Quantized control of stochastic linear systems.

摘要

This thesis considers a feedback control system where a plant is actuated by a quantized control. The measurements are assumed to be disturbed by an additive wideband noise in the feedback loop. The nonlinear control in the presence of the noise may cause the system to be variable structure. Variable structure systems disturbed by the noise exhibit sliding modes on the switching manifold. The system behavior is analyzed and compared with the deterministic case. The performance and behavior of the system in the steady state are examined and compared via a quadratic performance index. In order to improve the performance and reduce the noise effect, two types of quantizers are employed to represent different level of optimality. If the quantizer causes a high gain in the system due to quantization of a small measurement for a fixed quantization level, the quantized control systems can be represented by a singularly perturbed model and analyzed by two approximate reduced-order models. It is shown that the slow model approximates the system in the sliding mode with an error of an order of the estimated singular perturbation parameter. When the system is unstable around the origin due to unstable subsystems, linear optimal controls using LQG formulation are investigated to stabilize the system in a region around the origin while the quantized control guides the system to the region. The performance and behavior of the stabilized system are examined via a quadratic performance index in the steady state. Also, the performance and the chattering are considered in the case of stable systems using a dead-zone quantizer. The controller design scheme for the quantized control system can be extended to the discrete-time systems by investigating the design parameters, such as the bounds on the control and the bound on the sampling period. The stabilization of the unstable systems is considered around the origin, and the performance is analyzed in the steady state. Numerical examples are presented and discussed for various parameters as illustrations.