Intelligent optimal tracking with asymmetric constraints of a nonlinear wastewater treatment system

This article considers the robust tracking control problem of uncertain nonlinear systems with asymmetric input constraints. Initially, the tracking error dynamics and the desired trajectory dynamics are constructed as an augmented system. Then, with a discounted value function being introduced for the nominal augmented system, the original tracking control problem is transformed into a constrained optimal control problem. To solve the constrained optimal control problem, its related Hamilton–Jacobi–Bellman equation (HJBE) is developed. After that, a critic approximator is constructed to solve the HJBE in the reinforcement learning framework. To tune the parameters used in the critic approximator, a novel concurrent learning technique is introduced, which could remove the persistence of excitation condition. Moreover, the uniform ultimate boundedness of the tracking error and the parameters' estimation error of the critic approximator is assured via the Lyapunov's approach. Finally, a spring‐mass‐damper mechanical system and a robot manipulator system are given to validate the theoretical claims.

Section: Background and Motivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust tracking control with reinforcement learning for nonlinear‐constrained systems

Tang

Hong

2022

“…Adaptive dynamic programming (ADP) is a combination of dynamic programming and the actor-critic structure in reinforcement learning, which has been extensively adopted in the field of intelligent control and also paid great attentions. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] It is a powerful technique to research the optimal control of nonlinear systems, which can constantly approach the optimal solution of the HJB equation to achieve the purpose of optimal control.…”

Section: Introductionmentioning

confidence: 99%

Value‐iteration‐based affine nonlinear optimal control involving admissibility discussion

Wang

Ren

2022

Self Cite

In this article, the admissibility analysis of the value‐iteration‐based control policy is investigated for affine nonlinear dynamics. First, a series of admissible control criteria are discussed for nonlinear and linear systems. With the help of these criteria, it is more convenient to determine whether an iterative control policy is admissible or not compared with the previous work. Second, once the iterative control policy is established to be admissible by the criteria, the stability of the closed‐loop systems using the control law can be guaranteed. In addition, under certain conditions, the admissibility and asymptotic stability similar to policy iteration can be obtained. Finally, two numerical examples with the physical background are afforded to validate the effectiveness of presented theoretical results.

“…12,13 As stated in the survey, 14 ADP algorithms in terms of iteration can be divided into two categories: value iteration 15,16 and policy iteration. 17,18 So far, a large number of results based on ADP have been obtained to solve various control problems, such as optimal control with constrained control inputs, [19][20][21] optimal tracking control, [22][23][24] networked control, 25 robust control, 26,27 and event-triggered control, [28][29][30] which strongly show the applicability and great potential of ADP algorithms. In Reference 16, the convergence of the adaptive critic algorithm was proven and the algorithm procedure was given.…”

Section: Introductionmentioning

confidence: 99%

“…By constructing an augmented system and the discounted cost function, an off‐policy RL approach was developed to handle the

{H}_{\infty }

tracking problem in Reference 24. In order to ensure the excellent performance of wastewater treatment processes, the symmetric and asymmetric constrained control input based on ADP algorithms were studied in References 20 and 21, respectively. In this article, we can obtain the satisfying numerical solution of the unknown nonlinear dynamics with multi‐player nonzero‐sum game by using the adaptive critic method.…”

Section: Introductionmentioning

confidence: 99%

Multi‐event‐triggered adaptive critic control with guaranteed cost for discrete‐time nonlinear nonzero‐sum games

Wang

Qiao

2022

Self Cite

In this article, a new event‐based adaptive critic algorithm with multiple triggering conditions is investigated to address multi‐player nonzero‐sum game problems for discrete‐time nonlinear dynamics. In order to improve resource utilization while ensure mutual independence among players, the corresponding novel triggering conditions are designed for each player. The corresponding control input is updated only when the relevant triggering condition is violated. It is emphasized that these triggering conditions are established based on the iteration of the time‐triggered mechanism. Then, according to the setting triggering conditions, we prove that the real cost function possesses a predetermined upper bound, which realizes the cost guarantee of the controlled system. Additionally, the multi‐player closed‐loop system is proved to be asymptotically stable and the multi‐event‐triggered control method is implemented by constructing three kinds of neural networks. Finally, the effectiveness of the developed multi‐event‐triggered control approach is verified through conducting two simulation examples.