A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Macroscopic modelling and robust control of bi-modal multi-region urban road networks

The paper concerns the integration of a bi-modal Macroscopic Fundamental Diagram (MFD) modelling for mixed traffic in a robust control framework for congested single- and multi-region urban networks. The bi-modal MFD relates the accumulation of cars and buses and the outflow (or circulating flow) in homogeneous (both in the spatial distribution of congestion and the spatial mode mixture) bi-modal traffic networks. We introduce the composition of traffic in the network as a parameter that affects the shape of the bi-modal MFD. A linear parameter varying model with uncertain parameter the vehicle composition approximates the original nonlinear system of aggregated dynamics when it is near the equilibrium point for single- and multi-region cities governed by bi-modal MFDs. This model aims at designing a robust perimeter and boundary flow controller for single- and multi-region networks that guarantees robust regulation and stability, and thus smooth and efficient operations, given that vehicle composition is a slow time-varying parameter. The control gain of the robust controller is calculated off-line using convex optimisation. To evaluate the proposed scheme, an extensive simulation-based study for single- and multi-region networks is carried out. To this end, the heterogeneous network of San Francisco where buses and cars share the same infrastructure is partitioned into two homogeneous regions with different modes of composition. The proposed robust control is compared with an optimised pre-timed signal plan and a single-region perimeter control strategy. Results show that the proposed robust control can significantly: (i) reduce the overall congestion in the network; (ii) improve the traffic performance of buses in terms of travel delays and schedule reliability, and; (iii) avoid queues and gridlocks on critical paths of the network

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

Gain-scheduling LPV control for autonomous vehicles including friction force estimation and compensation mechanism

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This study presents a solution for the integrated longitudinal and lateral control problem of urban autonomousvehicles. It is based on a gain-scheduling linear parameter-varying (LPV) control approach combined with the use of anUnknown Input Observer (UIO) for estimating the vehicle states and friction force. Two gain-scheduling LPV controllers are usedin cascade configuration that use the kinematic and dynamic vehicle models and the friction and observed states provided bythe Unknown Input Observer (UIO). The LPV–UIO is designed in an optimal manner by solving a set of linear matrix inequalities(LMIs). On the other hand, the design of the kinematic and dynamic controllers lead to solve separately two LPV–LinearQuadratic Regulator problems formulated also in LMI form. The UIO allows to improve the control response in disturbanceaffected scenarios by estimating and compensating the friction force. The proposed scheme has been integrated with atrajectory generation module and tested in a simulated scenario. A comparative study is also presented considering the casesthat the friction force estimation is used or not to show its usefulnessPeer ReviewedPostprint (author's final draft

Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system