Adaptive Critic for Event-Triggered Unknown Nonlinear Optimal Tracking Design With Wastewater Treatment Applications

Advanced Optimal Tracking Control With Stability Guarantee via Novel Value Learning Formulation

In this article, to solve the optimal tracking control problem (OTCP) for discrete-time (DT) nonlinear systems, general value iteration (GVI) scheme and online value iteration (VI) algorithms with novel value function are discussed. First, the disadvantage of the traditional value function for the OTCP is presented and the novel value function is introduced. Second, we analyze the monotonicity and convergence of GVI and establish the admissibility condition of GVI to evaluate the admissibility of the current iterative control. Note that a novel approach is introduced to analyze the admissibility. Third, based on the attraction domain, improved control policies with online VI can be obtained by judging the location of the current tracking error and reference point. Finally, the stability of the online VI-based control system is guaranteed. Besides, we provide two simulation examples to show the performance of the proposed methods.

Event-Triggered Constrained Optimal Control for Organic Rankine Cycle Systems via Safe Reinforcement Learning

The organic Rankine cycle (ORC) is an effective application for converting low-grade heat sources into power and is crucial for environmentally friendly production and energy recovery. However, the inherent complexity of the mechanism, its strong and unidentified nonlinearity, and the presence of control constraints severely impair the design of its optimal controller. To solve these issues, this study provides a novel event-triggered (ET) constrained optimal control approach for the ORC systems based on a safe reinforcement learning technique to find the optimal control law. Instead of employing the usual non-quadratic integral form to solve the control-limited optimal control problems, a constraint handling strategy based on a relaxed weighted barrier function (BF) technique is proposed. By adding the BF terms to the original value function, a modified value iteration algorithm is developed to make the control input solutions that tend to violate the constraints be pushed back and maintained in their safe sets. In addition, the ET mechanism proposed in this article is critically required for the ORC systems, and it can significantly reduce the computational load. The combination of these two techniques allows the ORC systems to achieve set-point tracking control and satisfy the control restrictions. The proposed approach is conducted based on a heuristic dynamic programming framework with three neural networks (NNs) involved. The safety and convergence of the proposed approach and the stability of the closed-loop system are analyzed. Simulation results and comparisons are presented to demonstrate its effectiveness.

Event-Based Adaptive NN Fixed-Time Cooperative Formation for Multiagent Systems

This article focuses on the fixed-time formation control problem for nonlinear multiagent systems (MASs) with dynamic uncertainties and limited communication resources. Under the framework of the backstepping method, a time-varying formation function is introduced in the controller design. To attain the prescribed transient and steady-state performance of MASs, a fixed-time prescribed performance function (FTPPF) is designed and the further coordinate transformation addressing the zero equilibrium point problem is removed. To achieve better approximating performance, a neural network (NN)-based composite dynamic surface control (CDSC) strategy is proposed, where the CDSC scheme is consisted of prediction errors and serial-parallel estimation models. According to the signals generated by the estimation models, disturbance observers are established to overcome the difficulty from approximating errors and mismatched disturbances. Moreover, an improved dynamic event-triggered mechanism and varying threshold parameters are constructed to reduce the signal transmission frequency. Via the Lyapunov stability theory, all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, the simulation results verify the effectiveness of the developed CDSC strategy.

Optimal H∞ tracking control of nonlinear systems with zero-equilibrium-free via novel adaptive critic designs

In this paper, a novel adaptive critic control method is designed to solve an optimal H_∞ tracking control problem for continuous nonlinear systems with nonzero equilibrium based on adaptive dynamic programming (ADP). To guarantee the finiteness of a cost function, traditional methods generally assume that the controlled system has a zero equilibrium point, which is not true in practical systems. In order to overcome such obstacle and realize H_∞ optimal tracking control, this paper proposes a novel cost function design with respect to disturbance, tracking error and the derivative of tracking error. Based on the designed cost function, the H_∞ control problem is formulated as two-player zero-sum differential games, and then a policy iteration (PI) algorithm is proposed to solve the corresponding Hamilton-Jacobi-Isaacs (HJI) equation. In order to obtain the online solution to the HJI equation, a single-critic neural network structure based on PI algorithm is established to learn the optimal control policy and the worst-case disturbance law. It is worth mentioning that the proposed adaptive critic control method can simplify the controller design process when the equilibrium of the systems is not zero. Finally, simulations are conducted to evaluate the tracking performance of the proposed control methods.

Evolving and Incremental Value Iteration Schemes for Nonlinear Discrete-Time Zero-Sum Games

In this article, evolving and incremental value iteration (VI) frameworks are constructed to address the discrete-time zero-sum game problem. First, the evolving scheme means that the closed-loop system is regulated by using the evolving policy pair. During the control stage, we are committed to establishing the stability criterion in order to guarantee the availability of evolving policy pairs. Second, a novel incremental VI algorithm, which takes the historical information of the iterative process into account, is developed to solve the regulation and tracking problems for the nonlinear zero-sum game. Via introducing different incremental factors, it is highlighted that we can adjust the convergence rate of the iterative cost function sequence. Finally, two simulation examples, including linear and nonlinear systems, are conducted to demonstrate the performance and the validity of the proposed evolving and incremental VI schemes.

Neural-Network-Based Adaptive Event-Triggered Asymptotically Consensus Tracking Control for Nonlinear Nonstrict-Feedback MASs: An Improved Dynamic Surface Approach

In this article, the asymptotic tracking control problem for a class of nonlinear multi-agent systems (MASs) is researched by the combination of radial basis function neural networks (RBF NNs) and an improved dynamic surface control (DSC) technology. It's important to emphasize that the MASs studied in this article are nonlinear and nonstrict-feedback systems, where the nonlinear functions are unknown. In order to satisfy the requirement that all items in the controller must be available, the unknown nonlinearities in the system are flexibly approximated by utilizing RBF NNs technique. Moreover, the issue of ``complexity explosion'' in the backstepping procedure is handled by improving the traditional DSC technology, and meanwhile, the influences of the boundary layers caused by the filters in the DSC procedure are eliminated skillfully through the compensation terms. In addition, the relative threshold event-triggered strategy is developed for the designed controllers to reduce the waste of communication resources, where Zeno phenomenon is successfully avoided. It is observed that the new presented control strategy ensures that all the closed-loop systems variables are uniformly ultimately bounded (UUB), and furthermore all the outputs of followers are able to track the output of the leader with zero tracking errors. Finally, the simulation results are presented to show the effectiveness of the obtained design scheme.