Computing large deviation prefactors of stochastic dynamical systems based on machine learning

We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.

Dynamic Constraint-Driven Event-Triggered Control of Strict-Feedback Systems Without Max/Min Values on Irregular Constraints

This work proposes an event-triggered adaptive control approach for a class of uncertain nonlinear systems under irregular constraints.Unlike the constraints considered in most existing papers,here the external irregular constraints are considered and a constraints switching mechanism(CSM)is introduced to circumvent the difficulties arising from irregular output constraints.Based on the CSM,a new class of generalized barrier functions are constructed,which allows the control results to be independent of the maximum and minimum values(MMVs)of constraints and thus extends the existing results.Finally,we proposed a novel dynamic constraint-driven event-triggered strategy(DCDETS),under which the stress on signal transmission is reduced greatly and no constraints are violated by making a dynamic trade-off among system state,external constraints,and inter-execution intervals.It is proved that the system output is driven to close to the reference trajectory and the semi-global stability is guaranteed under the proposed control scheme,regardless of the external irregular output constraints.Simulation also verifies the effectiveness and benefits of the proposed method.

Robust adaptive dynamic surface control for nonlinear uncertain systems

We propose a new method for robust adaptive backstepping control of nonlinear systems with parametric uncertainties and disturbances in the strict feedback form. The method is called dynamic surface control. Traditional backstepping algorithms require repeated differentiations of the modelled nonlinearities. The addition of n first order low pass filters allows the algorithm to be implemented without differentiating any model nonlinearities, thus ending the complexity arising due to the 'explosion of terms' that makes other methods difficult to implement in practice. The combined robust adaptive backstepping/first order filter system is proved to be semiglobally asymptotically stable for sufficiently fast filters by a singular perturbation approach. The simulation results demonstrate the feasibility and effectiveness of the controller designed by the method.

A Dynamical System-Based Framework for Dimension Reduction

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a nonlinear flow towards a lower-dimensional subspace;the projection onto the subspace gives the low-dimensional embedding.Training the model involves identifying the nonlinear flow and the subspace.Following the equation discovery method,we represent the vector field that defines the flow using a linear combination of dictionary elements,where each element is a pre-specified linear/nonlinear candidate function.A regularization term for the average total kinetic energy is also introduced and motivated by the optimal transport theory.We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method.We also show how the DDR method can be trained using a gradient-based optimization method,where the gradients are computed using the adjoint method from the optimal control theory.The DDR method is implemented and compared on synthetic and example data sets to other dimension reduction methods,including the PCA,t-SNE,and Umap.

Eigenstructure assignment in a class of second-order dynamic systems

Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.

Formation-Containment Control Using Dynamic Event-Triggering Mechanism for Multi-Agent Systems

The paper proposes a novel approach for formationcontainment control based on a dynamic event-triggering mechanism for multi-agent systems.The leader-leader and follower-follower communications are reduced by utilizing the distributed dynamic event-triggered framework.We consider two separate sets of design parameters:one set comprising control and dynamic event-triggering parameters for the leaders and a second set similar to the first one with different values for the followers.The proposed algorithm includes two novel stages of codesign optimization to simultaneously compute the two sets of parameters.The design optimizations are convex and use the weighted sum approach to enable a structured trade-off between the formation-containment convergence rate and associated communications.Simulations based on non-holonomic mobile robot multi-agent systems quantify the effectiveness of the proposed approach.

Implementation and Evaluation of Local Dynamic Map in Safety Driving Systems

Cooperative safety driving systems using vehicle-to-vehicle and vehicle-to infrastructure communication are developed. Sensor data of vehicles and infrastructures are communicated in the cooperative safety driving system. LDM (Local Dynamic Map) is standardized by ETSI (European Telecommunications Standards Institute) to manage the vehicle sensor data and the map data. Implementations of LDM are reported on documents of ETSI, but there are no numerical results. The implementations of LDM are deployed the database management system. We think that the response time of the database becomes higher as the number of vehicles grows. In this paper, we have implemented and evaluated the LDM with the collision detection application.

Resilient Fixed-Order Distributed Dynamic Output Feedback Load Frequency Control Design for Interconnected Multi-Area Power Systems

The paper proposes a novel H∞ load frequency control(LFC) design method for multi-area power systems based on an integral-based non-fragile distributed fixed-order dynamic output feedback(DOF) tracking-regulator control scheme. To this end, we consider a nonlinear interconnected model for multiarea power systems which also include uncertainties and timevarying communication delays. The design procedure is formulated using semi-definite programming and linear matrix inequality(LMI) method. The solution of the proposed LMIs returns necessary parameters for the tracking controllers such that the impact of model uncertainty and load disturbances are minimized. The proposed controllers are capable of receiving all or part of subsystems information, whereas the outputs of each controller are local. These controllers are designed such that the resilient stability of the overall closed-loop system is guaranteed. Simulation results are provided to verify the effectiveness of the proposed scheme. Simulation results quantify that the distributed(and decentralized) controlled system behaves well in presence of large parameter perturbations and random disturbances on the power system.

Implementation of configuration dependent stiffness proportional damping for the dynamics of rigid multi-block systems

The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid muhi-block systems.The stiff- ness proportional damping is constructed for the prescribed damping ratio,based on the non-zero fundamental frequency ef- fective during the time interval while the boundary conditions remain essentially constant.At this time interval,the funda- mental frequency can be estimated without complete eigenvalue analysis.The damping coefficients will vary while the damp- ing ratio remains the same throughout the entire analysis.A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases.These procedures were implemented in the development of the dis- tinet element method for the dynamic analyses of piled multi-block systems.The analysis results |or the single-block and two-block systems were in a good agreement with the analytic predictions.Applications to the seismic analyses of piled four- block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.

