This article addresses the fully distributed (FD) output feedback full states consensus tracking problem for high-order multiagent systems with general nonlinearities under the directed graph. In each agent, a novel FD estimator is established to estimate the leader’s states, which only needs three variables’ information from each parent agent without considering their orders. Meanwhile, it is independent of the graph’s scale and does not rely on any global information. Then, instead of the backstepping method and based on the constructed compensator, an output-dependent dynamic gain method is used to design the FD output feedback protocol avoiding the repeated derivatives of the nonlinearities. Based on a new lemma, it is proved that using the proposed FD protocol, global full states consensus stability can be guaranteed and the consensus error can converge to zero asymptotically. The proposed method can not only achieve the consensus in FD fashion but also extremely relax the conditions on nonlinearities which satisfy the local Lipschitz condition with a more general incremental rate containing output and compensator states information. Finally, a numerical example is given to verify the effectiveness of the proposed method.

Prismatic waves carry steeply dipping structural information that primaries cannot contain. Therefore, prismatic waves are separately used in some migration methods to improve the illumination and imaging effect on steeply dipping structures. Least-squares reverse time migration of prismatic waves (LSRTM-P) can produce high-resolution images with improved steeply dipping structures. However, viscoelasticity exists widely on the Earth, which poses great difficulty for imaging. The effect of attenuation on prismatic waves is difficult to be compensated when conducting LSRTM-P because prismatic waves have three propagation paths. To overcome this problem, a$Q$-compensated LSRTM ($Q$-LSRTM)-P method is proposed by deriving$Q$-compensated forward-propagated operators and backward-propagated adjoint operators of prismatic waves, which compensates for$Q$attenuation along all the three propagation paths of prismatic waves. The proposed$Q$-LSRTM-P is conducted to update the image after applying the conventional$Q$-LSRTM. Besides, the proposed method can be adapted to the irregular surface media. Numerical examples on two synthetic and a field datasets verify that our method can produce better imaging results with clearer steeply dipping structures, higher signal-to-noise ratio (SNR), higher resolution, and more balanced amplitude than noncompensated LSRTM-P and conventional$Q$-LSRTM.

This paper addresses an optimization issue that the Nelder-Mead (NM) method is implemented to optimize initial database which is used to design Database-Driven (DD) proportional-integral-derivative (PID) controller. As it is well recognized that PID controller, which is considerable applied in industrial processes, is adopted and the parameters tuning are based on DD approach without requirement of model information. The existing DD approach needs to collect a batch of closed-loop operation data, which is used to generate initial database. It is still an open problem that the way of processing data involved in initial database. The proposed scheme considers the NM method, as a free derivative method, to optimize initial database. However, in the evaluation stage, the NM method requires the model information to calculate the output aiming at comparing objective function, therefore, a better vertex can be computed. The fictitious reference iterative tuning (FRIT) is introduced in the proposed scheme to generate fictitious output based on the fictitious reference which is obtained based on input and output data stored in initial database. As a result, the optimized initial database is accomplished, based on which the PID controller then can be designed in Just-in-Time manner. In addition, the efficiency of the proposed scheme is illustrated with a numerical example.

As a nonlinear control algorithm, database-driven PID control (DD-PID) approach has been proposed to learn PID parameters based on a database. This method is based on a strategy in which PID parameters are determined based on neighboring data extracted based on the similarity between the query (current input/output data) and the information vector contained in the database. Since sorting operation is required in extracting the neighbor data, it is impossible to finish the calculation within a certain sampling interval for systems with fast response time, which is one of the hindrances in industrial applications. In addition, the DD-PID requires a large amount of storage memory in the database in order to obtain the desired control performance. On the other hand, one of the neural networks is the cerebellar model articulation controller (CMAC). It is a table-referenced adaptive learning controller. The major advantage of this method lies in the reduction of memory and computational load. This paper discusses a realization of the DD-PID by effectively utilizing the advantage of the CMAC.

This paper addresses a regulation problem of non-linear systems via database-driven nonlinear generalized predictive controller without model information. In industrial processes, lots of controlled systems with unknown time-delay and strong nonlinearity, are difficult to be handled in terms of control performance. Advanced controllers are considered to be established to deal with those nonlinear systems. In several design methods, advanced controllers are designed based on model information. However, it is time- and cost-consuming to identify the model of controlled systems, and requires regular maintenance to maintain acceptable performance. The database-driven approach has been attracted attentions to tackle those issues without model information. The controller can be designed and tuned only based on data, which is the main feature of this approach. Besides, the database-driven approach can deal with strong nonlinear systems. Additionally, the Generalized Predictive Control (GPC) is one of predictive controllers and widely applied in industrial processes. The GPC controller is developed based on multi-step prediction, therefore, it is effective to those systems subject to unknown or time-delay. As a result, a nonlinear GPC controller in the proposed scheme inherits the advantage of GPC, and is also tuned by the database-driven approach. The effectiveness and benefits of the proposed scheme are demonstrated through a numerical simulation and a comparative study.

This paper addresses a design problem of a Proportional-Integral-Derivative (PID) controller with new adaptive updating rule based on Reinforcement Learning (RL) approach for nonlinear systems. A new design scheme that RL can be used to complement the conventional control technology PID is presented. In this study, a single Radial Basis Function (RBF) network is introduced to calculate the control policy function of Actor and the value function of Critic simultaneously. Regarding to the PID controller structure, the inputs of RBF network are system error, the difference of output as well as the second order difference of output, and they are defined as system states. The Temporal Difference (TD) error in this study is newly defined and involves the error criterion which is defined by the difference between one-step ahead prediction and the reference value. The gradient descent method is adopted based on TD error performance index, then the updating rules can be obtained. Therefore, the network weights and the kernel function can be calculated in an adaptive manner. Finally, the numerical simulations are conducted in nonlinear systems to illustrate the efficiency and robustness of the proposed scheme.