Nonlinear model predictive control based on predicted state error convergence

Systems subject to nonholonomic constraints or nonintegrable conservation laws may be modeled as driftless nonlinear control systems. Such systems are not stabilizable using continuous time-invariant state feedback. Time varying or piecewise continuous feedback are the only stabilization strategies currently available. This paper presents a new feedback stabilization algorithm for this class of systems by choosing the control action based on a gradient matrix to reduce the predicted state error. This approach is similar to the model predictive control but does not consider optimality nor constraints explicitly. As a result, the on-line computation load is greatly reduced. Existing stability analysis techniques for model predictive control are not directly applicable due to the lack of local stabilizability. We show that under the full rank condition of a gradient matrix, the closed loop system is globally asymptotically stable. Examples of several nonlinear control systems are included to illustrate the proposed method.