Reachability analysis of discrete-time systems with disturbances

Published versio

Online Abstractions for Interconnected Multi-Agent Control Systems

In this report, we aim at the development of an online abstraction framework for multi-agent systems under coupled constraints. The motion capabilities of each agent are abstracted through a finite state transition system in order to capture reachability properties of the coupled multi-agent system over a finite time horizon in a decentralized manner. In the first part of this work, we define online abstractions by discretizing an overapproximation of the agents' reachable sets over the horizon. Then, sufficient conditions relating the discretization and the agent's dynamics properties are provided, in order to quantify the transition possibilities of each agent.Comment: 22 pages. arXiv admin note: text overlap with arXiv:1603.0478

Vehicle-in-the-loop validation of autonomous cars

Validation of autonomous driving (AD) cars is a difficult task because of the complexity that results from the integration of multiple systems and the variety of operating conditions. To this end, testing with real vehicles is crucial to ensure a thorough validation of AD cars. However, testing AD vehicles in public roads is not viable in early stages of the development cycle. An alternative is to conduct tests in controlled environments, such as proving grounds.This thesis proposes a framework for modelling, analysis, and control of tests-scenarios for validation of autonomous cars by exposing the vehicle-under-test to a traffic scenario at a test track, where mobile test-targets represent other road users. The framework is suitable for leader-follower, multi-agent systems where the motion of the followers should be coordinated with the motion of an externally controlled leader. Scenarios are modelled as switched systems. The feasibility of the scenario is investigated using backward reachability analysis. A constrained optimal control problem is formulated to control the state of the multi-agent system through a sequence of goal sets. Simulation results illustrate the usefulness of the framework.A second contribution in this thesis is a novel method for decentralized computation of backward reachable sets and robust control invariant sets. The method is applicable to large-scale systems arising from the interconnection of multiple subsystems with linear dynamics. Polyhedral constraints and additive disturbances are considered. Compared to the standard centralized procedure for computation of control invariant sets, the proposed method is more efficient for large-scale systems where the coupling among the subsystems is sparse

Sparse and Constrained Stochastic Predictive Control for Networked Systems

This article presents a novel class of control policies for networked control of Lyapunov-stable linear systems with bounded inputs. The control channel is assumed to have i.i.d. Bernoulli packet dropouts and the system is assumed to be affected by additive stochastic noise. Our proposed class of policies is affine in the past dropouts and saturated values of the past disturbances. We further consider a regularization term in a quadratic performance index to promote sparsity in control. We demonstrate how to augment the underlying optimization problem with a constant negative drift constraint to ensure mean-square boundedness of the closed-loop states, yielding a convex quadratic program to be solved periodically online. The states of the closed-loop plant under the receding horizon implementation of the proposed class of policies are mean square bounded for any positive bound on the control and any non-zero probability of successful transmission

Green Scheduling of Control Systems

Electricity usage under peak load conditions can cause issues such as reduced power quality and power outages. For this reason, commercial electricity customers are often subject to demand-based pricing, which charges very high prices for peak electricity demand. Consequently, reducing peaks in electricity demand is desirable for both economic and reliability reasons. In this thesis, we investigate the peak demand reduction problem from the perspective of safe scheduling of control systems under resource constraint. To this end, we propose Green Scheduling as an approach to schedule multiple interacting control systems within a constrained peak demand envelope while ensuring that safety and operational conditions are facilitated. The peak demand envelope is formulated as a constraint on the number of binary control inputs that can be activated simultaneously. Using two different approaches, we establish a range of sufficient and necessary schedulability conditions for various classes of affine dynamical systems. The schedulability analysis methods are shown to be scalable for large-scale systems consisting of up to 1000 subsystems. We then develop several scheduling algorithms for the Green Scheduling problem. First, we develop a periodic scheduling synthesis method, which is simple and scalable in computation but does not take into account the influence of disturbances. We then improve the method to be robust to small disturbances while preserving the simplicity and scalability of periodic scheduling. However the improved algorithm usually result in fast switching of the control inputs. Therefore, event-triggered and self-triggered techniques are used to alleviate this issue. Next, using a feedback control approach based on attracting sets and robust control Lyapunov functions, we develop event-triggered and self-triggered scheduling algorithms that can handle large disturbances affecting the system. These algorithms can also exploit prediction of the disturbances to improve their performance. Finally, a scheduling method for discrete-time systems is developed based on backward reachability analysis. The effectiveness of the proposed approach is demonstrated by an application to scheduling of radiant heating and cooling systems in buildings. Green Scheduling is able to significantly reduce the peak electricity demand and the total electricity consumption of the radiant systems, while maintaining thermal comfort for occupants