Identification and control of dynamic systems using neural networks.

The aim of this thesis is to contribute in solving problems related to the on-line identification and control of unknown dynamic systems using feedforward neural networks. In this sense, this thesis presents new on-line learning algorithms for feedforward neural networks based upon the theory of variable structure system design, along with mathematical proofs regarding the convergence of solutions given by the algorithms; the boundedness of these solutions; and robustness features of the algorithms with respect to external perturbations affecting the neural networks' signals. In the thesis, the problems of on-line identification of the forward transfer operator, and the inverse transfer operator of unknown dynamic systems are also analysed, and neural networks-based identification schemes are proposed. These identification schemes are tested by computer simulations on linear and nonlinear unknown plants using both continuous-time and discrete-time versions of the proposed learning algorithms. The thesis reports about the direct inverse dynamics control problems using neural networks, and contributes towards solving these problems by proposing a direct inverse dynamics neural network-based control scheme with on-line learning capabilities of the inverse dynamics of the plant, and the addition of a feedback path that enables the resulting control scheme to exhibit robustness characteristics with respect to external disturbances affecting the output of the system. Computer simulation results on the performance of the mentioned control scheme in controlling linear and nonlinear plants are also included. The thesis also formulates a neural network-based internal model control scheme with on-line estimation capabilities of the forward transfer operator and the inverse transfer operator of unknown dynamic systems. The performance of this internal model control scheme is tested by computer simulations using a stable open-loop unknown plant with output signal corrupted by white noise. Finally, the thesis proposes a neural network-based adaptive control scheme where identification and control are simultaneously carried out

RONAALP: Reduced-Order Nonlinear Approximation with Active Learning Procedure

Many engineering applications rely on the evaluation of expensive, non-linear high-dimensional functions. In this paper, we propose the RONAALP algorithm (Reduced Order Nonlinear Approximation with Active Learning Procedure) to incrementally learn a fast and accurate reduced-order surrogate model of a target function on-the-fly as the application progresses. First, the combination of nonlinear auto-encoder, community clustering and radial basis function networks allows to learn an efficient and compact surrogate model with limited training data. Secondly, the active learning procedure overcome any extrapolation issue when evaluating the surrogate model outside of its initial training range during the online stage. This results in generalizable, fast and accurate reduced-order models of high-dimensional functions. The method is demonstrated on three direct numerical simulations of hypersonic flows in chemical nonequilibrium. Accurate simulations of these flows rely on detailed thermochemical gas models that dramatically increase the cost of such calculations. Using RONAALP to learn a reduced-order thermodynamic model surrogate on-the-fly, the cost of such simulation was reduced by up to 75% while maintaining an error of less than 10% on relevant quantities of interest.Comment: 38 pages, 16 figure

A neural network-based trajectory planner for redundant systems using direct inverse modeling

Redundant (i.e., under-determined) systems can not be trained effectively using direct inverse modeling with supervised learning, for reasons well out-lined by Michael Jordan at MIT. There is a loop-hole , however, in Jordan\u27s preconditions, which seems to allow just such an architecture. A robot path planner implementing a cerebellar inspired habituation paradigm with such an architecture will be introduced. The system, called ARTFORMS, for Adaptive Redundant Trajectory Formation System uses on-line training of multiple CMACS. CMACs are locally generalizing networks, and have an a priori deterministic geometric input space mapping. These properties together with on-line learning and rapid convergence satisfy the loop-hole conditions. Issues of stability/plasticity, presentation order and generalization, computational complexity, and subsumptive fusion of multiple networks are discussed. Two implementations are described. The first is shown not to be goal directed enough for ultimate success. The second, which is highly successful, is made more goal directed by the addition of secondary training, which reduces the dimensionality of the problem by using a set of constraint equations. Running open loop with respect to posture (the system metric which reduces dimensionality) is seen to be the root cause of the first system\u27s failure, not the use of the direct inverse method. In fact, several nice properties of direct inverse modeling contribute to the system\u27s convergence speed, robustness and compliance. The central problem used to demonstrate this method is the control of trajectory formation for a planar kinematic chain with a variable number of joints. Finally, this method is extended to implement adaptive obstacle avoidance

ADVANCES IN SYSTEM RELIABILITY-BASED DESIGN AND PROGNOSTICS AND HEALTH MANAGEMENT (PHM) FOR SYSTEM RESILIENCE ANALYSIS AND DESIGN

Failures of engineered systems can lead to significant economic and societal losses. Despite tremendous efforts (e.g., $200 billion annually) denoted to reliability and maintenance, unexpected catastrophic failures still occurs. To minimize the losses, reliability of engineered systems must be ensured throughout their life-cycle amidst uncertain operational condition and manufacturing variability. In most engineered systems, the required system reliability level under adverse events is achieved by adding system redundancies and/or conducting system reliability-based design optimization (RBDO). However, a high level of system redundancy increases a system's life-cycle cost (LCC) and system RBDO cannot ensure the system reliability when unexpected loading/environmental conditions are applied and unexpected system failures are developed. In contrast, a new design paradigm, referred to as resilience-driven system design, can ensure highly reliable system designs under any loading/environmental conditions and system failures while considerably reducing systems' LCC. In order to facilitate the development of formal methodologies for this design paradigm, this research aims at advancing two essential and co-related research areas: Research Thrust 1 - system RBDO and Research Thrust 2 - system prognostics and health management (PHM). In Research Thrust 1, reliability analyses under uncertainty will be carried out in both component and system levels against critical failure mechanisms. In Research Thrust 2, highly accurate and robust PHM systems will be designed for engineered systems with a single or multiple time-scale(s). To demonstrate the effectiveness of the proposed system RBDO and PHM techniques, multiple engineering case studies will be presented and discussed. Following the development of Research Thrusts 1 and 2, Research Thrust 3 - resilience-driven system design will establish a theoretical basis and design framework of engineering resilience in a mathematical and statistical context, where engineering resilience will be formulated in terms of system reliability and restoration and the proposed design framework will be demonstrated with a simplified aircraft control actuator design problem