Event-based model predictive controllers

Abstract

This thesis, mainly lie within the area of Model Predictive Control (MPC) which is a well-known control methodology and the emerging field of event-based control. In particular, this work has been focused on event-based designs of various MPC schemes. Although MPC schemes have conspicuous advantages they are considered to be computationally demanding so it seems useful to update the optimal control recalculation as rarely as possible. To achieve that, we use event-based designs which appear to improve the requirements for computation resources (eg. more efficient resource allocation), and, at the same time, preserve the stability and the convergence properties of the system. Moreover, extensions on this approach can in fact be helpful in networks to decrease control traffic.In the early stages of our research we were first acquainted with the MPC framework for controlling real robotic systems. We applied the (Nonlinear)MPC framework and tackled the problem of driving a manipulator that initially does not interact with the environment to a desired position and then apply a desired force on a planar surface. The transition fromthe no-contact case to the contact case was smooth and no impact effects occurred, see Chapter $9$. Although MPC can be considered a natural candidate for more ``humane-like" control methodologies, it was apparent that it was computationally demanding. This realization led us to the question ``How often do we need to compute the control law?". At that point the idea of using the control trajectory that MPC provides in open-loop fashion when it is needed was already known. However, it did not provide guarantees on how large delays can be handled without resulting to instability.The event-based designs for general nonlinear systems was the framework that provided us with the theoretic tools to tackle the fundamental question on how large the inter-sampling times of Model Predictive Controllers can be. A stepping stone was to provide the general event-based control design that was presented for continuous systems, to its discrete-counterpart. That is given in Chapter 2, where an event-triggered strategy is proposed for general discrete-time systems and also more specific results are derived for linear discrete-time systems. Moreover, some results are given in the context of self-triggered control. The first approach for event-triggered MPC is also presented for linear systems.Using the above framework, in Chapter 3 we combine the event-triggered framework with MPC and derive some results on how often to compute the control law. The condition that is monitored in order to find whether or not the control law should be computed is not an ad-hoc criterion. On the contrary, the notion of Input-to-State stability (ISS) is used in order to derive a triggering condition which is based on a measurement error.This approach results to less conservative results in terms of computation, with respect to the traditional time-triggering scheme. Also,stability and convergence properties of the closed-loop system are preserved. In particular, we can derive that the system is ISS with respect to measurements errors and that the solution of the closed-loop system converges to a bounded set.Note also, that the systems in hand are constrained nonlinear systems subject to additive disturbances. In Chapter 3 the centralized, the decentralized case as well as the linear time invariant case are treated while in Chapter 4, the Event-Triggered MPC (ET-MPC) is utilized for deriving triggering conditions for a team of agents that are cooperating in a common environment.In the aforementioned Chapters we are considering dynamics in the discrete-time domain, while in Chapter 6 the continuous counterpart was presented. Note that, although the basic idea is the same (the goal is to compute less frequently the control law) the derivation is significantly different.In Chapter 5, an enhanced ET-MPC scheme is presented. The idea is to measure the error in order not only to check if the triggering condition still holds, but also to utilize this error in order to ``correct" the control input during the inter-sampling periods. This is achieved using tools from second variation methodologies (perturbation analysis).In the subsequent Chapters, the extension of the event-based MPC framework to a Self-Triggering MPC (ST-MPC) setup is presented. Using this framework the need for continuously measuring the error and checking the triggering condition is relaxed. Specific results on ST-MPC are given for an underwater nonholonomic vehicle, see Chapter 7. The validity of the results has been proven with an experiment in the Control Systems Laboratory, NTUA. Finally, in Chapter 8, a team of agents are considered, that are being controlled locally through ST-MPC. This set-up provides interesting results in terms of reduced communication between the agents.

H διατριβη αυτή εχει ασχοληθει με τα κατωθι:Α) Ανάπτυξη πλαισίου για μεθοδολογίες ελέγχου βασισμένες σε διεγέρσεις από συμβάντα σε συστήματα μη-γραμμικά αλλά και γραμμικά διακριτού χρόνου.Β) Δημιουργία πλαισίου για μεθοδολογίες προβλεπτικού ελέγχου βασισμένες σε διεγέρσεις από συμβάντα σε συστήματα μη-γραμμικά αλλά και γραμμικά, συγκεντρωμένα αλλά και απόκεντρωμένα, καθώς και σε συστήματα διακριτού αλλά και συνεχούς χρόνου τα οποία επηρεάζονται από διαταραχές.Γ) Δημιουργία πλαισίου για συνεργατικό προβλεπτικό έλεγχο πολλών πρακτόρων βασισμένο σε διεγέρσεις από συμβάντα.Δ) Δημιουργία πλαισίου για συνεργατικό προβλεπτικό έλεγχο ενός αλλά και πολλών μη ολονομικών πρακτόρων βασισμένο σε διεγέρσεις από το ίδιο το σύστημα.