Novel Coordinate Transformations Combined Adaptive Robust Control for Two-Order Nonlinear Systems with Input and State Constraints

Although barrier Lyapunov function (BLF)-based approaches simplify the handling process for state constraints, the feasibility conditions on virtual controllers considerably limit their application in practice. Therefore, to remove the feasibility conditions and achieve better results in industrial applications, in this paper, a novel control design is presented for two-order nonlinear systems subject to input and state constraints. Namely, a piecewise but continuously differentiable state-projection function that possesses two key properties is presented to address the state constraints. Based on this approach, a novel coordinate transformation is proposed to build a constrained adaptive robust controller. Since the control parameter of the virtual controller varies exponentially with the state-projection function, the feasibility condition can be essentially satisfied. As a result, tedious offline computations for feasibility verification can be avoided, which makes it possible to handle much tighter state constraint boundaries. Moreover, a smooth function and an auxiliary variable are employed to address the input constraint. The satisfaction of constraints and the stability of systems are rigorously proven in theory. Comparative simulations and experiments on a typical two-order linear motor system demonstrate that the proposed method has good adaptability under different state constraints and can achieve better control performance in practical systems.