Aiguo Wu

Distinguishing Lorenz and Chen Systems Based Upon Hamiltonian Energy Theory

Solving the linear first-order Partial Differential Equations (PDEs) derived from the unified Lorenz system, it is found that there is a unified Hamiltonian (energy function) for the Lorenz and Chen systems, and the unified energy function shows a hyperboloid of one sheet for the Lorenz system and an ellipsoidal surface for the Chen system in three-dimensional phase space, which can be used to explain that the Lorenz system is not equivalent to the Chen system. Using the unified energy function, we obtain two generalized Hamiltonian realizations of these two chaotic systems, respectively. Moreover, the energy function and generalized Hamiltonian realization of the Lu system and a four-dimensional hyperchaotic Lorenz-type system are also discussed.

Robust control of small-scale unmanned helicopter with matched and mismatched disturbances

Abstract In this paper, a novel robust control method for small-scale unmanned helicopter with matched and mismatched disturbances is investigated. The control objective is to make the helicopter track the predefined position and yaw angle reference trajectories. First, the helicopter model is linearized with approximate feedback linearization technique. Then, by using the estimation of the mismatched disturbances and their derivatives, the helicopter system is reconstructed to an equivalent system, where the mismatched disturbances are turned into the major matched component and minor mismatched component. These disturbances are suppressed by feedforward technique and H ∞ feedback control algorithm. Finally, simulation results demonstrate the effectiveness and robustness of the proposed control strategy for small-scale unmanned helicopter in the presence of both matched and mismatched disturbances. The proposed novel robust control method can attenuate the mismatched disturbances from the state variables of the reconstructed system.

Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points

Chaotic dynamics exists in many natural systems, such as weather and climate, and there are many applications in different disciplines. However, there are few research results about chaotic conservative systems especially the smooth hyperchaotic conservative system in both theory and application. This paper proposes a five-dimensional (5D) smooth autonomous hyperchaotic system with nonhyperbolic fixed points. Although the proposed system includes four linear terms and four quadratic terms, the new system shows complicated dynamics which has been proven by the theoretical analysis. Several notable properties related to conservative systems and the existence of perpetual points are investigated for the proposed system. Moreover, its conservative hyperchaotic behavior is illustrated by numerical techniques including phase portraits and Lyapunov exponents.

Species-Based Chaotic Hybrid Optimizing Algorithm and its Application in Image Detection

An evolutionary image-detection method based on a novel chaotic hybrid optimizing algorithm (CHOA) is proposed. The method combines the strengths of particle swarm optimization (PSO), genetic algorithms (GAs), and chaotic dynamics (CD), and involves the standard velocity and position update rules of PSOs with the ideas of selection, crossover, and mutation from GA. In addition, the notion of species is introduced into the proposed CHOA to enhance its performance in solving multimodal problems. The effectiveness of the species-based chaotic hybrid optimizing algorithm (SCHOA) is proven through simulations and benchmarking, and finally, it is successfully applied to solve a multitemplate matching (MTM) problem in the printed circuit board (PCB) industry, as well as circle-detection problems. To make it more powerful in solving circle-detection problems in complicated circumstances, the notion of “tolerant radius” is proposed and incorporated into the SCHOA method. Simulation tests were undertaken on several hand-drawn sketches and natural photos, and the effectiveness of the proposed method was clearly shown through the test results.