Provably safe cruise control of vehicular platoons

We synthesize performance-aware safe cruise control policies for longitudinal motion of platoons of autonomous vehicles. Using set-invariance theories, we guarantee infinite-time collision avoidance in the presence of bounded additive disturbances, while ensuring that the length and the cruise speed of the platoon are bounded within specified ranges. We propose: 1) a centralized control policy and 2) a distributed control policy, where each vehicle's control decision depends solely on its relative kinematics with respect to the platoon leader. Numerical examples are included.NSF; CPS-1446151; CMMI-1400167; FA 9550-15-1-0186 - AFOSR; Schlumberger Foundation Faculty for the Future Fellowship; FA 9550-15-1-0186 - AFOSR; NSF; ECCS-1550016; CNS 123922

Computation of Parameter Dependent Robust Invariant Sets for LPV Models with Guaranteed Performance

This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As the real-time measurements of the scheduling parameters are typically available, in the presented formulation, we allow the RCI set description along with the invariance-inducing controller to be scheduling parameter dependent. The considered formulation thus leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequality (LMI) conditions via Polya's relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. In addition to ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. The reported numerical example shows that the presented iterative algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting scheduling parameter information.Comment: 32 pages, 5 figure

Control of Constrained Dynamical Systems with Performance Guarantees: With Application to Vehicle motion Control

In control engineering, models of the system are commonly used for controller design. A standard control design problem consists of steering the given system output (or states) towards a predefined reference. Such a problem can be solved by employing feedback control strategies. By utilizing the knowledge of the model, these strategies compute the control inputs that shrink the error between the system outputs and their desired references over time. Usually, the control inputs must be computed such that the system output signals are kept in a desired region, possibly due to design or safety requirements. Also, the input signals should be within the physical limits of the actuators. Depending on the constraints, their violation might result in unacceptable system failures (e.g. deadly injury in the worst case). Thus, in safety-critical applications, a controller must be robust towards the modelling uncertainties and provide a priori guarantees for constraint satisfaction. A fundamental tool in constrained control application is the robust control invariant sets (RCI). For a controlled dynamical system, if initial states belong to RCI set, control inputs always exist that keep the future state trajectories restricted within the set. Hence, RCI sets can characterize a system that never violates constraints. These sets are the primary ingredient in the synthesis of the well-known constraint control strategies like model predictive control (MPC) and interpolation-based controller (IBC). Consequently, a large body of research has been devoted to the computation of these sets. In the thesis, we will focus on the computation of RCI sets and the method to generate control inputs that keep the system trajectories within RCI set. We specifically focus on the systems which have time-varying dynamics and polytopic constraints. Depending upon the nature of the time-varying element in the system description (i.e., if they are observable or not), we propose different sets of algorithms.The first group of algorithms apply to the system with time-varying, bounded uncertainties. To systematically handle the uncertainties and reduce conservatism, we exploit various tools from the robust control literature to derive novel conditions for invariance. The obtained conditions are then combined with a newly developed method for volume maximization and minimization in a convex optimization problem to compute desirably large and small RCI sets. In addition to ensuring invariance, it is also possible to guarantee desired closed-loop performance within the RCI set. Furthermore, developed algorithms can generate RCI sets with a predefined number of hyper-planes. This feature allows us to adjust the computational complexity of MPC and IBC controller when the sets are utilized in controller synthesis. Using numerical examples, we show that the proposed algorithms can outperform (volume-wise) many state-of-the-art methods when computing RCI sets.In the other case, we assume the time-varying parameters in system description to be observable. The developed algorithm has many similar characteristics as the earlier case, but now to utilize the parameter information, the control law and the RCI set are allowed to be parameter-dependent. We have numerically shown that the presented algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting parameter information.Lastly, we demonstrate how we can utilize some of these algorithms to construct a computationally efficient IBC controller for the vehicle motion control. The devised IBC controller guarantees to meet safety requirements mentioned in ISO 26262 and the ride comfort requirement by design

Computation of Robust Control Invariant Sets with Predefined Complexity for Uncertain Systems

This paper presents an algorithm that computes polytopic robust control-invariant (RCI) sets for rationally parameter-dependent systems with additive disturbances. By means of novel LMI feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user-defined level of complexity. Unlike many similar approaches, fixed state feedback structure is not imposed. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise-affine controller based on offline computations

Formal Synthesis of Control Strategies for Positive Monotone Systems

We design controllers from formal specifications for positive discrete-time monotone systems that are subject to bounded disturbances. Such systems are widely used to model the dynamics of transportation and biological networks. The specifications are described using signal temporal logic (STL), which can express a broad range of temporal properties. We formulate the problem as a mixed-integer linear program (MILP) and show that under the assumptions made in this paper, which are not restrictive for traffic applications, the existence of open-loop control policies is sufficient and almost necessary to ensure the satisfaction of STL formulas. We establish a relation between satisfaction of STL formulas in infinite time and set-invariance theories and provide an efficient method to compute robust control invariant sets in high dimensions. We also develop a robust model predictive framework to plan controls optimally while ensuring the satisfaction of the specification. Illustrative examples and a traffic management case study are included.Comment: To appear in IEEE Transactions on Automatic Control (TAC) (2018), 16 pages, double colum

Minimally Constrained Stable Switched Systems and Application to Co-simulation

We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by applications to (co-)simulation, where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.Comment: Technical report complementing the following conference publication: Gomes, Cl\'audio, Beno\^it Legat, Rapha\"el Jungers, and Hans Vangheluwe. "Minimally Constrained Stable Switched Systems and Application to Co-Simulation." In IEEE Conference on Decision and Control. Miami Beach, FL, USA, 201

Distributed Model Predictive Control Using a Chain of Tubes

A new distributed MPC algorithm for the regulation of dynamically coupled subsystems is presented in this paper. The current control action is computed via two robust controllers working in a nested fashion. The inner controller builds a nominal reference trajectory from a decentralized perspective. The outer controller uses this information to take into account the effects of the coupling and generate a distributed control action. The tube-based approach to robustness is employed. A supplementary constraint is included in the outer optimization problem to provide recursive feasibility of the overall controllerComment: Accepted for presentation at the UKACC CONTROL 2016 conference (Belfast, UK