Hybrid TDOA/FDOA and track optimization of UAV swarm based on A-optimality

The source location based on the hybrid time difference of arrival(TDOA)/frequency difference of arrival(FDOA) is a basic problem in wireless sensor networks, and the layout of sensors in the hybrid TDOA/FDOA positioning will greatly affect the accuracy of positioning. Using unmanned aerial vehicle(UAV) as base stations, by optimizing the trajectory of the UAV swarm, an optimal positioning configuration is formed to improve the accuracy of the target position and velocity estimation. In this paper, a hybrid TDOA/FDOA positioning model is first established, and the positioning accuracy of the hybrid TDOA/FDOA under different positioning configurations and different measurement errors is simulated by the geometric dilution of precision(GDOP) factor. Second, the Cramer-Rao lower bound(CRLB) matrix of hybrid TDOA/FDOA location under different moving states of the target is derived theoretically, the objective function of the track optimization is obtained, and the track of the UAV swarm is optimized in real time. The simulation results show that the track optimization effectively improves the accuracy of the target position and velocity estimation.

TDOA and track optimization of UAV swarm based on D-optimality

To solve the problem of time difference of arrival(TDOA)positioning and tracking of targets by the unmanned aerial vehicles(UAV)swarm in future air combat,this paper adopts the TDOA positioning method and uses time difference sensors of the UAV swarm to locate target radiation sources.Firstly,a TDOA model for the target is set up for the UAV swarm under the condition that the error variance varies with the received signal-to-noise ratio.The accuracy of the positioning error is analyzed by geometric dilution of precision(GDOP).The D-optimality criterion of the positioning model is theoretically derived.The target is positioned and settled,and the maximum value of the Fisher information matrix determinant is used as the optimization objective function to optimize the track of the UAV in real time.Simulation results show that the track optimization improves the positioning accuracy and stability of the UAV swarm to the target.

Running safety and seismic optimization of a fault-crossing simply-supported girder bridge for high-speed railways based on a train-track-bridge coupling system

Bridges crossing active faults are more likely to suffer serious damage or even collapse due to the wreck capabilities of near-fault pulses and surface ruptures under earthquakes.Taking a high-speed railway simply-supported girder bridge with eight spans crossing an active strike-slip fault as the research object,a refined coupling dynamic model of the high-speed train-CRTS III slab ballastless track-bridge system was established based on ABAQUS.The rationality of the established model was thoroughly discussed.The horizontal ground motions in a fault rupture zone were simulated and transient dynamic analyses of the high-speed train-track-bridge coupling system under 3-dimensional seismic excitations were subsequently performed.The safe running speed limits of a high-speed train under different earthquake levels(frequent occurrence,design and rare occurrence)were assessed based on wheel-rail dynamic(lateral wheel-rail force,derailment coefficient and wheel-load reduction rate)and rail deformation(rail dislocation,parallel turning angle and turning angle)indicators.Parameter optimization was then investigated in terms of the rail fastener stiffness and isolation layer friction coefficient.Results of the wheel-rail dynamic indicators demonstrate the safe running speed limits for the high-speed train to be approximately 200 km/h and 80 km/h under frequent and design earthquakes,while the train is unable to run safely under rare earthquakes.In addition,the rail deformations under frequent,design and rare earthquakes meet the safe running requirements of the high-speed train for the speeds of 250,100 and 50 km/h,respectively.The speed limits determined for the wheel-rail dynamic indicators are lower due to the complex coupling effect of the train-track-bridge system under track irregularity.The running safety of the train was improved by increasing the fastener stiffness and isolation layer friction coefficient.At the rail fastener lateral stiffness of 60 kN/mm and isolation layer friction coefficients of 0.9 and 0.8,respectively,the safe running speed limits of the high-speed train increased to 250 km/h and 100 km/h under frequent and design earthquakes,respectively.

