This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems. Unlike existing optimal state feedback control, the control input of the optimal parallel control is introduced into the feedback system. However, due to the introduction of control input into the feedback system, the optimal state feedback control methods can not be applied directly. To address this problem, an augmented system and an augmented performance index function are proposed firstly. Thus, the general nonlinear system is transformed into an affine nonlinear system. The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically. It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function. Moreover, an adaptive dynamic programming &#x0028 ADP &#x0029 technique is utilized to implement the optimal parallel tracking control using a critic neural network &#x0028 NN &#x0029 to approximate the value function online. The stability analysis of the closed-loop system is performed using the Lyapunov theory, and the tracking error and NN weights errors are uniformly ultimately bounded &#x0028 UUB &#x0029 . Also, the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals. Finally, the effectiveness of the developed optimal parallel control method is verified in two cases.

Parallel control for optimal tracking via adaptive dynamic programming

Briefing: An investigation and outline of MetaControl and DeControl in Metaverses for control intelligence and knowledge automation are presented. Prescriptive control with prescriptive knowledge and parallel philosophy is proposed as the starting point for the new control philosophy and technology, especially for computational control of metasystems in cyber-physical-social systems. We argue that circular causality, the generalized feedback mechanism for complex and purposive systems, should be adapted as the fundamental principle for control and management of metasystems with metacomplexity in metaverses. Particularly, an interdisciplinary approach is suggested for MetaControl and DeControl as a new form of intelligent control based on five control metaverses: Meta Verses, MultiVerses, InterVerses, TransVerse, and Deep Verses. 

https://ieeexplore.ieee.org/ielx7/6570654/9915488/09915522.pdf

The DAO to MetaControl for MetaSystems in Metaverses: The System of Parallel Control Systems for Knowledge Automation and Control Intelligence in CPSS

This paper investigates the consensus problem for linear multi-agent systems with the heterogeneous disturbances generated by the Brown motion. Its main contribution is that a control scheme is designed to achieve the dynamic consensus for the multi-agent systems in directed topology interfered by stochastic noise. In traditional ways, the coupling weights depending on the communication structure are static. A new distributed controller is designed based on Riccati inequalities, while updating the coupling weights associated with the gain matrix by state errors between adjacent agents. By introducing time-varying coupling weights into this novel control law, the state errors between leader and followers asymptotically converge to the minimum value utilizing the local interaction. Through the Lyapunov directed method and Ito formula, the stability of the closed-loop system with the proposed control law is analyzed. Two simulation results conducted by the new and traditional schemes are presented to demonstrate the effectiveness and advantage of the developed control method.

Consensus Control of Leader-Following Multi-Agent Systems in Directed Topology With Heterogeneous Disturbances

A novel adaptive dynamic programming based on tracking error for nonlinear discrete-time systems

This article is concerned with a new generalized actor-critic learning (GACL) optimal control method. It aims at the optimal energy control and management for smart home systems, which is expected to minimize the consumption cost for home users. In the present GACL optimal control method, it is the first time that three iteration processes, which are global iteration, local iteration, and interior iteration, respectively, are established to obtain the optimal energy control law. The main contribution of the developed method is to establish a common iteration structure for both value and policy iterations in adaptive dynamic programming based on a control law sequence in each iteration for periodic time-varying systems, instead of a single control law, and simultaneously accelerates the convergence rate. The monotonicity, convergence, and optimality of the iterative value function for the GACL optimal control method are proven. Finally, numerical results and comparisons are displayed to show the superiority of the developed method.

Generalized Actor-Critic Learning Optimal Control in Smart Home Energy Management

In this paper, a new parallel controller is developed for continuous-time linear systems The main contribution of the method is to establish a new parallel control law, where both state and control are considered as the input The structure of the parallel control is provided, and the relationship between the parallel control and traditional feedback controls is presented Considering the situations that the systems are controllable and incompletely controllable, the properties of the parallel control law are analyzed The parallel controller design algorithms are given under the conditions that the systems are controllable and incompletely controllable Finally, numerical simulations are carried out to demonstrate the effectiveness and applicability of the present method

Parallel control for continuous-time linear systems: A case study

In this article, a novel distributed policy iteration algorithm is established for infinite horizon optimal control problems of continuous-time nonlinear systems. In each iteration of the developed distributed policy iteration algorithm, only one controller’s control law is updated and the other controllers’ control laws remain unchanged. The main contribution of the present algorithm is to improve the iterative control law one by one, instead of updating all the control laws in each iteration of the traditional policy iteration algorithms, which effectively releases the computational burden in each iteration. The properties of distributed policy iteration algorithm for continuous-time nonlinear systems are analyzed. The admissibility of the present methods has also been analyzed. Monotonicity, convergence, and optimality have been discussed, which show that the iterative value function is nonincreasingly convergent to the solution of the Hamilton–Jacobi–Bellman equation. Finally, numerical simulations are conducted to illustrate the effectiveness of the proposed method.

Continuous-Time Distributed Policy Iteration for Multicontroller Nonlinear Systems

This article presents a novel data-based fault-tolerant control method for multicontroller linear systems via distributed policy iteration. The traditional fault-tolerant control methods based on policy iteration may cause a huge-computational burden under the situation of high-dimension control laws. In order to solve this problem, a novel distributed policy iteration method is presented, where only one iterative control law is updated in each iteration, to realize the fault-tolerant control of multicontroller linear systems. The main contributions can be highlighted as follows: 1) a novel data-based distributed policy iteration method is presented to reduce the computational burden; 2) the fault-tolerant control method is presented via designing fault compensators; and 3) the developed data-based method only requires the partial system information. First, the model-based fault-tolerant control via distributed policy iteration and fault compensation is provided. Based on the model-based method, a data-based fault-tolerant control method is presented. Finally, numerical experiments are given to show the performance of the presented method.

A Novel Data-Based Fault-Tolerant Control Method for Multicontroller Linear Systems via Distributed Policy Iteration

In this paper, optimal control problems with constraints on summation of auxiliary utility function are called constrained cost optimal control problems and a constrained cost policy iteration adaptive dynamic programming (ADP) algorithm is developed to solve constrained cost optimal control problems for discrete-time nonlinear systems. A convergence analysis is developed to guarantee that the iterative value functions nonin-creasingly convergent to the approximate optimal value function. It is also proven that any of the iterative control policy is feasible and can stabilize the nonlinear systems. Finally, a simulation example is given to illustrate the performance of the developed constrained cost policy iteration algorithm.

Policy Iteration Algorithm for Constrained Cost Optimal Control of Discrete-Time Nonlinear System

This paper presents a continuous-time linear parallel control by modeling the derivative of system control with respect to time The framework and properties of continuous-time linear parallel control are first presented Then, considering the controllability, the pole assignment theorems will be analyzed Finally, two examples show the correctness of continuous-time linear parallel control

Hongyang Li

Papers

Parallel control for continuous-time linear systems: A case study

Continuous-Time Distributed Policy Iteration for Multicontroller Nonlinear Systems

A Novel Data-Based Fault-Tolerant Control Method for Multicontroller Linear Systems via Distributed Policy Iteration

Policy Iteration Algorithm for Constrained Cost Optimal Control of Discrete-Time Nonlinear System

Continuous-Time Linear Parallel Control