Adaptive Fuzzy Dynamic Surface Control for Uncertain Nonlinear Systems

In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of ＂explosion of complexity＂ in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller （SMC）. Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.

Robust Output Feedback Control for a Class of Nonlinear Systems with Input Unmodeled Dynamics

The robust global stabilization problem of a class of uncertain nonlinear systems with input unmodeled dynamics is considered using output feedback, where the uncertain nonlinear terms satisfy a far more relaxed condition than the existing triangulartype condition. Under the assumption that the input unmodeled dynamics is minimum-phase and of relative degree zero, a dynamic output compensator is explicitly constructed based on the nonseparation principle. An example illustrates the usefulness of the proposed method.

Consensus Control of Multi-Agent Systems Using Fault-Estimation-in-the-Loop:Dynamic Event-Triggered Case

The paper develops a novel framework of consensus control with fault-estimation-in-the-loop for multi-agent systems(MASs)in the presence of faults.A dynamic event-triggered protocol(DETP)by adding an auxiliary variable is utilized to improve the utilization of communication resources.First,a novel estimator with a noise bias is put forward to estimate the existed fault and then a consensus controller with fault compensation(FC)is adopted to realize the demand of reliability and safety of addressed MASs.Subsequently,a novel consensus control framework with fault-estimation-in-the-loop is developed to achieve the predetermined consensus performance with the l_(2)-l_(∞)constraint by employing the variance analysis and the Lyapunov stability approaches.Furthermore,the desired estimator and controller gains are obtained in light of the solution to an algebraic matrix equation and a linear matrix inequality in a recursive way,respectively.Finally,a simulation result is employed to verify the usefulness of the proposed design framework.

Correcting dynamic residual aberrations of conformal optical systems using AO technology

This paper analyses the dynamic residual aberrations of a conformal optical system and introduces adaptive optics （AO） correction technology to this system. The image sharpening AO system is chosen as the correction scheme.Communication between MATLAB and Code V is established via ActiveX technique in computer simulation.The SPGD algorithm is operated at seven zoom positions to calculate the optimized surface shape of the deformable mirror.After comparison of performance of the corrected system with the baseline system,AO technology is proved to be a good way of correcting the dynamic residual aberration in conformal optical design.

Dynamic Consensus of High-order Multi-agent Systems and Its Application in the Motion Control of Multiple Mobile Robots

In this paper, the leader-following consensus problem for multi-agent linear dynamic systems is considered. All agents and leader have identical multi-input multi-output （MIMO） linear dynamics that can be of any order, and only the output information of each agent is delivered throughout the communication network. When the interaction topology is fixed, the leader-following consensus is attained by Ho~ dynamic output feedback control, and the sufficient condition of robust controllers is equal to the solvability of linear matrix inequality （LMI）. The whole analysis is based on spectral decomposition and an equivalent decoupled structure achieved, and the stability of the system is proved. Finally, we extended the theoretical results to the case that the interaction topology is switching. The simulation results for multiple mobile robots show the effectiveness of the devised methods.

Reconstructing the Nonlinear Dynamical Systems by Evolutionary Computation Techniques

We introduce a new dynamical evolutionary algorithm（DEA） based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems （mainly the Lorenz and Chen systems）. The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems.

CONCEPTUAL ANALYSIS AND RANDOM ATTRACTOR FOR DISSIPATIVE RANDOM DYNAMICAL SYSTEMS

The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems （RDS）, which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.

Numerical Simulation of Dynamic Response of Towed Systems

In this paper, the dynamic response of undersea -+towed systems is numerically simulated. A two body towed system is especially considered in detail. The factors influencing the heave of towed-bodies, such as the weight of the towed-body (in sea water), the length and the weight (in sea water) per unit length of the cable between towed-bodies and towing ship, are investigated in detail. Calculations show that the two-body towed system can greatly increases the stability of the towed system.

Bipartite Formation Tracking for Multi-Agent Systems Using Fully Distributed Dynamic Edge-Event-Triggered Protocol

In this study,the bipartite time-varying output formation tracking problem for heterogeneous multi-agent systems(MASs)with multiple leaders and switching commu-nication networks is considered.Note that the switching communication networks may be connected or disconnected.To address this problem,a novel reduced-dimensional observer-based fully distributed asynchronous dynamic edge-event-triggered output feedback control protocol is developed,and the Zeno behavior is ruled out.The theoretical analysis gives the admissible switching frequency and switching width under the proposed control protocol.Different from the existing works,the control protocol reduces the dimension of information to be transmitted between neighboring agents.Moreover,since an additional positive internal dynamic variable is introduced into the triggering functions,the control protocol can guarantee a larger inter-event time interval compared with previous results.Finally,a simulation example is given to verify the effectiveness and performance of the theoretical result.

Quantized dynamic output feedback control for networked control systems

The problem of the quantized dynamic output feedback controller design for networked control systems is mainly discussed. By using the quantized information of the system measurement output and the control input, a novel networked control system model is described. This model includes many networkinduced features, such as multi-rate sampled-data, quantized signal, time-varying delay and packet dropout. By constructing suitable Lyapunov-Krasovskii functional, a less conservative stabilization criterion is established in terms of linear matrix inequalities. The quantized control strategy involves the updating values of the quantizer parameters μi（i = 1, 2）（μi take on countable sets of values which dependent on the information of the system measurement outputs and the control inputs）. Furthermore, a numerical example is given to illustrate the effectiveness of the proposed method.

Controllable Subspaces of Open Quantum Dynamical Systems

This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.