Introduction As the development of the aircraft

Introduction As the development of the aircraft technology, for superior maneuver and reliability, more and more advanced aircraft, even unmanned aerial vehicles and missiles, deploy multiple and redundant effectors on their bodies. Therefore, an appropriate control allocation method is necessary for the control systems of these aircraft to use their effectors efficiently. Control allocation is a hot issue in the field of flight control. Many methods have been proposed for solving various control allocation problems [1]. Most of the time, the control allocation problem can be represented as an optimization problem. Therefore, the designed control allocation methods are usually based on some optimization methods. For an aircraft, its control allocation problem is apparently related to its effectors. Sometimes some unconventional effectors will make the control allocation problem different from the conventional problems and difficult to be solved. A characteristic example is the innovative control β(1,3)-d-glucan synthase (ICE) aircraft which is introduced by Lockheed Martin Tactical Aircraft Systems [2]. This aircraft uses several distributed arrays each of which contains lots of actuators as effectors. The particularity is that each actuator can only provide either full or no control energy [3]. We can group those actuators which have almost the same full control energies together and then the control allocation problem of the ICE aircraft can be translated into an integer programming problem with some constraints. Actually, the integer constraints are present in many aircraft effectors, such as the reaction control system (RCS) and so on. Different from the normal linear programming or quadratic programming problem, most of the integer programming problems are non-deterministic polynomial hard (NP-hard) problems and their optimum solutions are usually hard to be obtained. Some classical methods, such as the branch-bound method and cutting plane method, are usually used to solve the integer linear programming problem and they are effective when the scale of the problem is small. However, with the increase of the scale of the problem, the computational complexities of the classical methods will increase rapidly and cannot meet the practical requirements. Therefore, the metaheuristic algorithms have attracted more and more attentions. There have been recently many studies using metaheuristic algorithms to solve aircraft control allocation problems [4–7]. The cuckoo search algorithm (CSA) is a relatively novel and promising metaheuristic algorithm proposed by Yang and Deb [8]. Some studies have demonstrated that its search capability is better than many other metaheuristic algorithms [9,10]. Therefore, the CSA has been applied to many application domains, such as parallel machine scheduling [11], total cost of ownership for supplier selection problem [12], maximum power point tracking for Photovoltaic System [13] and structural damage identification [14]. However, the efficiency of the basic CSA is still unsatisfactory. Therefore, the algorithm need be improved when medusa is used. In this paper, an improved CSA is proposed for solving the aircraft control allocation problem with integer constraints. The remaining sections of this paper are organized as follows. Section 2 describes the aircraft control allocation problem with integer constraints. Section 3 formulates the design of the control allocation method based on an improved CSA. The simulation results established upon the proposed method and some compared methods are given in Section 4. Finally, some concluding remarks are summarized in Section 5.
Problem formulation
Design of control allocation method
Simulation In this section, the effectiveness of the proposed improved CSA in aircraft control allocation is verified. The control allocation method based on the proposed algorithm is applied to the ICE aircraft linearized lateral-directional model which can be described via Eq. (1). The states can be defined as where represents the body-axis lateral velocity, and represent the body-axis roll rate, yaw rate and roll angle, respectively. The configuration is illustrated in Fig. 1.