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: PDF (409 KB)

**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

ISSN : 1796-203X

Volume : 3 Issue : 9 Date : September 2008

Hopping Robot

Page(s): 50-57

Full Text: PDF (409 KB)

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.

regulation, hopping robot