Lyapunov-based adaptive model predictive control for unconstrained non-linear systems with parametric uncertainties

In this study, a simple Lyapunov-based adaptive model predictive control (MPC) is proposed to stabilise a class of unconstrained non-linear systems with constant parametric uncertainties. In the proposed MPC design, the uncertain parameters are estimated online with an adaptive updating law, and the estimated parameters are guaranteed bounded. A Lyapunov-based constraint is employed in the adaptive MPC to ensure the stability of the closed-loop system. By using the control Lyapunov function-based constraint, terminal penalties in traditional MPC can be avoided, such that computational burden is significantly reduced. Both theoretical results and numerical examples demonstrate that, with the proposed adaptive MPC, states of the closed-loop system can be stabilised, while the adaptive estimated parameters are bounded.