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895.2
Control Systems and Optimal Control
echoes the challenges raised from a philosophical perspective by Wallach and Allen [4], Lin
et al. [2] and Goodall [3]. This chapter begins with a brief introduction to principles of
optimal control and how ethical considerations map mathematically into costs or constraints.
The following sections discuss particular ethical reasoning relevant to automated vehicles
and whether these decisions are best formulated as costs or constraints. The choice depends
on a number of factors including the desire to weigh ethical implications against other pri-
orities and the information available to the vehicle in making the decision. Since the vehicle
must rely on limited and uncertain information, it may be more reasonable for the vehicle to
focus on avoiding collisions rather than attempting to determine the outcome of those colli-
sions or the resulting injury to humans. The chapter concludes with examples of ethical
constraints implemented as control laws and a reflection on whether human override and the
ubiquitous “big red button” are consistent with an ethical automated vehicle.
5.2 Control Systems and Optimal Control
Chapter 4 outlined some of the ethical frameworks applicable to automated vehicles. The
first step towards implementing these as control algorithms in a vehicle is to similarly
characterize the vehicle control problem in a general way. Figure. 5.1 illustrates a canonical
schematic representation of a closed-loop control system. The system consists of a plant,
or object to be controlled (in this case, an autonomous vehicle), a controller and a set of
goals or objectives to satisfy. The basic objective of control system design is to choose a
set of control inputs (brake, throttle, steering and gear position for a car) that will achieve
the desired goals. The resulting control laws, in general, consist of a priori knowledge
of the goals and a model of the vehicle (feedforward control) together with the means to
correct errors by comparing measurements of the environment and the actual vehicle
motion (feedback control).
Many approaches have been formulated over the years to produce control laws for dif-
ferent goals and different types of systems. One such method is optimal control, originally
developed for the control of rockets in seminal papers by Pontryagin and his colleagues [5].
Fig. 5.1 A schematic representation, or block diagram, of a control system showing how control
inputs derive from goals and feedback
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