any other region, and more, it can be applied to predictive studies (before each earthquake scenarios). The mathematical formulation gives choice for regarding, to the optic of minimizing the error, either for the: 1) very little damaged building (D0-D2 degree) or 2) highly damaged building (D4-D5 degree). These two different kinds of optics are adapted for the people who make organizational decisions as for mitigation measures and urban planning in the first case and civil protection and urgent action after a seismic event in the second case. The insight is used in the framework of seismic scenarios and offers advancing of damage estimation for the area in which no recent data, or either no data regarding vulnerability, are available.

Global Inverse Optimal Tracking Control of Underactuated Omni-directional Intelligent Navigators （ODINs）

This paper presents a design of optimal controllers with respect to a meaningful cost function to force an underactuated omni-directional intelligent navigator （ODIN） under unknown constant environmental loads to track a reference trajectory in two-dimensional space. Motivated by the vehicle＇s steering practice, the yaw angle regarded as a virtual control plus the surge thrust force are used to force the position of the vehicle to globally track its reference trajectory. The control design is based on several recent results developed for inverse optimal control and stability analysis of nonlinear systems, a new design of bounded disturbance observers, and backstepping and Lyapunov＇s direct methods. Both state- and output-feedback control designs are addressed. Simulations are included to illustrate the effectiveness of the proposed results.

An improved multi-objective optimization algorithm for solving flexible job shop scheduling problem with variable batches

In order to solve the flexible job shop scheduling problem with variable batches,we propose an improved multiobjective optimization algorithm,which combines the idea of inverse scheduling.First,a flexible job shop problem with the variable batches scheduling model is formulated.Second,we propose a batch optimization algorithm with inverse scheduling in which the batch size is adjusted by the dynamic feedback batch adjusting method.Moreover,in order to increase the diversity of the population,two methods are developed.One is the threshold to control the neighborhood updating,and the other is the dynamic clustering algorithm to update the population.Finally,a group of experiments are carried out.The results show that the improved multi-objective optimization algorithm can ensure the diversity of Pareto solutions effectively,and has effective performance in solving the flexible job shop scheduling problem with variable batches.

Particle swarm optimization and its application to seismic inversion of igneous rocks

In order to improve the fine structure inversion ability of igneous rocks for the exploration of underlying strata, based on particle swarm optimization(PSO), we have developed a method for seismic wave impedance inversion. Through numerical simulation, we tested the effects of different algorithm parameters and different model parameterization methods on PSO wave impedance inversion, and analyzed the characteristics of PSO method. Under the conclusions drawn from numerical simulation, we propose the scheme of combining a cross-moving strategy based on a divided block model and high-frequency filtering technology for PSO inversion. By analyzing the inversion results of a wedge model of a pitchout coal seam and a coal coking model with igneous rock intrusion, we discuss the vertical and horizontal resolution, stability and reliability of PSO inversion. Based on the actual seismic and logging data from an igneous area, by taking a seismic profile through wells as an example, we discuss the characteristics of three inversion methods, including model-based wave impedance inversion, multi-attribute seismic inversion based on probabilistic neural network(PNN) and wave impedance inversion based on PSO.And we draw the conclusion that the inversion based on PSO method has a better result for this igneous area.

The forward and inverse problem of cardiac magnetic fields based on concentric ellipsoid torso-heart model

This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source--a current dipole and volume currents. Then by using the simulated magnetic fields based on torso-heart model as input, the cardiac current sources--an array of current dipoles by optimal constrained linear inverse method are constructed. Next, the current dipole array reconstruction considering boundaries is compared with that in an unbounded homogeneous medium. Furthermore, the influence of random noise on reconstruction is also considered and the reconstructing effect is judged by several reconstructing parameters.

A hyperchaotic system stabilization via inverse optimal control and experimental research

In this paper, some basic dynamical properties of a four-dimensional autonomous hyperchaotic system are investi- gated by means of Poincare mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this new hyperchaotic system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment. An efficient approaching is developed for global asymptotic stabilization of this four-dimensional hyperchaotic system. Based on the method of inverse optimal control for nonlinear systems, a linear state feedback is electronically implemented. It is remarkably simple as compared with other chaos control ways, like nonlinear state feedback.

