Memoryless coding scheme based on spherical polar coordinates for control under data rate constraint

Under finite data rate communication constraint, it is difficult at present to determine the precise lower bound of the channel data rate for achieving a control goal using memoryless coding scheme, and it is useful to work out as many memoryless coding schemes as possible for a control task. Based on spherical polar coordinates, the authors propose a new memoryless time varying coding scheme to asymptotically stabilise a discrete linear time invariant system through channel of finite data rate between the sensor and the controller. One attractive property of the authors proposed coding scheme is that a definite relation between quantised data and the corresponding quantisation error is established, which facilitates the analysis of system stability and the determination of data rate. Also, adopting spherical polar coordinates makes the problem of finding the parameters of the quantiser and the controller easy to solve.