Decentralized adaptive tracking control scheme for nonlinear large-scale interconnected systems via adaptive dynamic programming

Robust Adaptive Control for a Small Unmanned Helicopter Using Reinforcement Learning

This article presents a novel adaptive controller for a small-size unmanned helicopter using the reinforcement learning (RL) control methodology. The helicopter is subject to system uncertainties and unknown external disturbances. The dynamic unmodeling uncertainties of the system are estimated online by the actor network, and the tracking performance function is optimized via the critic network. The estimation error of the actor-critic network and the external unknown disturbances are compensated via the nonlinear robust component based on the sliding mode control method. The stability of the closed-loop system and the asymptotic convergence of the attitude tracking error are proved via the Lyapunov-based stability analysis. Finally, real-time experiments are performed on a helicopter control testbed. The experimental results show that the proposed controller achieves good control performance.

Decentralized Neurocontroller Design With Critic Learning for Nonlinear-Interconnected Systems

We consider the decentralized control problem of a class of continuous-time nonlinear systems with mismatched interconnections. Initially, with the discounted cost functions being introduced to auxiliary subsystems, we have the decentralized control problem converted into a set of optimal control problems. To derive solutions to these optimal control problems, we first present the related Hamilton-Jacobi-Bellman equations (HJBEs). Then, we develop a novel critic learning method to solve these HJBEs. To implement the newly developed critic learning approach, we only use critic neural networks (NNs) and tune their weight vectors via the combination of a modified gradient descent method and concurrent learning. By using the present critic learning method, we not only remove the restriction of initial admissible control but also relax the persistence-of-excitation condition. After that, we employ Lyapunov's direct method to demonstrate that the critic NNs' weight estimation error and the states of closed-loop auxiliary systems are stable in the sense of uniform ultimate boundedness. Finally, we separately provide a nonlinear-interconnected plant and an unstable interconnected power system to validate the present critic learning approach.

Decentralized Event-Driven Constrained Control Using Adaptive Critic Designs

We study the decentralized event-driven control problem of nonlinear dynamical systems with mismatched interconnections and asymmetric input constraints. To begin with, by introducing a discounted cost function for each auxiliary subsystem, we transform the decentralized event-driven constrained control problem into a group of nonlinear H₂ -constrained optimal control problems. Then, we develop the event-driven Hamilton-Jacobi-Bellman equations (ED-HJBEs), which arise in the nonlinear H₂ -constrained optimal control problems. Meanwhile, we demonstrate that all the solutions of the ED-HJBEs together keep the overall system stable in the sense of uniform ultimate boundedness (UUB). To solve the ED-HJBEs, we build a critic-only architecture under the framework of adaptive critic designs. The architecture only employs critic neural networks and updates their weight vectors via the gradient descent method. After that, based on the Lyapunov approach, we prove that the UUB stability of all signals in the closed-loop auxiliary subsystems is assured. Finally, simulations of an illustrated nonlinear interconnected plant are provided to validate the present designs.

Dynamic Event-Sampled Control of Interconnected Nonlinear Systems Using Reinforcement Learning

We develop a decentralized dynamic event-based control strategy for nonlinear systems subject to matched interconnections. To begin with, we introduce a dynamic event-based sampling mechanism, which relies on the system's states and the variables generated by time-based differential equations. Then, we prove that the decentralized event-based controller for the whole system is composed of all the optimal event-based control policies of nominal subsystems. To derive these optimal event-based control policies, we design a critic-only architecture to solve the related event-based Hamilton-Jacobi-Bellman equations in the reinforcement learning framework. The implementation of such an architecture uses only critic neural networks (NNs) with their weight vectors being updated through the gradient descent method together with concurrent learning. After that, we demonstrate that the asymptotic stability of closed-loop nominal subsystems and the uniformly ultimate boundedness stability of critic NNs' weight estimation errors are guaranteed by using Lyapunov's approach. Finally, we provide simulations of a matched nonlinear-interconnected plant to validate the present theoretical claims.

Approximate Dynamic Programming for Nonlinear-Constrained Optimizations

In this paper, we study the constrained optimization problem of a class of uncertain nonlinear interconnected systems. First, we prove that the solution of the constrained optimization problem can be obtained through solving an array of optimal control problems of constrained auxiliary subsystems. Then, under the framework of approximate dynamic programming, we present a simultaneous policy iteration (SPI) algorithm to solve the Hamilton-Jacobi-Bellman equations corresponding to the constrained auxiliary subsystems. By building an equivalence relationship, we demonstrate the convergence of the SPI algorithm. Meanwhile, we implement the SPI algorithm via an actor-critic structure, where actor networks are used to approximate optimal control policies and critic networks are applied to estimate optimal value functions. By using the least squares method and the Monte Carlo integration technique together, we are able to determine the weight vectors of actor and critic networks. Finally, we validate the developed control method through the simulation of a nonlinear interconnected plant.

Decentralized Event-Triggered Online Adaptive Control of Unknown Large-Scale Systems Over Wireless Communication Networks

In this article, a novel online decentralized event-triggered control scheme is proposed for a class of nonlinear interconnected large-scale systems subject to unknown internal system dynamics and interconnected terms. First, by designing a neural network-based identifier, the unknown internal dynamics of the interconnected systems is reconstructed. Then, the adaptive critic design method is used to learn the approximate optimal control policies in the context of event-triggered mechanism. Specifically, the event-based control processes of different subsystems are independent, asynchronous, and decentralized. That is, the decentralized event-triggering conditions and the controllers only rely on the local state information of the corresponding subsystems, which avoids the transmissions of the state information between the subsystems over the wireless communication networks. Then, with the help of Lyapunov's theorem, the states of the developed closed-loop control system and the critic weight estimation errors are proved to be uniformly ultimately bounded. Finally, the effectiveness and applicability of the event-based control method are verified by an illustrative numerical example and a practical example.

Learning-Based Adaptive Attitude Control of Spacecraft Formation With Guaranteed Prescribed Performance

This paper investigates a novel leader-following attitude control approach for spacecraft formation under the preassigned two-layer performance with consideration of unknown inertial parameters, external disturbance torque, and unmodeled uncertainty. First, two-layer prescribed performance is preselected for both the attitude angular and angular velocity tracking errors. Subsequently, a distributed two-layer performance controller is devised, which can guarantee that all the involved closed-loop signals are uniformly ultimately bounded. In order to tackle the defect of statically two-layer performance controller, learning-based control strategy is introduced to serve as an adaptive supplementary controller based on adaptive dynamic programming technique. This enhances the adaptiveness of the statically two-layer performance controller with respect to unexpected uncertainty dramatically, without any prior knowledge of the inertial information. Furthermore, by employing the robustly positively invariant theory, the input-to-state stability is rigorously proven under the designed learning-based distributed controller. Finally, two groups of simulation examples are organized to validate the feasibility and effectiveness of the proposed distributed control approach.