Stability in Probability and Inverse Optimal Control of Evolution Systems Driven by Levy Processes

This paper first develops a Lyapunov-type theorem to study global well-posedness(existence and uniqueness of the strong variational solution)and asymptotic stability in probability of nonlinear stochastic evolution systems(SESs)driven by a special class of Levy processes,which consist of Wiener and compensated Poisson processes.This theorem is then utilized to develop an approach to solve an inverse optimal stabilization problem for SESs driven by Levy processes.The inverse optimal control design achieves global well-posedness and global asymptotic stability of the closed-loop system,and minimizes a meaningful cost functional that penalizes both states and control.The approach does not require to solve a Hamilton-Jacobi-Bellman equation(HJBE).An optimal stabilization of the evolution of the frequency of a certain genetic character from the population is included to illustrate the theoretical developments.

Sensitivity and inverse analysis methods for parameter intervals

This paper proposes a sensitivity analysis method for engineering parameters using interval analyses.This method substantially extends the application of interval analysis method.In this scheme,parameter intervals and decision-making target intervals are determined using the interval analysis method.As an example,an inverse analysis method for uncertainty is presented.The intervals of unknown parameters can be obtained by sampling measured data.Even for limited measured data,robust results can also be obtained with the inverse analysis method,which can be intuitively evaluated by the uncertainty expressed in terms of an interval.For complex nonlinear problems,an iteratively optimized inverse analysis model is proposed.In a given set of loose parameter intervals,all the unknown parameter intervals that satisfy the measured information can be obtained by an iteratively optimized inverse analysis model.The influences of measured precisions and the number of parameters on the results of the inverse analysis are evaluated.Finally,the uniqueness of the interval inverse analysis method is discussed.

Developing a Secure Framework Using Feature Selection and Attack Detection Technique

Intrusion detection is critical to guaranteeing the safety of the data in the network.Even though,since Internet commerce has grown at a breakneck pace,network traffic kinds are rising daily,and network behavior characteristics are becoming increasingly complicated,posing significant hurdles to intrusion detection.The challenges in terms of false positives,false negatives,low detection accuracy,high running time,adversarial attacks,uncertain attacks,etc.lead to insecure Intrusion Detection System(IDS).To offset the existing challenge,the work has developed a secure Data Mining Intrusion detection system(DataMIDS)framework using Functional Perturbation(FP)feature selection and Bengio Nesterov Momentum-based Tuned Generative Adversarial Network(BNM-tGAN)attack detection technique.The data mining-based framework provides shallow learning of features and emphasizes feature engineering as well as selection.Initially,the IDS data are analyzed for missing values based on the Marginal Likelihood Fisher Information Matrix technique(MLFIMT)that identifies the relationship among the missing values and attack classes.Based on the analysis,the missing values are classified as Missing Completely at Random(MCAR),Missing at random(MAR),Missing Not at Random(MNAR),and handled according to the types.Thereafter,categorical features are handled followed by feature scaling using Absolute Median Division based Robust Scalar(AMDRS)and the Handling of the imbalanced dataset.The selection of relevant features is initiated using FP that uses‘3’Feature Selection(FS)techniques i.e.,Inverse Chi Square based Flamingo Search(ICS-FSO)wrapper method,Hyperparameter Tuned Threshold based Decision Tree(HpTT-DT)embedded method,and Xavier Normal Distribution based Relief(XavND-Relief)filter method.Finally,the selected features are trained and tested for detecting attacks using BNM-tGAN.The Experimental analysis demonstrates that the introduced DataMIDS framework produces an accurate diagnosis about the attack with low computation time.The work avoids false alarm rate of attacks and remains to be relatively robust against malicious attacks as compared to existing methods.

