Extended Ellipsoidal Outer-Bounding Set-Membership Estimation for Nonlinear Discrete-Time Systems with Unknown-but-Bounded Disturbances

This paper develops an extended ellipsoidal outer-bounding set-membership estimation (EEOB-SME) algorithm with high accuracy and efficiency for nonlinear discrete-time systems under unknown-but-bounded (UBB) disturbances. The EEOB-SME linearizes the first-order terms about the current state estimations and bounds the linearization errors by ellipsoids using interval analysis for nonlinear equations of process and measurement equations, respectively. It has been demonstrated that the EEOB-SME algorithm is stable and the estimation errors of the EEOB-SME are bounded when the nonlinear system is observable. The EEOB-SME decreases the computation load and the feasible sets of EEOB-SME contain more true states. The efficiency of the EEOB-SME algorithm has been shown by a numerical simulation under UBB disturbances

Exponential Estimates and Stabilization of Discrete-Time Singular Time-Delay Systems Subject to Actuator Saturation

This paper is concerned with exponential estimates and stabilization of a class of discrete-time singular systems with time-varying state delays and saturating actuators. By constructing a decay-rate-dependent Lyapunov-Krasovskii function and utilizing the slow-fast decomposition technique, an exponential admissibility condition, which not only guarantees the regularity, causality, and exponential stability of the unforced system but also gives the corresponding estimates of decay rate and decay coefficient, is derived in terms of linear matrix inequalities (LMIs). Under the proposed condition, the exponential stabilization problem of discrete-time singular time-delay systems subject actuator saturation is solved by designing a stabilizing state feedback controller and determining an associated set of safe initial conditions, for which the local exponential stability of the saturated closed-loop system is guaranteed. Two numerical examples are provided to illustrate the effectiveness of the proposed results

Neural Networks: Training and Application to Nonlinear System Identification and Control

This dissertation investigates training neural networks for system identification and classification. The research contains two main contributions as follow:1. Reducing number of hidden layer nodes using a feedforward componentThis research reduces the number of hidden layer nodes and training time of neural networks to make them more suited to online identification and control applications by adding a parallel feedforward component. Implementing the feedforward component with a wavelet neural network and an echo state network provides good models for nonlinear systems.The wavelet neural network with feedforward component along with model predictive controller can reliably identify and control a seismically isolated structure during earthquake. The network model provides the predictions for model predictive control. Simulations of a 5-story seismically isolated structure with conventional lead-rubber bearings showed significant reductions of all response amplitudes for both near-field (pulse) and far-field ground motions, including reduced deformations along with corresponding reduction in acceleration response. The controller effectively regulated the apparent stiffness at the isolation level. The approach is also applied to the online identification and control of an unmanned vehicle. Lyapunov theory is used to prove the stability of the wavelet neural network and the model predictive controller. 2. Training neural networks using trajectory based optimization approachesTraining neural networks is a nonlinear non-convex optimization problem to determine the weights of the neural network. Traditional training algorithms can be inefficient and can get trapped in local minima. Two global optimization approaches are adapted to train neural networks and avoid the local minima problem. Lyapunov theory is used to prove the stability of the proposed methodology and its convergence in the presence of measurement errors. The first approach transforms the constraint satisfaction problem into unconstrained optimization. The constraints define a quotient gradient system (QGS) whose stable equilibrium points are local minima of the unconstrained optimization. The QGS is integrated to determine local minima and the local minimum with the best generalization performance is chosen as the optimal solution. The second approach uses the QGS together with a projected gradient system (PGS). The PGS is a nonlinear dynamical system, defined based on the optimization problem that searches the components of the feasible region for solutions. Lyapunov theory is used to prove the stability of PGS and QGS and their stability under presence of measurement noise

Reconstruction of gasoline engine in-cylinder pressures using recurrent neural networks

Knowledge of the pressure inside the combustion chamber of a gasoline engine would provide very useful information regarding the quality and consistency of combustion and allow significant improvements in its control, leading to improved efficiency and refinement. While measurement using incylinder pressure transducers is common in laboratory tests, their use in production engines is very limited due to cost and durability constraints. This thesis seeks to exploit the time series prediction capabilities of recurrent neural networks in order to build an inverse model accepting crankshaft kinematics or cylinder block vibrations as inputs for the reconstruction of in-cylinder pressures. Success in this endeavour would provide information to drive a real time combustion control strategy using only sensors already commonly installed on production engines. A reference data set was acquired from a prototype Ford in-line 3 cylinder direct injected, spark ignited gasoline engine of 1.125 litre swept volume. Data acquired concentrated on low speed (1000-2000 rev/min), low load (10-30 Nm brake torque) test conditions. The experimental work undertaken is described in detail, along with the signal processing requirements to treat the data prior to presentation to a neural network. The primary problem then addressed is the reliable, efficient training of a recurrent neural network to result in an inverse model capable of predicting cylinder pressures from data not seen during the training phase, this unseen data includes examples from speed and load ranges other than those in the training case. The specific recurrent network architecture investigated is the non-linear autoregressive with exogenous inputs (NARX) structure. Teacher forced training is investigated using the reference engine data set before a state of the art recurrent training method (Robust Adaptive Gradient Descent – RAGD) is implemented and the influence of the various parameters surrounding input vectors, network structure and training algorithm are investigated. Optimum parameters for data, structure and training algorithm are identified

Identification and Control of Nonlinear Singularly Perturbed Systems Using Multi-time-scale Neural Networks

Many industrial systems are nonlinear with "slow" and "fast" dynamics because of the presence of some ``parasitic" parameters such as small time constants, resistances, inductances, capacitances, masses and moments of inertia. These systems are usually labeled as "singularly perturbed" or ``multi-time-scale" systems. Singular perturbation theory has been proved to be a useful tool to control and analyze singularly perturbed systems if the full knowledge of the system model parameters is available. However, the accurate and faithful mathematical models of those systems are usually difficult to obtain due to the uncertainties and nonlinearities. To obtain the accurate system models, in this research, a new identification scheme for the discrete time nonlinear singularly perturbed systems using multi-time-scale neural network and optimal bounded ellipsoid method is proposed firstly. Compared with other gradient descent based identification schemes, the new identification method proposed in this research can achieve faster convergence and higher accuracy due to the adaptively adjusted learning gain. Later, the optimal bounded ellipsoid based identification method for discrete time systems is extended to the identification of continuous singularly perturbed systems. Subsequently, by adding two additional terms in the weight's updating laws, a modified identification scheme is proposed to guarantee the effectiveness of the identification algorithm during the whole identification process. Lastly, through introducing some filtered variables, a robust neural network training algorithm is proposed for the system identification problem subjected to measurement noises. Based on the identification results, the singular perturbation theory is introduced to decompose a high order multi-time-scale system into two low order subsystems -- the reduced slow subsystem and the reduced fast subsystem. Then, two controllers are designed for the two subsystems separately. By using the singular perturbation theory, an adaptive controller for a regulation problem is designed in this research firstly. Because the system order is reduced, the adaptive controller proposed in this research has a simpler structure and requires much less computational resources, compared with other conventional controllers. Afterward, an indirect adaptive controller is proposed for solving the trajectory tracking problem. The stability of both identification and control schemes are analyzed through the Lyapunov approach, and the effectiveness of the identification and control algorithms are demonstrated using simulations and experiments