Adaptive noise cancellation using adaptive filters is a known method for removing noise that interferes with signal measurements. The adaptive noise canceller performs filtering based on the current situation through a windowing process. The shape of the window function determines the tracking performance of the adaptive noise canceller with respect to the fluctuation of the property of the unknown system that noise (reference signal) passes. However, the shape of the window function in the field of adaptive filtering has not yet been considered in detail. This study mathematically treats the effect of the window function on the adaptive noise canceller and proposes an optimization method for the window function in situations where offline processing can be performed, such as biomedical signal measurements. We also demonstrate the validity of the optimized window function through numerical experiments.

As a fundamental building block of multirate systems, the downsampler, also known as the decimator, is a periodically time-varying linear system. An eigensignal of the downsampler is defined to be an input signal which appears at the output unaltered or scaled by a non-zero coefficient. In this paper, the eigensignals are studied and characterized in the time and z domains. The time-domain characterization is carried out using number theoretic principles, while the one-sided z-transform and Lambert-form series are used for the transform-domain characterization. Examples of non-trivial eigensignals are provided. These include the special classes of multiplicative and completely multiplicative eigensignals. Moreover, the locus of poles of eigensignals with rational z transforms are identified.

A computed torque controller for a dynamic model of nonholonomic mobile robots with bounded external disturbance is proposed to treat the adaptive tracking control problem using the separated design method. A velocity controller is first designed for the kinematic steering system to make the tracking error approaching to zero asympotically. Then, a computed torque controller is designed such that the true mobile robot velocity converges to the desired velocity controller. In each step, the controllers are designed independently, and this will simplify the design of controllers. A novel stability analysis involving the estimation of some differential inequalities is also given to guarantee the stability of the closed-loop system. Moreover, the regulation problem and the tracking problem will be treated using the proposed controller. In particular, the mobile robots can globally follow any path such as a straight-line, a circle and the path approaching to the origin. Furthermore, the problems of back-into-garage parking and the parallel parking problem can also be solved using the proposed controller. Some interesting simulation results are given to illustrate the effectiveness of the proposed tracking control law.

A general tracking control problem for mobile robots is proposed and solved using the backstepping technique. A global result is given for the kinematic steering system to make the tracking error approaching to zero asymptotically. Based on our efforts, the proposed controller can solve both the tracking problem and the regulation problem of mobile robots. In particular, mobile robots can now globally follow any differentiable with bounded velocities path such as a straight line, a circle and the path approaching to the origin using the proposed controller. Moreover, the problem of back-into-garage parking is also solved by our approach. Some interesting simulation results are given to illustrate the effectiveness of the proposed tracking control laws.