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Abstract-This paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom. Control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the results; these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable.

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Reference and command governors are add-on control schemes which enforce state and control constraints on pre-stabilized systems by modifying, whenever necessary, the reference. This paper surveys the extensive literature concerning the development of such schemes for linear and nonlinear systems. The treatment of unmeasured disturbances and parametric uncertainties is also detailed. Generalizations, including extended command governors, feedforward reference governors, reduced order reference governors, parameter governors, networked reference governors, and decentralized/distributed reference governors, are discussed. Practical applications of these techniques are presented and surveyed as well. A comprehensive list of references is included. Connections with related approaches, including model predictive control and input shaping, are discussed. Opportunities and directions for future research are highlighted.

Discrete‐time, linear control systems with specified pointwise‐in‐time constraints, such as those imposed by actuator saturation, are considered. The constraints are enforced by the addition of a nonlinear ‘reference governor’ that attenuates, when necessary, the input commands. Because the constraints are satisfied, the control system remains linear and undesirable response effects such as instability due to saturation are avoided. The nonlinear action of the reference governor is defined in terms of a finitely determined maximal output admissible set and can be implemented on‐line for systems of moderately high order. The main result is global in nature: if the input command converges to a statically admissible input and the initial state of the system belongs to the maximal output admissible set, the eventual action of the reference governor is a unit delay.