Event-based performance guaranteed tracking control for constrained nonlinear system via adaptive dynamic programming method

An optimal tracking control problem for a class of nonlinear systems with guaranteed performance and asymmetric input constraints is discussed in this paper.The control policy is implemented by adaptive dynamic programming(ADP)algorithm under two event-based triggering mechanisms.It is often challenging to design an optimal control law due to the system deviation caused by asymmetric input constraints.First,a prescribed performance control technique is employed to guarantee the tracking errors within predetermined boundaries.Subsequently,considering the asymmetric input constraints,a discounted non-quadratic cost function is introduced.Moreover,in order to reduce controller updates,an event-triggered control law is developed for ADP algorithm.After that,to further simplify the complexity of controller design,this work is extended to a self-triggered case for relaxing the need for continuous signal monitoring by hardware devices.By employing the Lyapunov method,the uniform ultimate boundedness of all signals is proved to be guaranteed.Finally,a simulation example on a mass–spring–damper system subject to asymmetric input constraints is provided to validate the effectiveness of the proposed control scheme.

Optimal tracking control for automatic transmission shift process

In order to improve the shift quality, a linear quadratic optimal tracking control algorithm for automatic transmission shift process is proposed. The dynamic equations of the shift process are derived using a Lagrange method. And a powertrain model is built in the Matlab/Simulink and veri- fied by the measurements. Considering the shift jerk and friction loss during the shift process, the tracking trajectories of the turbine speed and output shaft speed are defined. Furthermore, the linear quadratic optimal tracking control performance index is proposed. Based on the Pontryagin＇ s mini- mum principle, the optimal control law of the shift process is presented. Finally, the simulation study of the 1 - 2 upshift process under different load conditions is carried out with the powertrain model. The simulation results demonstrate that the shift jerk and friction loss can be significantly re- duced by applying the proposed optimal tracking control method.

Optimal tracking control for linear time-delay large-scale systems with persistent disturbances

An optimal tracking control （OTC） problem for linear time-delay large-scale systems affected by external persistent disturbances is investigated. Based on the internal model principle, a disturbance compensator is constructed. The system with persistent disturbances is transformed into an augmented system without persistent disturbances. The original OTC problem of linear time-delay system is transformed into a sequence of linear two- point boundary value （TPBV） problems by introducing a sensitivity parameter and expanding Maclaurin series around it. By solving an OTC law of the augmented system, the OTC law of the original system is obtained. A numerical simulation is provided to illustrate the effectiveness of the proposed method.

Optimal tracking control for nonlinear large-scale systems with persistent disturbances

This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances.The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms.Based on the internal model principle,a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances.According to the sensitivity approach,the optimal tracking control law for the ith nonlinear subsystem can be obtained.The optimal tracking control law for the nonlinear large-scale systems can be obtained.A numerical simulation shows that the method is effective.

Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.

Off-policy integral reinforcement learning optimal tracking control for continuous-time chaotic systems

This paper estimates an off-policy integral reinforcement learning（IRL） algorithm to obtain the optimal tracking control of unknown chaotic systems. Off-policy IRL can learn the solution of the HJB equation from the system data generated by an arbitrary control. Moreover, off-policy IRL can be regarded as a direct learning method, which avoids the identification of system dynamics. In this paper, the performance index function is first given based on the system tracking error and control error. For solving the Hamilton–Jacobi–Bellman（HJB） equation, an off-policy IRL algorithm is proposed.It is proven that the iterative control makes the tracking error system asymptotically stable, and the iterative performance index function is convergent. Simulation study demonstrates the effectiveness of the developed tracking control method.

Best tracking performance for integrator and dead time plant

The optimal tracking performance for integrator and dead time plant in the case where plant uncertainty and control energy constraints are to be considered jointly is inrestigated. Firstly, an average cost function of the tracking error and the plant input energy over a class of stochastic model errors are defined. Then, we obtain an internal model controller design method that minimizes the average performance and further studies optimal tracking performance for integrator and dead time plant in the simultaneous presence of plant uncertainty and control energy constraint. The results can be used to evaluate optimal tracking performance and control energy in practical designs.

