For absolute value terms related to yaw velocity generated by cross-flow effect and the unmodeled factors, a nonlinear parameter-varying (NPV) model is established with absolute value disturbances to regulate the heading of unmanned surface vehicle (USV) by state feedback (SF) control with a NPV disturbance observer (NPVDO). Firstly, the model of NPVDO is designed with gains to estimate the non-differentiable absolute disturbance. Secondly, a Lyapunov function is constructed with full states and varying parameter to solve the gains with NPVDO stability conditions by Euler homogeneity. Thirdly, since the NPVDO stability conditions contain the coupling term between the observer gain and the Lyapunov matrix, it is decoupled into NPVDO-sum of squares (SOS) conditions by the projection theorem and matrix transformation to solve NPVDO gains. Finally, a robust SF with NPVDO is designed for heading regulation with NPV model. Simulations and experiments indicate that NPVDO has a superior performance on parameter variation suppression and nonlinear non-differentiable disturbance estimation by comparing with other methods to reduce heading errors.

For the nonlinear parameter-varying (NPV) model of unmanned surface vehicle (USV) with the consideration of the velocities on yaw and surge as well as wave disturbances, a robust H ∞ control method is proposed based on extended homogeneous polynomial Lyapunov function (EHPLF) to regulate heading for the superior performance on the rapidity, accuracy and robustness. Firstly, a NPV model of heading error is established to design a general form of a state feedback controller with a robust H ∞ performance. Secondly, a Lyapunov matrix with full states and varying parameter is constructed to derive the robust H ∞ global exponential stability conditions by Euler’s homogeneity relation for the NPV system, known as the EHPLF stability conditions. Thirdly, since the EHPLF stability conditions consist of a set of nonlinear coupled inequalities that cannot be directly solved by sum of squares (SOS) toolboxes, they are decoupled with matrix transformations to obtain the EHPLF-SOS stability conditions, which is solved for the parameters of the state feedback controller. Finally, the simulation results indicate that EHPLF method exhibits a superior performance on dynamic, steady-state and robustness.

An improved predictive control strategy is proposed to regulate the speed for permanent magnet synchronous motor. Firstly, the motor model is discretized by Taylor series to obtain the expected voltage vector, and a novel cost function is reconstructed with only voltage variables for predictive control, which avoids weight-adjustment. Secondly, the angle of expected voltage vector is obtained by Clark transformation to select the sector, whose voltage vectors are the candidate voltage vectors to reduce calculations. Finally, the optimal voltage vector is determined to switch the inverter by the minimum of the cost function among the candidate voltage vectors. Superior control performance is verified in experiments compared to conventional predictive speed control.