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

Symmetrization for Quantum Networks: a continuous-time approach

In this paper we propose a continuous-time, dissipative Markov dynamics that asymptotically drives a network of n-dimensional quantum systems to the set of states that are invariant under the action of the subsystem permutation group. The Lindblad-type generator of the dynamics is built with two-body subsystem swap operators, thus satisfying locality constraints, and preserve symmetric observables. The potential use of the proposed generator in combination with local control and measurement actions is illustrated with two applications: the generation of a global pure state and the estimation of the network size.Comment: submitted to MTNS 201

Stability and weight smoothing in CMAC neural networks

Although the CMAC (Cerebellar Model Articulation Controller) neural network has been successfully used in control systems for many years, its property of local generalization, the availability of trained information for network responses at adjacent untrained locations, although responsible for the networks rapid learning and efficient implementation, results in network responses that is, when trained with sparse or widely spaced training data, spiky in nature even when the underlying function being learned is quite smooth. Since the derivative of such a network response can vary widely, the CMAC\u27s usefulness for solving optimization problems as well as for certain other control system applications can be severely limited. This dissertation presents the CMAC algorithm in sufficient detail to explore its strengths and weaknesses. Its properties of information generalization and storage are discussed and comparisons are made with other neural network algorithms and with other adaptive control algorithms. A synopsis of the development of the fields of neural networks and adaptive control is included to lend historical perspective. A stability analysis of the CMAC algorithm for open-loop function learning is developed. This stability analysis casts the function learning problem as a unique implementation of the model reference structure and develops a Lyapunov function to prove convergence of the CMAC to the target model. A new CMAC learning rule is developed by treating the CMAC as a set of simultaneous equations in a constrained optimization problem and making appropriate choices for the weight penalty matrix in the cost equation. This dissertation then presents a new CMAC learning algorithm which has the property of weight smoothing to improve generalization, function approximation in partially trained networks and the partial derivatives of learned functions. This new learning algorithm is significant in that it derives from an optimum solution and demonstrates a dramatic performance improvement for function learning in the presence of widely spaced training data. Developed from a completely unique analytical direction, this algorithm represents a coupling and extension of single- and multi-resolution CMAC algorithms developed by other researchers. The insights derived from the analysis of the optimum solution and the resulting new learning rules are discussed and suggestions for future work are presented

Integrated Robust Optimal Design (IROD) via sensitivity minimization

A novel Integrated Robust Optimal Design (IROD) methodology is presented in this work which combines a traditional sensitivity theory with relatively new dvancements in Bilinear Matrix Inequality (BMI) constrained optimization problems. IROD provides the least conservative approach for robust control synthesis. The proposed methodology is demonstrated using numerical examples of integrated control-structure design problem for combine harvester header and excavator linkages. The IROD methodology is compared with the state of the art sequential design method using the two application examples, and the results show that the proposed methodology provides a viable alternative for robust controller synthesis and often times offers even a better performance than competing methods. Although this method requires linearization of nonlinear system at each system parameter optimization step, a technique to linearized Differential Algebraic Equations (DAE) is presented which allows use of symbolic approach for linearization. This technique avoids repetitive linearizations. For the nonlinear systems with parametric uncertainties which can not be linearized at operating points, a new methodology is proposed for robust feedback linearization using sensitivity dynamics-based formulation. The feedback linearization approach is used for systems with augmented sensitivity dynamics and used to refine control input to improve robustness. The method is demonstrated using an example of a position tracking control of a hydraulic actuator. The robustness of controller design is demonstrated by considering variations in fluid density parameter. The results show that the proposed methodology improves robustness of the feedback linearization to parametric variations