Time-Optimal Constrained Adaptive Robust Control of a Class of SISO Unmatched Nonlinear Systems

Adaptive robust control (ARC) has demonstrated its superiority in handling disturbances and parametric uncertainties in the past decades. However, the conventional ARC designs cannot effectively handle the hard state constraints. To deal with the state constraints while maintaining a good tracking performance and robustness, a two-layer constrained adaptive robust control (CARC) strategy is proposed in this paper. In the outer layer, a planner continuously monitors level of tracking errors. When the tracking errors become large, the planner redesigns the reference trajectory by solving a constrained optimization problem. In the inner layer, a Saturated-ARC controller is synthesized to achieve a high tracking performance in the presence of external disturbances and parametric modeling uncertainties. The interaction between the two layers was analyzed to achieve guaranteed performance. The optimization cost function can be arbitrarily selected based on different needs, with time-optimal trajectory tracking re-planning solved in this paper due to its wider potential applications. The focus of this paper is not on solving the optimization problems, but rather incorporating the existing algorithms into our two-layer structure. Unlike model predictive control (MPC) based strategies, the proposed design does not rely on the fast iterative computation of solving the constrained optimization problem to achieve stability and robustness. Comparative simulations were carried out on an unmatched system. The results demonstrate the improvement of the proposed design over the past ones in dealing with hard state constraints.