In this paper, the main issues of model-based control methods are first reviewed, followed by the motivations and the state of the art of the model-free adaptive control (MFAC). MFAC is a novel data-driven control method for a class of unknown nonaffine nonlinear discrete-time systems since neither explicit physical model nor Lyapunov stability theory or key technical lemma is used in the controller design and theoretical analysis except only for the input/output (I/O) measurement data. The basis of MFAC is the dynamic linearization data modeling method at each operating point of the closed-loop system. The established dynamic linearization data model is a virtual equivalent data relationship in the I/O sense to the original nonlinear plant by means of a novel concept called pseudo-partial derivative (PPD) or pseudo-gradient (PG) vector. Based on this virtual equivalent dynamic linearization data model and the time-varying PPD or PG estimation algorithm designed merely using the I/O measurements of a controlled plant, the MFAC system is constructed. The main contribution of this paper is that the theoretical analysis of the bounded-input bounded-output stability, the monotonic convergence of the tracking error dynamics, and the internal stability of the full form dynamic linearization based MFAC scheme are rigorously presented by the contraction mapping principle; the well known PID control and the traditional adaptive control for linear time-invariant systems are explicitly shown as the special cases of this MFAC. The simulation results verify the effectiveness of the proposed approach.

In this paper, a data-driven model-free adaptive control (MFAC) approach is proposed based on a new dynamic linearization technique (DLT) with a novel concept called pseudo-partial derivative for a class of general multiple-input and multiple-output nonlinear discrete-time systems. The DLT includes compact form dynamic linearization, partial form dynamic linearization, and full form dynamic linearization. The main feature of the approach is that the controller design depends only on the measured input/output data of the controlled plant. Analysis and extensive simulations have shown that MFAC guarantees the bounded-input bounded-output stability and the tracking error convergence.

Linearization is often used for nonlinear control system design but what degree of a linearization is sufficient for the controller design is always a question. In this work, a local compact form dynamic linearization (local-CFDL) is developed at first to transform the original nonlinear nonaffine system into an affine structure consisting of both an unknown residual nonlinear time-varying term and a linearly parametric term affine to the control input. A discrete-time extended state observer (DESO) is introduced to estimate the unknown residual nonlinear time-varying term as a new extended state. Then, a local-CFDL based DESO-MFAC is proposed where the estimation of DESO is incorporated to compensate for the disturbances and uncertainties. Furthermore, a local partial form dynamic linearization (local PFDL) is also presented using multi-lag inputs and partial derivatives. And, a corresponding local-PFDL based DESO-MFAC is proposed utilizing additional control information to improve control performance. The proposed two methods are both data-driven and do not require any explicit model information. Theoretical analysis shows the robust convergence of the proposed methods with disturbances. Simulations verify the effectiveness of the proposed method and show that the local-PFDL based DESO-MFAC outperforms the local-CFDL based one owing to the use of additional control information

In this paper, a novel model-free adaptive control (MFAC) algorithm based on a dual successive projection (DuSP)-MFAC method is proposed, and it is analyzed using the introduced DuSP method and the symmetrically similar structures of the controller and its parameter estimator of MFAC. Then, the proposed DuSP-MFAC scheme is successfully implemented in an autonomous car "Ruilong" for the lateral tracking control problem via converting the trajectory tracking problem into a stabilization problem by using the proposed preview-deviation-yaw angle. This MFAC-based lateral tracking control method was tested and demonstrated satisfactory performance on real roads in Fengtai, Beijing, China, and through successful participation in the Chinese Smart Car Future Challenge Competition held in 2015 and 2016.

The terminal iterative learning control (TILC) method is introduced for the first time into the field of train station stop control and three TILC-based algorithms are proposed in this study. The TILC-based train station stop control approach utilises the terminal stop position error in previous braking process to update the current control profile. The initial braking position, or the braking force, or their combination is chosen as the control input, and corresponding learning law is developed. The terminal stop position error of each algorithm is guaranteed to converge to a small region related with the initial offset of braking position with rigorous analysis. The validity of the proposed algorithms is verified by illustrative numerical examples.