Efficient algorithms for embedded optimisation-based control

Solving optimisation problem is computationally demanding, and hence Model Predictive Control (MPC), an optimisation-based control technology, is traditionally employed in applications with slow dynamics. In recent years, due to its ability to systematically handling constraints and multiple-input and multiple-output systems, MPC has been extended to many non-traditional areas, in particular networked or embedded applications. However, limited computational resources poses challenges for embedded implementation of MPC. Computational resources to solve MPC problem may be time-varying and insufficient at times. Moreover, the measurements transmitted through a communication network may be unavailable due to network congestion or packet dropouts. To enable MPC be more widely used in networked or embedded applications, this thesis addresses two aspects: (1) methods to efficiently solve the optimisation problem in embedded platforms and (2) methods to tackle time-varying computational resources. System of linear equations with the saddle point type is the main computational load in some MPC-tailored algorithms. Existing MPC-tailored algorithms have not exploited banded null bases in the sparse MPC formulation. In this thesis, an algorithm for exploiting banded null bases is presented. The proposed algorithm is tested with a wide range of MPC benchmark problems. Implementation results on an industrial embedded platform confirm that significant reduction in the runtime for the Alternating Direction Method of Multipliers (ADMM) can be achieved by the proposed algorithm. Methods for improving the conditioning of the banded bases are also developed. Event-triggered Sequence-based Anytime Control (E-SAC), recently proposed in the literature, can handle the time-varying computational resources effectively. The main idea of E-SAC is, when computing resources and measurements are available, to compute a sequence of tentative control inputs and store them in a buffer for potential future use. Existing E-SAC in the literature only features one control law in the buffer. In this thesis, E-SAC is extended to schemes featuring multiple control laws. Numerical simulations show that performance in terms of empirical closed-loop cost, channel utilisation and regions for stochastic stability guarantees could be improved, compared with the existing E-SAC. However, the current stability analysis framework for E-SAC, the State-dependent Random-time Drift approach, becomes combinatoric and difficult to use when extending to the multi-control law E-SAC. To overcome this, a new stability analysis method for E-SAC based on Markov jump system is developed. Using the proposed stability analysis method, stochastic stability conditions of existing E-SAC are also recovered as a special case. In addition, the proposed technique systematically extends to other more sophisticated E-SAC scheme for which, until now, no analytical expression had been obtained. Doctor of Philosophy