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Abstract-In this paper we address the actuator/sensor allocation problem for linear time invariant (LTI) systems. Given the structure of an autonomous linear dynamical system, the goal is to design the structure of the input matrix (commonly denoted by B) such that the system is structurally controllable with the restriction that each input be dedicated, i.e., it can only control directly a single state variable. We provide a methodology that addresses this design question: specifically, we determine the minimum number of dedicated inputs required to ensure such structural controllability, and characterize, and characterizes all (when not unique) possible configurations of the minimal input matrix B. Furthermore, we show that the proposed solution methodology incurs polynomial complexity in the number of state variables. By duality, the solution methodology may be readily extended to the structural design of the corresponding minimal output matrix (commonly denoted by C) that ensures structural observability.

This paper addresses the design of Model Predictive Control (MPC) laws to solve the trajectory-tracking problem and the path-following problem for constrained underactuated vehicles. By allowing an arbitrarily small asymptotic tracking error, we derive MPC laws where the size of the terminal set is only limited by the size of the system constraints. In fact, for the case of unconstrained inputs, the terminal set can be neglected and the resulting MPC controllers provide a global solution to the addressed constrained motion control problems. Simulation results are presented where the proposed MPC controllers are applied to 2-D and to 3-D moving vehicles.

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