Decentralized adaptive neural network control of interconnected nonlinear dynamical systems with application to power system

Traditional nonlinear techniques cannot be directly applicable to control large scale interconnected nonlinear dynamic systems due their sheer size and unavailability of system dynamics. Therefore, in this dissertation, the decentralized adaptive neural network (NN) control of a class of nonlinear interconnected dynamic systems is introduced and its application to power systems is presented in the form of six papers. In the first paper, a new nonlinear dynamical representation in the form of a large scale interconnected system for a power network free of algebraic equations with multiple UPFCs as nonlinear controllers is presented. Then, oscillation damping for UPFCs using adaptive NN control is discussed by assuming that the system dynamics are known. Subsequently, the dynamic surface control (DSC) framework is proposed in continuous-time not only to overcome the need for the subsystem dynamics and interconnection terms, but also to relax the explosion of complexity problem normally observed in traditional backstepping. The application of DSC-based decentralized control of power system with excitation control is shown in the third paper. On the other hand, a novel adaptive NN-based decentralized controller for a class of interconnected discrete-time systems with unknown subsystem and interconnection dynamics is introduced since discrete-time is preferred for implementation. The application of the decentralized controller is shown on a power network. Next, a near optimal decentralized discrete-time controller is introduced in the fifth paper for such systems in affine form whereas the sixth paper proposes a method for obtaining the L2-gain near optimal control while keeping a tradeoff between accuracy and computational complexity. Lyapunov theory is employed to assess the stability of the controllers --Abstract, page iv

DISCRETE-TIME ADAPTIVE CONTROL ALGORITHMS FOR REJECTION OF SINUSOIDAL DISTURBANCES

We present new adaptive control algorithms that address the problem of rejecting sinusoids with known frequencies that act on an unknown asymptotically stable linear time-invariant system. To achieve asymptotic disturbance rejection, adaptive control algorithms of this dissertation rely on limited or no system model information. These algorithms are developed in discrete time, meaning that the control computations use sampled-data measurements. We demonstrate the effectiveness of algorithms via analysis, numerical simulations, and experimental testings. We also present extensions to these algorithms that address systems with decentralized control architecture and systems subject to disturbances with unknown frequencies

Distributed adaptive control methods for uncertain multiagent systems with coupled dynamics

For a multiagent system, a major challenge is achieving overall system stability and performance in the presence of not only uncertainties but also coupled dynamics. Another challenge for these systems is designing distributed adaptive controllers with user-assigned positions in this case and defining the convergence rate of the reference model for each agent using only local (i.e., agent-based) information. Discrete-time architectures have an advantage over their continuous counterparts as they can be directly executed on embedded hardware without the need for discretization. Yet, because of the difficulty of ensuring Lyapunov difference expressions, their designs, which are based on quadratic Lyapunov-based frameworks, are highly complex. As a result, various existing continuous-time results using adaptive control methods to deal with system uncertainties and coupled dynamics in agents of a multiagent system cannot be directly applied to the discrete-time context as it can yield a loss of stability margins. To this end, this dissertation presents novel model reference and distributed/decentralized adaptive control algorithms designed for scalar and high-order uncertain multiagent systems in the presence of coupled dynamics that allows for choosing user-assigned positions for each agent. Specifically, this work proposes continuous and discrete-time distributed adaptive approaches for multiagent systems in the presence of agent-based uncertainties, uncertainty in actuator effectiveness, and unmeasurable coupled dynamics. Moreover, these solutions offer flexibility in positioning agents in space without using global information by user-assigned Laplacian matrix nullspaces. First, a literature review and motivation, followed by contribution, are given. Then, the problems are formulated for scalar and high-order multiagent systems, adaptive control designs along with the stability analyses are provided for continuous and discrete-time setting, and numerical and experimental examples are given to show efficacy of the proposed controllers. Finally, concluding remarks with potential research and published work are provided

Decentralized State Feedback and Near Optimal Adaptive Neural Network Control of Interconnected Nonlinear Discrete-Time Systems

In this paper, first a novel decentralized state feedback stabilization controller is introduced for a class of nonlinear interconnected discrete-time systems in affine form with unknown subsystem dynamics, control gain matrix, and interconnection dynamics by employing neural networks (NNs). Subsequently, the optimal control problem of decentralized nonlinear discrete-time system is considered with unknown internal subsystem and interconnection dynamics while assuming that the control gain matrix is known. For the near optimal controller development, the direct neural dynamic programming technique is utilized to solve the Hamilton-Jacobi-Bellman (HJB) equation forward-in-time. The decentralized optimal controller design for each subsystem utilizes the critic-actor structure by using NNs. All NN parameters are tuned online. By using Lyapunov techniques it is shown that all subsystems signals are uniformly ultimately bounded (UUB) for stabilization of such systems