OPTIMAL TRACK SEEKING CONTROL OF DUAL-STAGE ACTUATOR FOR HIGH DENSITY HARD DISK DRIVES

Based on generalized the variation method, by introducing Hamilton function and Lagrange multiplier, this paper proposed a linear quadratic optimal control strategy for an incomplete controllable system with fixed terminal state and time. Applying the proposed optimal control to the simple two-input dual-stage actuator magnetic head positioning system with three degrees-of-freedom, the simulation results show that the system has no residual vibration at the terminal position and time, which can reduce the total access time during head positioning process. To verify the validation of the optimal control strategy of three degrees-of-freedom spring-mass models in actual magnetic head positioning of hard disk drives, a finite element model of an actual magnetic head positioning system is presented. Substituting the optimal control force from simple three degrees-of-freedom spring-mass models into the finite element model, the simulation results show that the magnetic head also has no residual vibration at the end of track-to-track travel. That is to say, the linear quadratic optimal control technique based on simple two-input dual- stage actuator system with three degrees-of-freedom proposed in this paper is of high reliability for the industrial application of an actual magnetic head positioning system.

Best Tracking Performance under Plant Uncertainty and Control Energy Constraint

This paper has investigated best tracking performance for linear feedback control systems in the case that plant uncertainty and control effort need to be considered simultaneously. Firstly, an average integral square criterion of the tracking error and the plant input energy over a class of additive model errors is defined. Then, utilizing spectral factorization to minimize the performance index, we obtain an optimal controller design method, and furthermore study optimal tracking performance under plant uncertainty and control energy constraint. The results can be used to evaluate optimal average tracking performance and control energy in designing practical control systems.

Output neighboring-extremal and NCO tracking control in the optimal operation of CSTR

A new optimizing framework of process operation is proposed to deal with optimizing op- eration of continuous stirred tank reactor （CSTR）. The optimization framework includes two layers： the first layer, necessary condition of optimally （NCO） tracking controller, calculates the optimal set-point of the process; and the second layer, output neighboring-extremal controller, calculates the input values of the controlled plant. The algorithm design and convergent analysis of output neighboring-extremal controller are discussed emphatically, and in the case of existing parametric uncertainty, the approach is shown to converge to the optimum atmost in two iterations. At last the approach is illustrated by simulation results for a dynamic CSTR.

Robust parametric approach for tracking control of an air-breathing hypersonic cruise vehicle

To realize the stabilization and the tracking of flight control for an air-breathing hypersonic cruise vehicle, the linearization of the longitudinal model under trimmed cruise condition is processed firstly. Furthermore, the flight control problem is formulated as a robust model tracking control problem. And then, based on the robust parametric approach, eigenstructure assignment and reference model tracking theory, a parametric optimization method for robust controller design is presented. The simulation results show the effectiveness of the proposed approach.

Development of a Bias Compensating Q-Learning Controller for a Multi-Zone HVAC Facility

We present the development of a bias compensating reinforcement learning(RL)algorithm that optimizes thermal comfort(by minimizing tracking error)and control utilization(by penalizing setpoint deviations)in a multi-zone heating,ventilation,and air-conditioning(HVAC)lab facility subject to unmeasurable disturbances and unknown dynamics.It is shown that the presence of unmeasurable disturbance results in an inconsistent learning equation in traditional RL controllers leading to parameter estimation bias(even with integral action support),and in the extreme case,the divergence of the learning algorithm.We demonstrate this issue by applying the popular Q-learning algorithm to linear quadratic regulation(LQR)of a multi-zone HVAC environment and showing that,even with integral support,the algorithm exhibits bias issue during the learning phase when the HVAC disturbance is unmeasurable due to unknown heat gains,occupancy variations,light sources,and outside weather changes.To address this difficulty,we present a bias compensating learning equation that learns a lumped bias term as a result of disturbances(and possibly other sources)in conjunction with the optimal control parameters.Experimental results show that the proposed scheme not only recovers the bias-free optimal control parameters but it does so without explicitly learning the dynamic model or estimating the disturbances,demonstrating the effectiveness of the algorithm in addressing the above challenges.

