Data-Driven Nonlinear Control:Stabilization, Optimal Stabiliazation,and Output Tracking

ABSTRACT:For non-affine nonlinear plants, under the condition that only data is available rather than model, this thesis focuses three control problems:stabilizer design and estimation of the domain of attraction for the closed-loop, optimal stabilizer design, and output tracking controller design. The main contents and innovations are summarized as follows:1. A data-driven stabilizer design method is proposed, which can guarantee the asymptotic stability of the closed-loop and enlarge the estimate of the domain of attraction for the closed-loop. First, sufficient conditions for a feedback controller stabilizing the plant and estimating the domain of attraction for the closed-loop is given. Then, for a given control Lyapunov function, a controller is designed just using data, which satisfies sufficient conditions mentioned above. Finally, the estimate of the domain of attraction for the closed-loop is enlarged by finding an appropriate control Lyapunov function from a control Lyapunov function candidate set based on data.2. A data-driven optimal stabilizer design method based on approximate value iteration is proposed. First, the data-driven dynamic programming operator is well defined and its properties are investigated. Then, based on the data-driven dynamic programming operator, the data-driven approximate value iteration algorithm is proposed to obtain a sub-optimal controller. The data used in data-driven dynamic programming operator belongs to the data subset, whose elements make the difference of a positive-definite function to be negative-definite. Hence, the stability of the closed-loop is guaranteed.3. A data-driven output tracking controller design method is proposed. For a class of plant satisfying some assumptions, first, the solution or an approximate solution of the tracking equation is obtained from the state trajectory under a particular condition. Then, based on the solution or the approximate solution of the tracking equation, the state feedback controller containing the internal model of the reference signal is designed to exactly or approximately achieve the output tracking.