Efficient Real-Time Solutions for Nonlinear Model Predictive Control with Applications

Nonlinear Model Predictive Control is an advanced optimisation methodology widely used for developing optimal Feedback Control Systems that use mathematical models of dynamical systems to predict and optimise their future performance. Its popularity comes from its general ability to handle a wide range of challenges present when developing control systems such as input/output constraints, complex nonlinear dynamics multi-variable systems, dynamic systems with significant delays as well as handling of uncertainty, disturbances and fault-tolerance. One of the main and most important challenges is the computational burden associated with the optimisation, particularly when attempting to implement the underlying methods in fast/real-time systems. To tackle this, recent research has been focused on developing efficient real-time solutions or strategies that could be used to overcome this problem. In this case, efficiency may come in various different ways from mathematical simplifications, to fast optimisation solvers, special algorithms and hardware, as well as tailored auto-generated coding tool-kits which help to make an efficient overall implementation of these type of approaches. This thesis addresses this fundamental problem by proposing a wide variety of methods that could serve as alternatives from which the final user can choose from depending on the requirements specific to the application. The proposed approaches focus specifically of developing efficient real-time NMPC methods which have a significantly reduced computational burden whilst preserving desirable properties of standard NMPC such as nominal stability, recursive feasibility guarantees, good performance, as well as adequate numeric conditioning for their use in platforms with reduced numeric precision such as ``floats'' subject to certain conditions being met. One of the specific aims of this work is to obtain faster solutions than the popular ACADO toolkit, in particular when using condensing-based NMPC solutions under the Real-Time Iteration Scheme, considered for all practical purposes the state-of-the-art standard real-time solution to which all the approaches will be bench-marked against. Moreover, part of the work of this thesis uses the concept of ``auto-generation'' for developing similar tool-kits that apply the proposed approaches. To achieve this, the developed tool-kits were supported by the Eigen 3 library which were observed to result in even better computation times than the ACADO toolkit. Finally, although the work undertaking by this thesis does not look into robust control approaches, the developed methods could be used for improving the performance of the underlying ``online'' optimisation, eg. by being able to perform additional iterations of the underlying SQP optimisation, as well as be used in common robust frameworks where multi-model systems must be simultaneously optimised in real-time. Thus, future work will look into merging the proposed methods with other existing strategies to give an even wider range of alternatives to the final user.