摘要：This paper explores the algebraic essence of universal logic functions(ULFs)from an algebraic perspective.Under the framework of semi-tensor product of matrices,the"sequential nature"of ULFs is revealed.Utilizing the nature,a technique called universal transformation method is proposed,by which any ULF can be transformed into an equivalent expression with desired features that facilitate achieving specific objectives,such as modeling,analyzing and synthesizing universal logical systems.Furthermore,several useful logical operators are constructed in a mixed-dimensional situation,including power-raising operator,power-descending operator,erasure operator,and appending operator.Finally,these results are applied to model and analyze finite state machines and their networks,which demonstrate the practical value of the method and operators.

摘要：This study develops an event-triggered control strategy utilizing the fully actuated system approach for nonlinear intercon-nected large-scale systems containing actuator failures.First,to reduce the complexity of the design process,we transform the studied system into the form of a fully actuated system through a state transformation.Then,to address the unknown non-linear functions and actuator fault parameters,we employ neural networks and adaptive estimation techniques,respectively.Moreover,to reduce the control cost and improve the control efficiency,we introduce event-triggered inputs into the control strategy.It is proved by the Lyapunov stability analysis that all signals of the closed-loop system are bounded and the output of system eventually converge to a bounded region.The efficacy of the control approach is ultimately demonstrated via the simulation of an actual machine feeding system.

摘要：The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical performance,its compact form is developed herein.Through replacing the states and costates variation evolution with that of the controls,the dimension-reduced Evolution Partial Differential Equation(EPDE)only solves the control variables along the variation time to get the optimal solution,and the initial conditions for the definite solution may be arbitrary.With this equation,the scale of the resulting IVPs,obtained via the semi-discrete method,is significantly reduced and they may be solved with common Ordinary Differential Equation(ODE)integration methods conveniently.Meanwhile,the state and the costate dynamics share consistent stability in the numerical computation and this avoids the intrinsic numerical difficulty as in the indirect methods.Numerical examples are solved and it is shown that the compact form evolution equation outperforms the primary form in the precision,and the efficiency may be higher for the dense discretization.Actually,it is uncovered that the compact form of the augmented evolution equation is a continuous realization of the Newton type iteration mechanism.

摘要：In this paper,we study the issue of controlling a rotating flexible body-beam system(RFBBS)which consists of a tip mass attached to the free-end and a rigid disk attached to the clamped-end of an Euler-Bernoulli beam.The boundary control input is affected by both unknown disturbance and nonlinear input backlash.First,the input backlash is considered as desired control input combined with a nonlinear input error,converting it to an external disturbance,and then,the control signal is designed through the energy-based control method.Next,the closed-loop system's stability is analysed through Lyapunov direct method.Finally,the efficacy of the proposed control scheme is tested through numerical simulations utilizing the finite difference method.

摘要：In this paper,we consider a multiple-input single-output(MISO)Hammerstein system whose inputs and output are disturbed by unknown Gaussian white measurement noises.The parameter estimation of such a system is a typical errors-in-variables(EIV)nonlinear system identification problem.This paper proposes a bias-correction least squares(BCLS)identification methods to compute a consistent estimate of EIV MISO Hammerstein systems from noisy data.To obtain the unbiased parameter estimates of EIV MISO Hammerstein system,the analytical expression of estimated bias for the standard least squares(LS)algorithm is derived first,which is a function about the variances of noises.And then a recursive algorithm is proposed to estimate the unknown term of noises variances from noisy data.Finally,based on bias estimation scheme,the bias caused by the correlation between the input-output signals exciting the true system and the corresponding measurement noise,resulting in unbiased parameter estimates of the EIV MISO Hammerstein system.The performance of the proposed method is demonstrated through a simulation example and a chemical continuously stirred tank reactor(CSTR)system.

摘要：This paper investigates the consensus tracking control problem for high order nonlinear multi-agent systems subject to non-affine faults,partial measurable states,uncertain control coefficients,and unknown external disturbances.Under the directed topology conditions,an observer-based finite-time control strategy based on adaptive backstepping and is proposed,in which a neural network-based state observer is employed to approximate the unmeasurable system state variables.To address the complexity explosion problem associated with the backstepping method,a finite-time command filter is incorporated,with error compensation signals designed to mitigate the filter-induced errors.Additionally,the Butterworth low-pass filter is introduced to avoid the algebraic ring problem in the design of the controller.The finite-time stability of the closed-loop system is rigorously analyzed with the finite-time Lyapunov stability criterion,validating that all closed-loop signals of the system remain bounded within a finite time.Finally,the effectiveness of the proposed control strategy is verified through a simulation example.

