Stochastic Event-Based Control and Estimation

Digital controllers are traditionally implemented using periodic sampling, computation, and actuation events. As more control systems are implemented to share limited network and CPU bandwidth with other tasks, it is becoming increasingly attractive to use some form of event-based control instead, where precious events are used only when needed. Forms of event-based control have been used in practice for a very long time, but mostly in an ad-hoc way. Though optimal solutions to most event-based control problems are unknown, it should still be viable to compare performance between suggested approaches in a reasonable manner. This thesis investigates an event-based variation on the stochastic linear-quadratic (LQ) control problem, with a fixed cost per control event. The sporadic constraint of an enforced minimum inter-event time is introduced, yielding a mixed continuous-/discrete-time formulation. The quantitative trade-off between event rate and control performance is compared between periodic and sporadic control. Example problems for first-order plants are investigated, for a single control loop and for multiple loops closed over a shared medium. Path constraints are introduced to model and analyze higher-order event-based control systems. This component-based approach to stochastic hybrid systems allows to express continuous- and discrete-time dynamics, state and switching constraints, control laws, and stochastic disturbances in the same model. Sum-of-squares techniques are then used to find bounds on control objectives using convex semidefinite programming. The thesis also considers state estimation for discrete time linear stochastic systems from measurements with convex set uncertainty. The Bayesian observer is considered given log-concave process disturbances and measurement likelihoods. Strong log-concavity is introduced, and it is shown that the observer preserves log-concavity, and propagates strong log-concavity like inverse covariance in a Kalman filter. A recursive state estimator is developed for systems with both stochastic and set-bounded process and measurement noise terms. A time-varying linear filter gain is optimized using convex semidefinite programming and ellipsoidal over-approximation, given a relative weight on the two kinds of error

Iterative learning control: algorithm development and experimental benchmarking

This thesis concerns the general area of experimental benchmarking of Iterative Learning Control (ILC) algorithms using two experimental facilities. ILC is an approach which is suitable for applications where the same task is executed repeatedly over the necessarily finite time duration, known as the trial length. The process is reset prior to the commencement of each execution. The basic idea of ILC is to use information from previously executed trials to update the control input to be applied during the next one. The first experimental facility is a non-minimum phase electro-mechanical system and the other is a gantry robot whose basic task is to pick and place objects on a moving conveyor under synchronization and in a fixed finite time duration that replicates many tasks encountered in the process industries. Novel contributions are made in both the development of new algorithms and, especially, in the analysis of experimental results both of a single algorithm alone and also in the comparison of the relative performance of different algorithms. In the case of non-minimum phase systems, a new algorithm, named Reference Shift ILC (RSILC) is developed that is of a two loop structure. One learning loop addresses the system lag and another tackles the possibility of a large initial plant input commonly encountered when using basic iterative learning control algorithms. After basic algorithm development and simulation studies, experimental results are given to conclude that performance improvement over previously reported algorithms is reasonable. The gantry robot has been previously used to experimentally benchmark a range of simple structure ILC algorithms, such as those based on the ILC versions of the classical proportional plus derivative error actuated controllers, and some state-space based optimal ILC algorithms. Here these results are extended by the first ever detailed experimental study of the performance of stochastic ILC algorithms together with some modifications necessary to their configuration in order to increase performance. The majority of the currently reported ILC algorithms mainly focus on reducing the trial-to-trial error but it is known that this may come at the cost of poor or unacceptable performance along the trial dynamics. Control theory for discrete linear repetitive processes is used to design ILC control laws that enable the control of both trial-to-trial error convergence and along the trial dynamics. These algorithms can be computed using Linear Matrix Inequalities (LMIs) and again the results of experimental implementation on the gantry robot are given. These results are the first ever in this key area and represent a benchmark against which alternatives can be compared. In the concluding chapter, a critical overview of the results presented is given together with areas for both short and medium term further researc