Noise filtering of full-gravity gradient tensor data

In oil and mineral exploration, gravity gradient tensor data include higher- frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-tensor gradiometry （FTG） data are contaminated by high-frequency random noise. The separation of noise from high-frequency signals is one of the most challenging tasks in processing of gravity gradient tensor data. We first derive the Cartesian equations of gravity gradient tensors under the constraint of the Laplace equation and the expression for the gravitational potential, and then we use the Cartesian equations to fit the measured gradient tensor data by using optimal linear inversion and remove the noise from the measured data. Based on model tests, we confirm that not only this method removes the high- frequency random noise but also enhances the weak anomaly signals masked by the noise. Compared with traditional low-pass filtering methods, this method avoids removing noise by sacrificing resolution. Finally, we apply our method to real gravity gradient tensor data acquired by Bell Geospace for the Vinton Dome at the Texas-Louisiana border.

Attitude stabilization of rigid spacecraft implemented in backstepping control with input delay

A backstepping method is used for nonlinear spacecraft attitude stabilization in the presence of external disturbances and time delay induced by the actuator. The kinematic model is established based on modified Rodrigues parameters (MRPs). Firstly, we get the desired angular velocity virtually drives the attitude parameters to origin, and then backstep it to the desired control torque required for stabilization. Considering the time delay induced by the actuator, the control torque functions only after the delayed time, therefore time compensation is needed in the controller. Stability analysis of the close-loop system is given afterwards. The infinite dimensional actuator state is modeled with a first-order hyperbolic partial differential equation (PDE), the L-2 norm of the system state is constructed and is proved to be exponentially stable. An inverse optimality theorem is also employed during controller design. Simulation results illustrate the efficiency of the proposed control law and it is robust to bounded external disturbances and time delay mismatch.

Robust Adaptive Control of PVTOL System via Minimum Projection Method

＂Dynamic extension＂ is commonly used for stabilization of the planar vertical take off and landing （PVTOL） system. Most controllers designed by the method are based on ＂dynamic＂ control Lyapunov functions （CLFs）. We design a C^∞ differentiable ＂static＂ CLF for the PVTOL system by dynamic extension and minimum projection method. Then we propose an inverse optimal controller based on the static CLF that attains a gain margin. We design an adaptive control input and show the robustness of the controller by computer simulation.

SOLVING A CLASS OF INVERSE QP PROBLEMS BY A SMOOTHING NEWTON METHOD

We consider an inverse quadratic programming （IQP） problem in which the parameters in the objective function of a given quadratic programming （QP） problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. This problem can be formulated as a minimization problem with a positive semidefinite cone constraint and its dual （denoted IQD（A, b）） is a semismoothly differentiable （SC^1） convex programming problem with fewer variables than the original one. In this paper a smoothing Newton method is used for getting a Karush-Kuhn-Tucker point of IQD（A, b）. The proposed method needs to solve only one linear system per iteration and achieves quadratic convergence. Numerical experiments are reported to show that the smoothing Newton method is effective for solving this class of inverse quadratic programming problems.

The Inverse Classification Problem

In this paper, we examine an emerging variation of the classification problem, which is known as the inverse classification problem. In this problem, we determine the features to be used to create a record which will result in a desired class label. Such an approach is useful in applications in which it is an objective to determine a set of actions to be taken in order to guide the data mining application towards a desired solution. This system can be used for a variety of decision support applications which have pre-determined task criteria. We will show that the inverse classification problem is a powerful and general model which encompasses a number of different criteria. We propose a number of algorithms for the inverse classification problem, which use an inverted list representation for intermediate data structure representation and classification. We validate our approach over a number of real datasets.

H_∞ Inverse Optimal Adaptive Fault-Tolerant Attitude Control for Flexible Spacecraft with Input Saturation

An adaptive inverse optimal attitude controller for flexible spacecraft with fault-free actuator is designed based on adaptive control Lyapunov function and inverse optimal methodology subjected to unknown parameter uncertainties,external disturbances and input saturation.The partial loss of actuator effectiveness and the additive faults are considered simultaneously to deal with actuator faults,and the prior knowledge of bounds on the effectiveness factors of the actuators is assumed to be unknown.A fault-tolerant control version is designed to handle the system with actuator fault by introducing a parameter update law to estimate the lower bound of the partial loss of actuator effectiveness faults.The proposed fault-tolerant attitude controller ensures robustness and stabilization,and it achieves H_∞ optimality with respect to a family of cost functionals.The usefulness of the proposed algorithms is assessed and compared with the conventional approaches through numerical simulations.