https://www.fossen.biz/home/papers/JohansenFossen%20Automatica%202013.pdf

Control allocation—A survey

In this paper, we present two novel algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data. The algorithms have a number of common features. They are classified as one of the subspace model identification schemes, in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input-output data. This structure is then exploited in the calculation of a realization. Another common feature is their algorithmic organization: an RQ factorization followed by a singular value decomposition and the solution of an overdetermined set (or sets) of equations. The schemes assume that the underlying system has an output-error structure and that a measurable input sequence is available. The latter characteristic indicates that both schemes are versions of the MIMO Output-Error State Space model identification (MOESP) approach. The first algorithm is denoted in particular as the (elementary MOESP scheme)...

Subspace model identification-Part 1. The output-error state-space model identification class of algorithms

Autonomous vehicle field of study has seen considerable researches within three decades. In the last decade particularly, interests in this field has undergone tremendous improvement. One of the main aspects in autonomous vehicle is the path tracking control, focusing on the vehicle control in lateral and longitudinal direction in order to follow a specified path or trajectory. In this paper, path tracking control is reviewed in terms of the basic vehicle model usually used; the control strategies usually employed in path tracking control, and the performance criteria used to evaluate the controller's performance. Vehicle model is categorised into several types depending on its linearity and the type of behaviour it simulates, while path tracking control is categorised depending on its approach. This paper provides critical review of each of these aspects in terms of its usage and disadvantages/advantages. Each aspect is summarised for better overall understanding. Based on the critical reviews, main challenges in the field of path tracking control is identified and future research direction is proposed. Several promising advancement is proposed with the main prospect is focused on adaptive geometric controller developed on a nonlinear vehicle model and tested with hardware-in-the-loop (HIL). It is hoped that this review can be treated as preliminary insight into the choice of controllers in path tracking control development for an autonomous ground vehicle.

Modelling and Control Strategies in Path Tracking Control for Autonomous Ground Vehicles: A Review of State of the Art and Challenges

Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, ] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises Chapter 2: Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises Chapter 3: Lp-Spaces Convex functions and inequalities The Lp-spaces Approximation by continuous functions Exercises Chapter 4: Elementary Hilbert Space Theory Inner products and linear functionals Orthonormal sets Trigonometric series Exercises Chapter 5: Examples of Banach Space Techniques Banach spaces Consequences of Baire's theorem Fourier series of continuous functions Fourier coefficients of L1-functions The Hahn-Banach theorem An abstract approach to the Poisson integral Exercises Chapter 6: Complex Measures Total variation Absolute continuity Consequences of the Radon-Nikodym theorem Bounded linear functionals on Lp The Riesz representation theorem Exercises Chapter 7: Differentiation Derivatives of measures The fundamental theorem of Calculus Differentiable transformations Exercises Chapter 8: Integration on Product Spaces Measurability on cartesian products Product measures The Fubini theorem Completion of product measures Convolutions Distribution functions Exercises Chapter 9: Fourier Transforms Formal properties The inversion theorem The Plancherel theorem The Banach algebra L1 Exercises Chapter 10: Elementary Properties of Holomorphic Functions Complex differentiation Integration over paths The local Cauchy theorem The power series representation The open mapping theorem The global Cauchy theorem The calculus of residues Exercises Chapter 11: Harmonic Functions The Cauchy-Riemann equations The Poisson integral The mean value property Boundary behavior of Poisson integrals Representation theorems Exercises Chapter 12: The Maximum Modulus Principle Introduction The Schwarz lemma The Phragmen-Lindelof method An interpolation theorem A converse of the maximum modulus theorem Exercises Chapter 13: Approximation by Rational Functions Preparation Runge's theorem The Mittag-Leffler theorem Simply connected regions Exercises Chapter 14: Conformal Mapping Preservation of angles Linear fractional transformations Normal families The Riemann mapping theorem The class L Continuity at the boundary Conformal mapping of an annulus Exercises Chapter 15: Zeros of Holomorphic Functions Infinite Products The Weierstrass factorization theorem An interpolation problem Jensen's formula Blaschke products The Muntz-Szas theorem Exercises Chapter 16: Analytic Continuation Regular points and singular points Continuation along curves The monodromy theorem Construction of a modular function The Picard theorem Exercises Chapter 17: Hp-Spaces Subharmonic functions The spaces Hp and N The theorem of F. and M. Riesz Factorization theorems The shift operator Conjugate functions Exercises Chapter 18: Elementary Theory of Banach Algebras Introduction The invertible elements Ideals and homomorphisms Applications Exercises Chapter 19: Holomorphic Fourier Transforms Introduction Two theorems of Paley and Wiener Quasi-analytic classes The Denjoy-Carleman theorem Exercises Chapter 20: Uniform Approximation by Polynomials Introduction Some lemmas Mergelyan's theorem Exercises Appendix: Hausdorff's Maximality Theorem Notes and Comments Bibliography List of Special Symbols Index

Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)

Variable time delays exist between the driver's inputs and the responses of the vehicle dynamic states during a critical steering course. And due to the delay of active brake actuators, a sideslip or a rollover may occur even to a vehicle with a traditional stability control system. In addition, the unnecessary intervention of rollover prevention controller may deteriorate yaw stability of a vehicle in these situations. To mitigate the adverse effect of time delay on vehicle stability control and to realize coordinated stability control, a novel three-dimensional dynamic stability controller (3DDSC) is designed for yaw stability control, yaw–roll stability control and rollover prevention control. The framework consists of a supervisor, an upper controller, and a lower controller. A nonlinear vehicle model is used in the supervisor to predict the vehicle's future states and to determine the control mode and the related controllable areas with active brake method. Then model predictive control is used in the upper controller to calculate the desired tire forces of four wheels under the constraints of the given controllable area; then, the desired tire forces are realized by a lower hydraulic pressure controller. The proposed 3DDSC is evaluated with a CarSim–MATLAB cosimulation and hardware-in-the-loop simulation. The results show that 3DDSC can achieve a seamless integration of lateral stability and rollover prevention in complicated steering maneuvers.

