Robust control and filtering for systems with state-dependent uncertainties and applications

Abstract

In mechanical systems, electronic circuits, and other fields of engineering, there exist many key structured subsystems, which mainly consist of core components with state-dependent uncertainties or state-dependent nonlinearities. To generate a suitable control law to overcome the imperfection of model and guarantee a certain performance against the presence of uncertainties or external disturbances, it is of great significance to research the problem of robust stability analysis and synthesis for this class of dynamic systems with state-dependent uncertainties. Based on a full understanding of the state of the art in state-dependent uncertain systems, this thesis focuses on robust control and filtering of state-dependent uncertain systems and applications. The novelty and contribution of the thesis lie in the following aspects: (1) Robust stability analysis and synthesis of state-dependent uncertain systems are systematically addressed by constructing a novel parameter-dependent Lyapunov function and less conservative results are obtained by utilizing properties of the time-derivatives of state-dependent parameters. The proposed robust controller design methodology is applied to stabilization and synchronization of Chua's oscillator; (2) A novel robust filter design method for state-dependent uncertain systems is presented by introducing a generalized filtering performance index-extended dissipativity. H∞, L2-L∞, passive and dissipative filtering problems can be solved successfully within a unified framework. The small current estimation problem of a tunnel diode circuit system under uncertain disturbances is solved by using the proposed robust filter design method; (3) A novel vibration sensor for real-time measurement of absolute vibration motion is developed based on a bio-inspired animal-limb-like structure with state-dependent nonlinearity. With this bio-inspired vibration sensor, the problems of error accumulation and real-time performance induced by traditional measurement method using accelerometer can be effectively eliminated. A model-based fault detection algorithm using the vibration sensor is presented to deal with the real-time detection problem of fast time-varying weak fault signal which cannot be exactly identified by existing frequency-based and wavelet-based fault detection methods; (4) Robust autonomous navigation of a tracked mobile robot with passive bio-inspired suspension based on double-layer nonlinear model predictive control (NMPC) is proposed to improve the trajectory tracking accuracy against the slippage disturbances caused by unexpected "slippery track" phenomenon. The double layer NMPC scheme can accurately track the global reference trajectory and perform local trajectory optimization in occurrence of slippage disturbances with less computational burden; (5) Through estimating human's motion, a vision-based robust controller with disturbance compensation is designed to achieve better smoothness, rapidity, and accuracy of human-robot following. The developed vision based robust following controller can effectively prevent the target out of the robot camera's field of view (FOV) leading to following failure in narrow environment. The corresponding simulations and experiments have demonstrated the effectiveness and advantages of the developed robust control and filtering methods for state-dependent uncertain systems.