Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE Using Neurodynamic Programming

Multistability and Robustness of Competitive Neural Networks With Time-Varying Delays

This article is devoted to analyzing the multistability and robustness of competitive neural networks (NNs) with time-varying delays. Based on the geometrical structure of activation functions, some sufficient conditions are proposed to ascertain the coexistence of equilibrium points, of them are locally exponentially stable, where represents a dimension of system and is the parameter related to activation functions. The derived stability results not only involve exponential stability but also include power stability and logarithmical stability. In addition, the robustness of stable equilibrium points is discussed in the presence of perturbations. Compared with previous papers, the conclusions proposed in this article are easy to verify and enrich the existing stability theories of competitive NNs. Finally, numerical examples are provided to support theoretical results.

Observer-Based Boundary Stabilization of Coupled Semilinear Reaction-Diffusion Neural Networks With Spatially Varying Coefficients via Event-Triggered Controller

The aim of this article is to propose an observer-based event-triggered Robin boundary control strategy for the exponential stabilization of the coupled semilinear reaction-diffusion neural networks with spatially varying coefficients. Toward this aim, we design an observer to estimate the value of system states by using some of these system values as the available measurement. An observer-based event-triggered boundary stabilizer is then presented to exponentially stabilize the considered systems with the Zeno behavior being excluded. Throughout this article, the main used method is backstepping, which yields an explicit expression of the control formulae. Moreover, we see that the proposed event-triggered boundary control scheme can ensure the desired level of control performance with fewer control law updates. A numerical example is finally given to illustrate the effectiveness of our proposed method.

Concurrent Learning Robust Adaptive Fault Tolerant Boundary Regulation of Hyperbolic Distributed Parameter Systems

This article develops a robust adaptive boundary output regulation approach for a class of complex anticollocated hyperbolic partial differential equations subjected to multiplicative unknown faults in both the boundary sensor and actuator. The regulator design is based on the internal model principle, which amounts to stabilize a coupled cascade system, which consists of a finite-dimensional internal model driven by a hyperbolic distributed parameter system (DPS). To this end, a systematic sliding mode equipped with a backstepping approach is developed such that the robust state feedback control can be realized. Moreover, since the available information is a faulty boundary measurement at the right side point, state estimation is required. However, due to the presence of boundary unknown faults, we need to solve an issue of joint fault-state estimation. Restrictive persistent excitation conditions are usually required to guarantee the exact estimation of faults but are unrealistic in practice. To this end, a novel concurrent learning (CL) adaptive observer is proposed so that exponential convergence is obtained. It is the first time that the spirit of CL is introduced to the field of DPSs. Consequently, the observer-based adaptive boundary fault tolerant control scheme is developed, and rigorous theoretical analysis is given such that the exponential output regulation can be achieved. Finally, the effectiveness of the proposed methodology is demonstrated via comparative simulations.

ADP-Based Event-Triggered Constrained Optimal Control on Spatiotemporal Process: Application to Temperature Field in Roller Kiln

The precise control of the spatiotemporal process in a roller kiln is crucial in the production of Ni-Co-Mn layered cathode material of lithium-ion batteries. Since the product is extremely sensitive to temperature distribution, temperature field control is of great significance. In this article, an event-triggered optimal control (ETOC) method with input constraints for the temperature field is proposed, which takes up an important position in reducing the communication and computation costs. A nonquadratic cost function is adopted to describe the system performance with input constraints. First, we present the problem description of the temperature field event-triggered control, where this field is described by a partial differential equation (PDE). Then, the event-triggered condition is designed according to the information of system states and control inputs. On this basis, a framework of the event-triggered adaptive dynamic programming (ETADP) method that is based on the model reduction technology is proposed for the PDE system. A critic network is used to approach the optimal performance index by a neural network (NN) together with that an actor network is used to optimize the control strategy. Furthermore, an upper bound of the performance index and a lower bound of interexecution times, as well as the stabilities of the impulsive dynamic system and the closed-loop PDE system, are also proved. Simulation verification demonstrates the effectiveness of the proposed method.

Adaptive Dynamic Programming-Based Cooperative Motion/Force Control for Modular Reconfigurable Manipulators: A Joint Task Assignment Approach

This article develops a cooperative motion/force control (CMFC) scheme based on adaptive dynamic programming (ADP) for modular reconfigurable manipulators (MRMs) with the joint task assignment approach. By separating terms depending on local variables only, the dynamic model of the entire MRM system can be regarded as a set of joint modules interconnected by coupling torque. In addition, the Jacobian matrix, which reflects the interaction force of the MRM end-effector, can be mapped into each joint. Using this approach, both the motion and force tasks on the end-effector of the entire MRM system can be assigned to each joint module cooperatively. Then, by substituting the actual states of coupled joint modules with their desired ones, the norm-boundedness assumption on the interconnection of joint module can be relaxed. By using the measured input-output data of each joint module, a neural network (NN)-based robust decentralized observer, which guarantees the observation error to be asymptotically stable is established. An improved local value function is constructed for each joint module to reflect the interconnection. Then, the local Hamilton-Jacobi-Bellman equation is solved by constructing a local critic NN with a nested learning structure. Hereafter, the ADP-based CMFC is obtained by the assistance of force feedback compensation. Based on the Lyapunov stability analysis, the closed-loop MRM system is guaranteed to be uniformly ultimately bounded under the present ADP-based CMFC scheme. The simulation on a two-degree of freedom MRM system demonstrates the effectiveness of the present control approach.

Multistability of Delayed Hybrid Impulsive Neural Networks With Application to Associative Memories

The important topic of multistability of continuous-and discrete-time neural network (NN) models has been investigated rather extensively. Concerning the design of associative memories, multistability of delayed hybrid NNs is studied in this paper with an emphasis on the impulse effects. Arising from the spiking phenomenon in biological networks, impulsive NNs provide an efficient model for synaptic interconnections among neurons. Using state-space decomposition, the coexistence of multiple equilibria of hybrid impulsive NNs is analyzed. Multistability criteria are then established regrading delayed hybrid impulsive neurodynamics, for which both the impulse effects on the convergence rate and the basins of attraction of the equilibria are discussed. Illustrative examples are given to verify the theoretical results and demonstrate an application to the design of associative memories. It is shown by an experimental example that delayed hybrid impulsive NNs have the advantages of high storage capacity and high fault tolerance when used for associative memories.

Boundary Control of 2-D Burgers' PDE: An Adaptive Dynamic Programming Approach

In this paper, an adaptive dynamic programming-based near optimal boundary controller is developed for partial differential equations (PDEs) modeled by the uncertain Burgers' equation under Neumann boundary condition in 2-D. Initially, Hamilton-Jacobi-Bellman equation is derived in infinite-dimensional space. Subsequently, a novel neural network (NN) identifier is introduced to approximate the nonlinear dynamics in the 2-D PDE. The optimal control input is derived by online estimation of the value function through an additional NN-based forward-in-time estimation and approximated dynamic model. Novel update laws are developed for estimation of the identifier and value function online. The designed control policy can be applied using a finite number of actuators at the boundaries. Local ultimate boundedness of the closed-loop system is studied in detail using Lyapunov theory. Simulation results confirm the optimizing performance of the proposed controller on an unstable 2-D Burgers' equation.