A Three-Dimensional Dynamics Control Framework of Vehicle Lateral Stability and Rollover Prevention via Active Braking With MPC

Vehicle rollover accidents are a particularly dangerous form of road accident. Commercial vehicles are especially prone to rollover accidents due to their high centres of gravity. A nonlinear control strategy is presented which guarantees asymptotic tracking of a yaw rate reference while bounding the roll angle, thus preventing rollover. A new computationally-efficient control allocation strategy is used to map controller commands to braking forces, taking into account actuator constraints. Simulations show that the strategy is capable of preventing rollover of a commercial van during various standard test manoeuvres.

Vehicle dynamics control and controller allocation for rollover prevention

Vehicle dynamics control systems, previously only intended for yaw stabilization, are now being extended to incorporate rollover mitigation via braking. Current systems typically use a heuristic approach to control allocation, often utilizing only a subset of the available actuators. In this article a computationally-efficient, optimization-based control allocation strategy is used to map controller commands to braking forces on all four wheels, taking into account actuator constraints. Simulations show that the strategy is capable of preventing vehicle rollover for various standard test manoeuvres.

/pdf/optimal-control-allocation-in-vehicle-dynamics-control-for-3dkwlbun94.pdf

Optimal control allocation in vehicle dynamics control for rollover mitigation

Vehicle rollover accidents are a particularly dangerous form of road accident. Existing vehicle dynamics controllers primarily deal with yaw stability, and are of limited use for dealing with problems of roll instability. This thesis deals with the development of a new type of vehicle dynamics control system, capable of preventing rollover accidents caused by extreme maneuvering. A control strategy based on limitation of the roll angle while following a yaw rate reference is presented. Methods for rollover detection are investigated. A new computationally–efficient control allocation strategy based on convex optimization is used to map the controller commands to the individual braking forces, taking into account actuator constraints. Simulations show that the strategy is capable of preventing rollover of a commercial van during various standard test maneuvers. (Less)

/pdf/vehicle-dynamics-control-for-rollover-prevention-2j32xqik44.pdf

Vehicle Dynamics Control for Rollover Prevention

The functionality of modern automotive vehicles is becoming increasingly dependent on control systems. Active safety is an area in which control systems play a pivotal role. Currently, rule-based control algorithms are widespread throughout the automotive industry. In order to improve performance and reduce development time, model-based methods may be employed. The primary contribution of this thesis is the development of a vehicle dynamics controller for rollover mitigation. A central part of this work has been the investigation of control allocation methods, which are used to transform high-level controller commands to actuator inputs in the presence of numerous constraints. Quadratic programming is used to solve a static optimization problem in each sample. An investigation of the numerical methods used to solve such problems was carried out, leading to the development of a modified active set algorithm. Vehicle dynamics control systems typically require input from a number of supporting systems, including observers and estimation algorithms. A key parameter for virtually all VDC systems is the friction coefficient. Model-based friction estimation based on the physically-derived brush model is investigated (A).

/pdf/model-based-vehicle-dynamics-control-for-active-safety-4tcwxa0ei0.pdf

Model-Based Vehicle Dynamics Control for Active Safety

We consider a linear single-track model of a truck-dolly-semitrailer by deriving Lagrange's equations with
the quasi-coordinates chosen as the body fixed longitudinal and lateral velocity of the truck, vx1 and vy1,
respectively, the yaw angle of the truck and the articulation angles of the dolly and the semi-trailer. The linear analysis and simulations are
carried out with a constant longitudinal velocity of 80 Kph for the passive vehicle, i.e. no steering on the dolly
or semitrailer. The analysis shows an increase in yaw rate gain for the dolly and semitrailer, compared to the
truck, for frequencies around 0.4 Hz on the truck steering angle. That is, we have a yaw rate RWA higher
than 1 when for frequencies around 0.4 Hz. We also observe a lateral acceleration gain, between 0.1 and 1 Hz,
for the dolly and semitrailer. Moreover, the phase angle has a higher frequency dependence for the dolly and
semitrailer both for yaw rate and lateral acceleration. Time simulations shows that the dolly and semitrailer
experience a time delay and an overshoot when the vehicle combination is subjected to various steering angle
maneuvers. This indicates that the vehicle combination is not as stable as the truck alone.

https://publications.lib.chalmers.se/records/fulltext/local_142991.pdf

Brad Schofield

Papers

Vehicle dynamics control and controller allocation for rollover prevention

Optimal control allocation in vehicle dynamics control for rollover mitigation

Vehicle Dynamics Control for Rollover Prevention

Model-Based Vehicle Dynamics Control for Active Safety

Derivation of linear single-track truck-dolly-semitrailer model with steerable axles