Reverse Engineering Biological Control Systems for Applications in Process Control.

The main emphasis of this dissertation is the development of nonlinear control strategies based on biological control systems. Commonly utilized biological control schemes have been studied in order to reverse engineer the important concepts for applications in process control. This approach has led to the development of a nonlinear habituating control strategy and nonlinear model reference adaptive control schemes. Habituating control is a controller design strategy for nonlinear systems with more manipulated inputs than controlled outputs. Nonlinear control laws that provide input-output linearization while simultaneously minimizing the cost of affecting control are derived. Local stability analysis shows the controller can provide a simple solution to singularity and non-minimum phase problems. A direct adaptive control strategy for a class of single-input, single-output non-linear systems is presented. The major advantage is that a detailed dynamic non-linear model is not required for controller design. Unknown controller functions in the associated input-output linearizing control law are approximated using locally supported radial basis functions. Lyapunov stability analysis is used to derive parameter update laws which ensure the state vector remains bounded and the plant output asymptotically tracks the output of a linear reference model. A nonlinear model reference adaptive control strategy in which a linear model (or multiple linear models) is embedded within the nonlinear controller is presented. The nonlinear control law is constructed by embedding linear controller gains derived from models obtained using standard linear system identification techniques within the associated input-output linearizing control law. Higher-order controller functions are approximated with radial basis functions. Lyapunov stability analysis is used to derive stable parameter update laws. The major disadvantage of the previous techniques is computational expense. Two modifications have been developed. First, the effective dimension is reduced by applying nonlinear principal component analysis to the state variable data obtained from open-loop tests. This allows basis functions to be placed in a lower dimensional space than the original state space. Second, the total number of basis functions is fixed a priori and an algorithm which adds/prunes basis function centers to surround the current operating point on-line is utilized

Robust Adaptive Control for Nonlinear Discrete-Time Systems by Using Multiple Models

Back propagation (BP) neural network is used to approximate the dynamic character of nonlinear discrete-time system. Considering the unmodeling dynamics of the system, the weights of neural network are updated by using a dead-zone algorithm and a robust adaptive controller based on the BP neural network is proposed. For the situation that jumping change parameters exist, multiple neural networks with multiple weights are built to cover the uncertainty of parameters, and multiple controllers based on these models are set up. At every sample time, a performance index function based on the identification error will be used to choose the optimal model and the corresponding controller. Different kinds of combinations of fixed model and adaptive model will be used for robust multiple models adaptive control (MMAC). The proof of stability and convergence of MMAC are given, and the significant efficacy of the proposed methods is tested by simulation

Data-driven adaptive model-based predictive control with application in wastewater systems

This study is concerned with the development of a new data-driven adaptive model-based predictive controller (MBPC) with input constraints. The proposed methods employ subspace identification technique and a singular value decomposition (SVD)-based optimisation strategy to formulate the control algorithm and incorporate the input constraints. Both direct adaptive model-based predictive controller (DAMBPC) and indirect adaptive model-based predictive controller (IAMBPC) are considered. In DAMBPC, the direct identification of controller parameters is desired to reduce the design effort and computational load while the IAMBPC involves a two-stage process of model identification and controller design. The former method only requires a single QR decomposition for obtaining the controller parameters and uses a receding horizon approach to process input/output data for the identification. A suboptimal SVD-based optimisation technique is proposed to incorporate the input constraints. The proposed techniques are implemented and tested on a fourth order non-linear model of a wastewater system. Simulation results are presented to compare the direct and indirect adaptive methods and to demonstrate the performance of the proposed algorithms

Adaptive, cautious, predictive control with Gaussian process priors

Nonparametric Gaussian Process models, a Bayesian statistics approach, are used to implement a nonlinear adaptive control law. Predictions, including propagation of the state uncertainty are made over a k-step horizon. The expected value of a quadratic cost function is minimised, over this prediction horizon, without ignoring the variance of the model predictions. The general method and its main features are illustrated on a simulation example

Nonlinear adaptive control using non-parametric Gaussian Process prior models

Nonparametric Gaussian Process prior models, taken from Bayesian statistics methodology are used to implement a nonlinear adaptive control law. The expected value of a quadratic cost function is minimised, without ignoring the variance of the model predictions. This leads to implicit regularisation of the control signal (caution), and excitation of the system. The controller has dual features, since it is both tracking a reference signal and learning a model of the system from observed responses. The general method and its main features are illustrated on a simulation example