A Kalman-Yakubovich-Popov-type lemma for systems with certain state-dependent constraints

In this note, a result is presented that may be considered an extension of the classical Kalman-Yakubovich-Popov (KYP) lemma. Motivated by problems in the design of switched systems, we wish to infer the existence of a quadratic Lyapunov function (QLF) for a nonlinear system in the case where a matrix defining one system is a rank-1 perturbation of the other and where switching between the systems is orchestrated according to a conic partitioning of the state space IRn. We show that a necessary and sufficient condition for the existence of a QLF reduces to checking a single constraint on a sum of transfer functions irrespective of problem dimension. Furthermore, we demonstrate that our conditions reduce to the classical KYP lemma when the conic partition of the state space is IRn, with the transfer function condition reducing to the condition of Strict Positive Realness

Topics in Automotive Rollover Prevention: Robust and Adaptive Switching Strategies for Estimation and Control

The main focus in this thesis is the analysis of alternative approaches for estimation and control of automotive vehicles based on sound theoretical principles. Of particular importance is the problem rollover prevention, which is an important problem plaguing vehicles with a high center of gravity (CG). Vehicle rollover is, statistically, the most dangerous accident type, and it is difficult to prevent it due to the time varying nature of the problem. Therefore, a major objective of the thesis is to develop the necessary theoretical and practical tools for the estimation and control of rollover based on robust and adaptive techniques that are stable with respect to parameter variations. Given this background, we first consider an implementation of the multiple model switching and tuning (MMST) algorithm for estimating the unknown parameters of automotive vehicles relevant to the roll and the lateral dynamics including the position of CG. This results in high performance estimation of the CG as well as other time varying parameters, which can be used in tuning of the active safety controllers in real time. We then look into automotive rollover prevention control based on a robust stable control design methodology. As part of this we introduce a dynamic version of the load transfer ratio (LTR) as a rollover detection criterion and then design robust controllers that take into account uncertainty in the CG position. As the next step we refine the controllers by integrating them with the multiple model switched CG position estimation algorithm. This results in adaptive controllers with higher performance than the robust counterparts. In the second half of the thesis we analyze extensions of certain theoretical results with important implications for switched systems. First we obtain a non-Lyapunov stability result for a certain class of linear discrete time switched systems. Based on this result, we suggest switched controller synthesis procedures for two roll dynamics enhancement control applications. One control design approach is related to modifying the dynamical response characteristics of the automotive vehicle while guaranteeing the switching stability under parametric variations. The other control synthesis method aims to obtain transient free reference tracking of vehicle roll dynamics subject to parametric switching. In a later discussion, we consider a particular decentralized control design procedure based on vector Lyapunov functions for simultaneous, and structurally robust model reference tracking of both the lateral and the roll dynamics of automotive vehicles. We show that this controller design approach guarantees the closed loop stability subject to certain types of structural uncertainty. Finally, assuming a purely theoretical pitch, and motivated by the problems considered during the course of the thesis, we give new stability results on common Lyapunov solution (CLS) existence for two classes of switching linear systems; one is concerned with switching pair of systems in companion form and with interval uncertainty, and the other is concerned with switching pair of companion matrices with general inertia. For both problems we give easily verifiable spectral conditions that are sufficient for the CLS existence. For proving the second result we also obtain a certain generalization of the classical Kalman-Yacubovic-Popov lemma for matrices with general inertia

A framework for integrating multi-accuracy spatial data in geographical applications

In recent years the integration of spatial data coming from different sources has become a crucial issue for many geographical applications, especially in the process of building and maintaining a Spatial Data Infrastructure (SDI). In such context new methodologies are necessary in order to acquire and update spatial datasets by collecting new measurements from different sources. The traditionalapproach implemented in GIS systems for updating spatial data does not usually consider the accuracy of these data, but just replaces the old geometries with the new ones. The application of such approach in the case of an SDI, where continuous and incremental updates occur, will lead very soon to an inconsistent spatial dataset withrespect to spatial relations and relative distances among objects. This paper addresses such problem and proposes a framework for representing multi-accuracy spatial databases, based on a statistical representation of the objects geometry, together with a method for the incremental and consistent update of the objects, that applies acustomized version of the Kalman filter.Moreover, the framework considers also the spatial relations among objects, since they represent a particular kind of observation that could be derived from geometries or be observed independently in the real world. Spatial relations among objects need also to be compared in spatial dataintegration and we show that they are necessary in order to obtain a correct result in merging objects geometries