Adaptive learning-based optimal tracking control system design and analysis of a disturbed nonlinear hypersonic vehicle model

We propose an adaptive learning-based optimal control scheme for height-velocity control models considering model uncertainties and external disturbances of hypersonic winged-cone vehicles.The longitudinal nonlinear model is first established and transformed into the control-oriented error equations,and the control scheme is organized by a steady-compensation combination.To overcome and eliminate the impact of model uncertainties and external disturbances,an adaptive radial basis function neural network(RBFNN)is designed by a q-gradient approach.Taking the height-velocity error system with estimated uncertainties into account,the adaptive learning-based optimal tracking control(ALOTC)scheme is proposed by combining the critic-only adaptive dynamic programming(ADP)framework and parameter optimization of system settling time.Furthermore,a novel weight update law is proposed to satisfy the online iteration requirements,and the algorithm convergence and closedloop stability are discussed by the Lyapunov theory.Finally,four simulation cases are provided to prove the effectiveness,accuracy,and robustness of the proposed scheme for the hypersonic longitudinal control system.

Adaptive Dynamic Programming-Based Attitude Optimal Tracking Control for a Quadrotor with Unmeasured Velocities and Model Uncertainties

This paper proposes an optimal output feedback tracking control scheme of the quadrotor unmanned aerial vehicle(UAV)attitude system with unmeasured angular velocities and model uncertainties.First,neural network(NN)is used to approximate the model uncertainties.Then,an NN velocity observer is established to estimate the unmeasured angular velocities.Further,a quadrotor output feedback attitude optimal tracking controller is designed,which consists of an adaptive controller designed by backstepping method and an optimal compensation term designed by adaptive dynamic programming.All signals in the closed-loop system are proved to be bounded.Finally,numerical simulation example shows that the quadrotor attitude tracking scheme is effective and feasible.

Optimal Decoupling Control Method and Its Application to a Ball Mill Coal-pulverizing System

Abstract-The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method is proposed, which can simultaneousiy provide optimal performance. The optimal decoupling controller is composed of an inner-loop decoupling controller and an outer-loop optimal tracking controller. First, by introducing one virtual control variable, the original differential equation on state is converted to a generalized system on output. Then, by introducing the other virtual control variable, and viewing the coupling terms as the measurable disturbances, the generalized system is open-loop decoupled. Finally, for the decoupled system, the optimal tracking control method is used. It is proved that the decoupling control is optimal for a certain performance index. Simulations on a ball mill coal-pulverizing system are conducted. The results show the effectiveness and superiority of the proposed method as compared with the conventional optimal quadratic tracking （LQT） control method.

A novel statistically tracked particle swarm optimization method for automatic generation control

Particle swarm optimization(PSO)is one of the popular stochastic optimization based on swarm intelligence algorithm.This simple and promising algorithm has applications in many research fields.In PSO,each particle can adjust its‘flying’according to its own flying experience and its companions’flying experience.This paper proposes a new PSO variant,called the statistically tracked PSO,which uses group statistical characteristics to update the velocity of the particle after certain iterations,thus avoiding localminima and helping particles to explore global optimum with an improved convergence.The performance of the proposed algorithm is tested on a deregulated automatic generation control problem in power systems and encouraging results are obtained.

ADAPTIVE TRACKING OF A CLASS OF FIRST-ORDER SYSTEMS WITH BINARY-VALUED OBSERVATIONS AND FIXED THRESHOLDS

This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A recursive projection algorithm is proposed for parameter estimation based on the statistical properties of the system noise. Then, an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectations of the innovation and output prediction with respect to the estimates, the closed-loop system is shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergence rate of the estimation error is also obtained. A numerical example is given to demonstrate the efficiency of the adaptive control law.