摘要：The objective of the current study is to investigate an adaptive predictive observer-based autopilot for a skid-to-turn(STT)missile model with uncertainties and unknown dynamic equations.A predictive control for the STT missile is designed based on nonlinear model predictive control(NMPC)using Taylor series expansion,after which,via a neural network(NN),unknown functions are approximated.The present study also evaluates an adaptive optimal observer of a new strategy-based nonlinear system.Specifically,to estimate the missile states such as normal acceleration and its derivatives for the future,originally the Taylor series states expansion was gained to any specified order,based on their receding horizons.To address the problem of prediction error,an analytic solution was prepared that led to a closed form regarding the nonlinear optimal observer.Out of the gains resulting from the analytic solution,as developed for the problem of prediction error,the selection of the proposed observer gain was optimally conducted to meet the stability condition.Thus,combining the adaptive predictive autopilot and the adaptive optimal observer scheme was implemented to secure the performance,which needed only estimated normal acceleration and its derivatives.Meanwhile,no angular velocity measurement or wind angle estimation was required.Ultimately,the proposed technique was found effective,as confirmed by the qualitative simulation results.

摘要：Considering the impact of terminal impact time constraints and the state information of maneuvering targets on the guidance accuracy in multi-UAV cooperative guidance,this paper proposes an impact time cooperative control guidance law(ITCCG)that combines the optimal error dynamics with an improved adaptive cubature Kalman filter(IACKF)algorithm.First,a terminal impact time feedback term is introduced into proportional navigation guidance based on the relative virtual guidance model,and terminal time control is achieved through optimal error dynamics.Then,the Huber loss function is used to reduce the impact of measurement outliers,and the diagonal decomposition is applied to address the issue of non-positive definite matrices that cannot undergo Cholesky decomposition.Finally,the ITCCG and IACKF algorithms combined achieve multi-UAV time-cooperated guidance based on maneuvering target state estimation.Simulation results show that the proposed algorithm effectively reduces the target state estimation error and achieves cooperative guidance within the desired time frame.

摘要：This paper proposes a robust control-oriented identification method for errors-in-variables(EIV)systems in output feedbacks using frequency-response(FR)experimental data.An important relation between such a closed-loop EIV system and its coprime factor(CF)uncertainty description is first derived,based on which the FR measurements suitable for plant CF identification are able to be generated.Different factorizations of a given controller in the closed-loop system can be made best use to adjust right coprime factors(RCFs)of the plant so as to realize an improvement on the signal-to-noise ratio of identification experimental data.Subsequently,a nominal RCF model is estimated by linear matrix inequalities from the applicable FR measurements and its associated worst-case errors are quantified from a priori and a posteriori information on the underlying system.A resulting RCF perturbation model set can then be described by the nominal RCF model and its worst-case error bounds.Such a model set capable of being stabilized by the given controller is ready for its robust stabilizing controller redesign and robust performance analysis.Finally,a numerical simulation is given to show the efficacy of the proposed identification method.

摘要：Pull-ups are a very common fitness exercise that can be seen in many gyms.For athletes,it is very important to perform pull-ups correctly and scientifically.The pull-up scoring method designed in this paper can score the quality of pull-up movement scientifically and objectively,and provide guidance to help athletes better complete the pull-up movement.In this method,the OpenPose algorithm is used to identify the coordinates of skeleton points,and then the coordinate data are processed by a Kalman filter to obtain coordinates closer to the true values.Finally,the filtered data are input into the scoring algorithm designed based on the fuzzy comprehensive evaluation algorithm,and the results of the pull-up quality score and the corresponding guidance are obtained.

摘要：This paper focuses on the leader-following positive consensus problems of heterogeneous switched multi-agent systems.First,a state-feedback controller with dynamic compensation is introduced to achieve positive consensus under average dwell time switching.Then sufficient conditions are derived to guarantee the positive consensus.The gain matrices of the control protocol are described using a matrix decomposition approach and the corresponding computational complexity is reduced by resorting to linear programming and co-positive Lyapunov functions.Finally,two numerical examples are provided to illustrate the results obtained.

摘要：The focus of this paper is on distributed average tracking(DAT)in the context of external disturbances,utilizing an event-triggered control mechanism.First,an event-triggered anti-disturbance DAT(ETAD-DAT)algorithm is proposed to reduce communication load in networked control systems by redesigning existing anti-disturbance DAT algorithms and disturbance observers.Furthermore,a fully distributed event-triggering condition is employed to schedule event times for each agent.Simulation results demonstrate that the proposed ETAD-DAT algorithm is able to achieve accurate average tracking of multiple time-varying reference signals despite the presence of external disturbances,while the communication efficiency can be improved obviously.

摘要：Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitrary number of switching matrices.The exponential stability and instability(ESI)conditions so obtained involve the supremum and infimum of ratios of certain quadratic forms of the matrices,leading to global time-averages of their activity intervals.Further,motivated by linear switching system examples of(ⅰ)instability with stable matrices and(ⅱ)stability with unstable matrices(found in the literature primarily for second-order systems),the proposed framework is generalized to establish ESI conditions that include both the activity intervals of the matrices and their switching rates,the latter being governed by a certain logarithmic measure of the normalized magnitudes of discontinuities caused by switching.In effect,(the new,globally averaged)dwell-time is flexibly traded,apparently for the first time,but under specific conditions(related,in part,to the eigenvalues of the matrices),for switching discontinuity-based conditions.Two further novel aspects of the proposed approach are:(ⅰ)For second-order matrices,switching lines in phase space can be chosen for periodic switching to stabilize or destabilize the system,and even generate oscillations,depending on the eigenvalues of the system matrices.But for third-(and higher)order matrices,such an analytically tractable(and controlled)periodical switching entails solution of an explicit non-convex multi-parameter optimization problem for which a stochastic optimization algorithm from the literature can be invoked.(ⅱ)Lower and upper bounds on the solutions of the system equations can be quantified to reflect the stability/instability/oscillatory property of the system.Illustrative examples,which demonstrate the novelty of the derived stability and instability conditions,are presented in part 2 which is advisedly to be read along with this part 1 for a coherent merging of theory with practice.

