Online constrained optimization based adaptive robust control of a class of MIMO nonlinear systems with matched uncertainties and input/state constraints

A performance oriented two-loop control approach is proposed for a class of multiple-input–multiple-output (MIMO) systems with input saturation, state constraints, matched parametric uncertainties and input disturbances. In the inner loop, a constrained adaptive robust control (ARC) law is synthesized to achieve the required robust tracking performances with respect to on-line replanned trajectory in the presence of input saturation and various types of matched uncertainties. In the outer loop, a replanned trajectory is generated by solving a constrained optimization algorithm online to minimize the converging time of the overall system response to the desired trajectory while not violating various constraints. Interaction of the two loops is explicitly characterized by a set of inequalities that the design variables of each loop have to satisfy. It is theoretically shown that the resulting closed-loop system can track feasible desired trajectories with a guaranteed converging time and steady-state tracking accuracy without violating the state constraints. Since the system in study is most appropriate to describe the dynamics of the robotic systems, the control of a two-axis planar robotic manipulator is used as an application example. Comparative simulation results demonstrate the advantage of the proposed approach over the traditional approaches in practical applications.