The purpose of this study was to develop a practical functional electrical stimulation (FES) controller for joint movements restoration based on an optimal control technique by cascading a linear model predictive control (MPC) and a nonlinear transformation. The cascading configuration was aimed to obtain an FES controller that is able to deal with a nonlinear system. The nonlinear transformation was utilized to transform the linear solution of linear MPC to become a nonlinear solution in form of optimized electrical stimulation intensity. Four different types of nonlinear functions were used to realize the nonlinear transformation. A simple parameter estimation to determine the value of the nonlinear transformation parameter was also developed. The tracking control capability of the proposed controller along with the parameter estimation was examined in controlling the 1-DOF wrist joint movement through computer simulation. The proposed controller was also compared with a fuzzy FES controller. The proposed MPC-FES controller with estimated parameter value worked properly and had a better control accuracy than the fuzzy controller. The parameter estimation was suggested to be useful and effective in practical FES control applications to reduce the time-consuming of determining the parameter value of the proposed controller.

This paper gives a systematic approach to generate a Markov chain by a discrete-valued auto-regressive equation, which is a a nonlinear auto-regressive equation having a discrete-valued solution. The power spectrum, the correlation function and the transition probability are explicitly obtained in terms of the discrete-valued auto-regressive equation. Some computer results are illustrated in figures.

This paper proposes a second order auto-regressive equation with discrete-valued random coefficients. The auto-regressive equation transforms an independent stochastic sequence into a binary sequence, which is a special case of a stationary Markov chain. The power spectrum, correlation function and the transition probability are explicitly obtained in terms of the random coefficients. Some computer results are illustrated in figures.