Distributed control for a class of nonlinear systems based on distributed high-gain observer.

This paper concerns the problem of designing distributed control law for a class nonlinear system in which the measurement outputs of the system are distributed in different subsystems. It leads to a challenge that the states of the original systems cannot be completely reconstructed by any single subsystem. In order to solve this problem, distributed state observers and the distributed observer-based distributed control problem emerges as the times require. However, the distributed observers problem of the nonlinear systems is rarely studied, and the distributed control law formed by distributed nonlinear observers has hardly ever been studied up to now. To this end, this paper develops the distributed high-gain observers for a class of nonlinear systems. Unlike the previous several results, our study has the ability to deal with model uncertainty, and devotes itself to overcoming the problem that the separation principle is not tenable. In addition, based on the state estimate generated by the designed distributed observer, an output feedback control law formed by applying the state estimate is developed. Furthermore, a class of sufficient conditions is proved for guaranteeing the error dynamics of the distributed observer and the state trajectory of the closed-loop system to enter an arbitrary small invariant set around the origin. Finally, the simulation results verify the effectiveness of the proposed method.

Composite Observer-Based Optimal Attitude-Tracking Control With Reinforcement Learning for Hypersonic Vehicles.

This article proposes an observer-based reinforcement learning (RL) control approach to address the optimal attitude-tracking problem and application for hypersonic vehicles in the reentry phase. Due to the unknown uncertainty and nonlinearity caused by parameter perturbation and external disturbance, accurate model information of hypersonic vehicles in the reentry phase is generally unavailable. For this reason, a novel synchronous estimation is proposed to construct a composite observer for hypersonic vehicles, which consists of a neural-network (NN)-based Luenberger-type observer and a synchronous disturbance observer. This solves the identification problem of nonlinear dynamics in the reference control and realizes the estimation of the system state when unknown nonlinear dynamics and unknown disturbance exist at the same time. By synthesizing the information from the composite observer, an RL tracking controller is developed to solve the optimal attitude-tracking control problem. To improve the convergence performance of critic network weights, concurrent learning is employed to replace the traditional persistent excitation condition with a historical experience replay manner. In addition, this article proves that the weight estimation error is bounded when the learning rate satisfies the given sufficient condition. Finally, the numerical simulation demonstrates the effectiveness and superiority of the proposed approaches to attitude-tracking control systems for hypersonic vehicles.

Distributed stochastic model predictive control for systems with stochastic multiplicative uncertainty and chance constraints.

The rapid development of technology and economy has led to the development of chemical processes, large-scale manufacturing equipment, and transportation networks, with their increasing complexity. These large systems are usually composed of many interacting and coupling subsystems. Moreover, the propagation and perturbation of uncertainty make the control design of such systems to be a thorny problem. In this study, for a complex system composed of multiple subsystems suffering from multiplicative uncertainty, not only the individual constraints of each subsystem but also the coupling constraints among them are considered. All the constraints with the probabilistic form are used to characterize the stochastic natures of uncertainty. This paper first establishes a centralized model predictive control scheme by integrating overall system dynamics and chance constraints as a whole. To deal with the chance constraint, based on the concept of multi-step probabilistic invariant set, a condition formulated by a series of linear matrix inequality is designed to guarantee the chance constraint. Stochastic stability can also be guaranteed by the virtue of nonnegative supermartingale property. In this way, instead of solving a non-convex and intractable chance-constrained optimization problem at each moment, a semidefinite programming problem is established so as to be realized online in a rolling manner. Furthermore, to reduce the computational burdens and amount of communication under the centralized framework, a distributed stochastic model predictive control based on a sequential update scheme is designed, where only one subsystem is required to update its plan by executing optimization problem at each time instant. The closed-loop stability in stochastic sense and recursive feasibility are ensured. A numerical example is employed to illustrate the efficacy and validity of the presented algorithm in this study.