Constrained Adaptive Control And Constrained Iterative Learning Control

Adaptive controllers are commonly designed to deal with constant parametric uncertainties. Iterative learning controllers can estimate and tackle those time-varying or fast time-varying uncertainties in iterations. Since the researches of nonparametric uncertain systems are inadequate, it is necessary to design iterative learning controllers for non-parametric systems. While considering the physical, position or orientation constraints in the operating environment, discussion of state or output constrained problems is becoming more and more important. In this paper, a novel Barrier Lyapunov Function is proposed to design state-constrained adaptive controllers and state-constrained iterative learning controllers. The controllers can ensure that the error converges, and the constrained system state is achieved.The main results and achievements are as follows:1. A novel Barrier function is proposed to design a state-constrained adaptive controller for a time-invariant system. State-constrained iterative learning control schemes are proposed respectively for systems with constant parametrization, time-varying parametrization, and a combined situation. Simulation results show the effectiveness of the method.2. State-constrained repetitive learning controllers are designed to deal with the initial condition problem in iterative learning control designs. With the help of constrained learning law, the system state can completely track the reference trajectory, while the quadratic of system error is constrained during all iterations.3. State-constrained iterative learning control is presented for a class of non-parametric uncertain systems. The nonparametric uncertainty of system dynamics are tackled through the robust treatment and learning mechanism. The performances of partially and fully saturated learning algorithms are characterized, respectively. It is shown that the system state can track the reference trajectory over the entire time interval as iteration increases, while the quadratic tracking error, as a measure of the constraint, is enforced to stay in the pre-specified range. The constrained system state is in turn achieved.4. For the time-varying robotic systems, a state-constrained iterative learning controller and a state-constrained repetitive learning controller are presented to achieve the complete tracking.