摘要：Bilinear structures are common in boost converters,and despite presenting interesting complexity,there are controls that have found general solutions under certain restrictions.Among these,the passive controls containing the error dynamics of boost converters for a certain output structure are notable.While passive controls based on passivity demonstrate adequate performance,this work proposes a perturbation control based on the antisymmetric structure of boost converters to achieve better performance in terms of convergence speed and mean square error.Additionally,the perturbation control requires less error information for constructing the control signal,because it does not need information from all states or the entire passive output.Besides,the perturbation control uses the passivity of boost converters to ensure its stability.And finally,the perturbation control is compared with passive controls in a boost converter.

摘要：In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1-4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.

摘要：Focusing on the rehabilitation training of hemiplegia patients,this paper proposes a gait-planning strategy based on a central pattern generator and an adaptive time-delay control scheme that utilizes recursive terminal sliding mode for lower limb rehabilitation exoskeleton robots.The central pattern generator network plans a reference gait trajectory for the affected leg,synchronized with the movement of the healthy leg.The proposed adaptive time-delay control scheme possesses a model-independent property due to the mechanism of time-delay estimation,with adaptive control gains that enhance the resilience against system perturbations and a recursive terminal sliding mode control component to achieve a fast convergence rate.According to the Lyapunov stability criterion,it is proved that the gait trajectory-tracking error is uniformly ultimately bounded.Experiments are conducted on a lower limb exoskeleton experimental platform,and the experimental results demonstrate the effectiveness and superiority of the proposed strategies.

摘要：The adaptive H∞ finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently transformed into a differential-algebraic system.Next,it is proved that the state feedback can be used as an adaptive H∞ finite-time boundedness controller of NSHS.Finally,the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.

摘要：The output regulation approach has effectively addressed the speed tracking and disturbance rejection problem of permanent magnet synchronous motor(PMSM).Although accurate speed tracking under time-varying load torque disturbance has been achieved,the number of disturbance frequencies should be known.In this paper,an adaptive observer-based error feedback control method is proposed,which can solve the speed tracking control problem of PMSM subject to completely unknown multi-frequency sinusoidal load torque disturbance,requiring only the upper bound of the number of disturbance frequencies.The design steps of this method can be divided into the following three steps.In step one,a filtered transformation is applied to convert the observer canonical form of the error system and the transformed exosystem into an adaptive observer form.In step two,an adaptive observer is designed to estimate the unknown parameters of the exosystem and states of the adaptive observer form.In step three,an adaptive observer-based error feedback controller is designed to solve this control problem.The effectiveness of the proposed method is demonstrated by experimental results.

摘要：Potential games(PG)have attracted the attention of many researchers because of its excellent properties and multi-PG are more flexible and extensible,which greatly improve the application range of PG.Consider that weights and states to each player are common and practical in many application scenarios,and in this paper,by introducing weight value and state into multi-PG,q-weighted PG and q-state PG are systematically discussed and analyzed to expand the types of PG,respectively.First,using semi-tensor product of matrices(STP),a matrix approach to the modeling of weighted PG is investigated,and the verification method of weighted PG is proposed by defining three matrices,and the problem of how to detect weighted PG can be transformed to solve an algebraic equation,which is composed of the above three matrices.Next,by bringing weight values into multi-PG and detecting the weighted PG for each group,the verification method is extended to the q-weighted PG.Second,the model of state-based PG is constructed,and the problem of how to detect state-based PG can be transformed to solve another algebraic equation,which is seen as an extension of the verification method of weighted PG.Subsequently,the verification of q-state PG is discussed.Finally,we use two examples to demonstrate the validation of obtained results.

摘要：In industrial control systems,such as power transmission facilities and water treatment plants,Programmable Logic Controllers(PLCs)can work consistently and stably over long periods if there are no faults.Black-box identification aims to automatically construct Petri net models with the help of I/O signals from PLC devices only.The main challenge is how to convert the infinitely long PLC signals into an event sequence,which is the foundation for subsequent modeling.The current algorithms are confronted with a number of challenges,including an exponential increase in the number of transitions,high time complexity,and susceptibility to noisy signals.To solve these problems,this paper proposes a new method for converting PLC signals into a transition sequence.The method is based on the principles of Boolean absorption law,which filters out noise information in the I/O signals.Then firing functions representing input-output causality are constructed from the filtered signals.Finally,the original signal sequence is traversed to generate a transition sequence.The experimental results show that these methods can rapidly identify a transition sequence.Compared to traditional methods,the proposed algorithms have polynomial time complexity.