Adaptive Asymptotic Tracking Control of MIMO Nonlinear Systems Subject to Asymmetric Full-State Constraints: A Removing Feasibility Condition Approach

This work develops an adaptive control scheme for MIMO nonlinear non-lower-triangular systems with asymmetric full-state constraints and unknown gain functions. First, in order to maintain the state constraints, a function that depends solely on the states of the system is proposed to replace the traditional Lyapunov barrier function that relies on the error signal. By means of an affine transformation, the original system is reconstructed to the current system that releases prior knowledge of the gain functions and removes the state constraints. Second, a coordinate transformation is introduced and integrated into each step of the adaptive control design procedure, which circumvents the feasibility condition for intermediate input signals. Under the developed control strategy, all system states are bounded and remain within constraint sets at any moment. Simultaneously, the output signals asymptotically track the reference trajectories to zero. Finally, the feasibility of the presented strategy is demonstrated based on simulation examples.