JOURNAL OF COMPUTERS (JCP)
ISSN : 1796-203X
Volume : 3    Issue : 9    Date : September 2008

An Efficient Finite-Input Receding Horizon Control Method and Its Application for the Pneumatic
Hopping Robot
Jian Wu and Sherif Abdelwahed
Page(s): 50-57
Full Text:
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Abstract
In this paper, a finite-input receding horizon controller (FIRHC) is proposed as motivated by the
need to use solenoid valves to control the motion of a pneumatic hoping robot. The controller aims
to the application on switching control systems in which only a finite number of control inputs are
available. The controller utilizes a model to predict system behavior along a finite forward horizon,
and establishes an optimization problem, and then finds an optimal control sequence that gives the
optimal cost and ultimately only the first element of the sequence is applied at each time step. The
stability issue of the controller is discussed as a terminal equality constraint is added. Since only
finite discrete inputs exist, the analytical solution is usually not possible to achieve, and exhaustive
search was generally the approach to get the optimal control input. As is known, the exhaustive
search becomes computationally prohibitive with an increasingly long horizon. An efficient modified
depth first search algorithm is proposed, namely, sorted depth first search (sDFS). It preserves the
completeness of exhaustive search, while significantly reducing time and space complexity. The
whole approach is applied to a pneumatic hopping robot system where the motion control is
re-formulated as an explicit energy regulation problem. The control goal is to maintain the system
energy at a desired level. An additional example on a three tank control system is used to further
illustrate the efficiency of sDFS method on the system with possession of a relatively large amount
of modes. Simulation results demonstrate the effectiveness of the proposed method.

Index Terms
receding horizon control, switching systems, finite control set, sorted depth first search, energy
regulation, hopping robot