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Title: Learning and intelligent control of nonlinear systems using dynamic neural networks
Authors: Zhang, Yinyan
Degree: Ph.D.
Issue Date: 2019
Abstract: Optimal control is concerned with finding a control law that drives a controlled system to a desired target in an optimal way, i.e., to minimize or maximize a predefined performance index. For nonlinear systems, the optimal control of nonlinear systems requires the solution of a partial differential equation, called the Hamilton-Jacobi-Bellman equation, for which the analytical solution is diffcult or even impossible to obtain. Consequently, efforts are made on the near-optimal control, which aims at finding an approximate solution to the optimal control problem. When the system parameters are unknown or the system dynamics is unknown, the near-optimal control problem becomes more difficult. In this thesis, we are concerned with the learning and intelligent control of nonlinear systems using dynamic neural networks. First, a unified online learning and near-optimal control framework is proposed for linear and nonlinear systems with parameter uncertainty. It is also proved that the proposed learning and near-optimal control law asymptotically converges to the optimal. The efficacy of the proposed framework and the theoretical results are validated by an application to underactuated surface vessels. Second, a learning and near-optimal control law, which is inherently real-time, is designed to tackle the contradictory between solution accuracy and solution speed for the optimal control of a general class of nonlinear systems with fully unknown parameters. The key technique in the proposed learning and near-optimal control is to design an auxiliary system, which can be viewed as a dynamic neural network, with the aid of the sliding mode control concept to learn the dynamics of the controlled nonlinear system. Based on the sliding-mode auxiliary system and approximation of the performance index, the proposed control law guarantees asymptotic stability of the closed-system and asymptotic optimality of the performance index with time. Third, a novel model-free learning and near-optimal control method is proposed for nonlinear systems via utilizing the Taylor expansion based problem relaxation, the universal approximation property of sigmoid neural networks, and the concept of sliding-mode control. By making approximation for the performance index, it is first relaxed to a quadratic program, and then a linear algebraic equation with unknown terms. An auxiliary system, which can be viewed as a dynamic neural network, is designed to reconstruct the input-to-output property of the control systems with unknown dynamics, so as to tackle the difficulty caused by the unknown terms, i.e., to learn the unknown dynamics.
Fourth, the learning and near-optimal distributed consensus of high-order nonlinear multi-agent systems consisting of heterogeneous agents is investigated. The consensus problem is formulated as a receding-horizon optimal control problem. For the situation with fully unknown system parameters, sliding-mode auxiliary systems, which could be viewed as dynamic neural networks and are independent for different agents, are built to reconstruct the input-output properties of agents. Based on the sliding-mode auxiliary systems, an adaptive near-optimal protocol is finally presented to control high-order nonlinear multi-agent systems with fully unknown parameters. Theoretical analysis shows that the proposed protocols can simultaneously guarantee the asymptotic optimality of the performance index and the asymptotic consensus of multi-agent systems. Fifth, inspired by the success of the learning and near-optimal control method, we consider a special physical system, i.e., redundant manipulators. Redundancy resolution is of great importance in the control of manipulators. Among the existing results for handling this issue, the quadratic program approaches, which are capable of optimizing performance indices subject to physical constraints, are widely used. However, the existing quadratic program approaches require exactly knowing all the physical parameters of manipulators, the condition of which may not hold in some practical applications. This fact motivates us to consider the application of learning and intelligent control techniques for simultaneous parameter learning and control. We establish the first adaptive dynamic neural network with online learning for the redundancy resolution of manipulators with unknown physical parameters so as to solve the intelligent control problem, which tackles the dilemmas in existing methods.
Subjects: Hong Kong Polytechnic University -- Dissertations
Automatic control
Neural networks (Computer science)
Pages: xxi, 177 pages : color illustrations
Appears in Collections:Thesis

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