Model-based control for automotive applications

The number of distributed control systems in modern vehicles has increased exponentially over the past decades. Today’s performance improvements and innovations in the automotive industry are often resolved using embedded control systems. As a result, a modern vehicle can be regarded as a complex mechatronic system. However, control design for such systems, in practice, often comes down to time-consuming online tuning and calibration techniques, rather than a more systematic, model-based control design approach. The main goal of this thesis is to contribute to a corresponding paradigm shift, targeting the use of systematic, model-based control design approaches in practice. This implies the use of control-oriented modeling and the specification of corresponding performance requirements as a basis for the actual controller synthesis. Adopting a systematic, model-based control design approach, as opposed to pragmatic, online tuning and calibration techniques, is a prerequisite for the application of state-of-the-art controller synthesis methods. These methods enable to achieve guarantees regarding robustness, performance, stability, and optimality of the synthesized controller. Furthermore, from a practical point-of-view, it forms a basis for the reduction of tuning and calibration effort via automated controller synthesis, and fulfilling increasingly stringent performance demands. To demonstrate these opportunities, case studies are defined and executed. In all cases, actual implementation is pursued using test vehicles and a hardware-in-the-loop setup. • Case I: Judder-induced oscillations in the driveline are resolved using a robustly stable drive-off controller. The controller prevents the need for re-tuning if the dynamics of the system change due to wear. A hardware-in-the-loop setup, including actual sensor and actuator dynamics, is used for experimental validation. • Case II: A solution for variations in the closed-loop behavior of cruise control functionality is proposed, explicitly taking into account large variations in both the gear ratio and the vehicle loading of heavy duty vehicles. Experimental validation is done on a heavy duty vehicle, a DAF XF105 with and without a fully loaded trailer. • Case III: A systematic approach for the design of an adaptive cruise control is proposed. The resulting parameterized design enables intuitive tuning directly related to comfort and safety of the driving behavior and significantly reduces tuning effort. The design is validated on an Audi S8, performing on-the-road experiments. • Case IV: The design of a cooperative adaptive cruise control is presented, focusing on the feasibility of implementation. Correspondingly, a necessary and sufficient condition for string stability is derived. The design is experimentally tested using two Citroën C4’s, improving traffic throughput with respect to standard adaptive cruise control functionality, while guaranteeing string stability of the traffic flow. The case studies consider representative automotive control problems, in the sense that typical challenges are addressed, being variable operating conditions and global performance qualifiers. Based on the case studies, a generic classification of automotive control problems is derived, distinguishing problems at i) a full-vehicle level, ii) an in-vehicle level, and iii) a component level. The classification facilitates a characterization of automotive control problems on the basis of the required modeling and the specification of corresponding performance requirements. Full-vehicle level functionality focuses on the specification of desired vehicle behavior for the vehicle as a whole. Typically, the required modeling is limited, whereas the translation of global performance qualifiers into control-oriented performance requirements can be difficult. In-vehicle level functionality focuses on actual control of the (complex) vehicle dynamics. The modeling and the specification of performance requirements are typically influenced by a wide variety of operating conditions. Furthermore, the case studies represent practical application examples that are specifically suitable to apply a specific set of state-of-the-art controller synthesis methods, being robust control, model predictive control, and gain scheduling or linear parameter varying control. The case studies show the applicability of these methods in practice. Nevertheless, the theoretical complexity of the methods typically translates into a high computational burden, while insight in the resulting controller decreases, complicating, for example, (online) fine-tuning of the controller. Accordingly, more efficient algorithms and dedicated tools are required to improve practical implementation of controller synthesis methods

Data-driven estimation of the maximum sampling interval: analysis and controller design for discrete-time systems

This article is concerned with data-driven analysis of discrete-time systems under aperiodic sampling, and in particular with a data-driven estimation of the maximum sampling interval (MSI). The MSI is relevant for analysis of and controller design for cyber-physical, embedded and networked systems, since it gives a limit on the time span between sampling instants such that stability is guaranteed. We propose tools to compute the MSI for a given controller and to design a controller with a preferably large MSI, both directly from a finite-length, noise-corrupted state-input trajectory of the system. We follow two distinct approaches for stability analysis, one taking a robust control perspective and the other a switched systems perspective on the aperiodically sampled system. In a numerical example and a subsequent discussion, we demonstrate the efficacy of our developed tools and compare the two approaches.Comment: 16 pages, 4 figure, 1 table. Now contains 1) a disturbance description via multipliers, 2) extended proofs and 3) an extensive numerical case study, including a comparison of different data lengths, a discussion of complexity and a comparison with set membership estimatio