Online adaptive neuro-fuzzy modelling and control of nonlinear dynamic systems

The engineering development of advanced technologies for monitoring, optimisation, fault detection and controller design all rely on the use of an accurate mathematical model of the system. The model should be interpretable and as simple as practicably possible to help develop an understanding of the system. In certain applications computational efficiency is also important. A good choice of model and the one investigated in this thesis, is the neuro-fuzzy (NF) model. It consists of fuzzy sets that describe a system’s nonlinearity within partitions of the input space through local dynamic models. NF models combine the merits of interpretation capability and learning nonlinear relationships. This thesis proposes new approaches for the data driven modelling and control of nonlinear dynamic systems based on NF models.

In the first part of this thesis, a NF model with flexible input space partition and flat model structure is proposed. The input space partition is key to the NF model because it determines the structure, complexity and overall performance of the model. Axis-orthogonal splitting is the most common partitioning strategy. It is computationally efficient and easy to interpret due to the flat model structure however suffers from the curse of dimensionality. An axis-oblique partitioning strategy is proposed to solve this issue by splitting the input space flexibly based on the underlying nonlinear processes of the system. However the axis-oblique partition requires a hierarchical model structure, which significantly reduces model transparency. The proposed NF model combines the capability of both axis-oblique partitioning and a flat model structure by introducing nonlinear optimisation to tune the split position and direction during model training. Thus the advantages of effective input space partitioning and good model interpretation capability are combined. Consequently the proposed NF model describes the system more accurately with fewer local models under the parallel model structure facilitating controller design.

In addition, in order to realise online adaption of the NF model under coloured noise, a recursive generalised least squares (RGLS) algorithm is proposed which yields consistent and unbiased parameter estimates. This approach significantly improves the model’s ability to describe the dynamics of complex systems in certain time varying systems and where offline training data is insufficient to cover the whole system operating space. The convergence of the proposed RGLS algorithm is proven and the convergence rate is explicitly stated. The efficacy of the proposed RGLS-NF model is verified in a complex real world application.

The final topic considered is the design of a NF model predictive controller (NFMPC) and use of the parallel distributed compensation (PDC) law to achieve the parallel computation of control. The performance of MPC depends on the quality of the model however a complex and accurate model leads to expensive computation, limiting the ability of MPC to solve real world problems. PDC provides a solution to overcome the computational bottleneck through piecewise linearisation, however this leads to greater workload in controller design due to the complexity of the model. To realise the control of fast dynamic complex systems using MPC a PDC scheme based on the NF model is proposed. This scheme provides a good trade-off between control performance and system complexity. The efficacy of the proposed NFMPC is verified by solving an autonomous vehicle path tracking problem which is prototyped and studied using hardware-in-the-loop (HiL) simulation