SummaryThis paper presents a fast terminal sliding-mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time-varying disturbances. Fast terminal sliding-mode finite-time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite-time control effort, the fast terminal sliding-mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high-precision output tracking performance in uncertain nonlinear systems. KEYWORDS differential evolution, differentiator, nonlinear systems, terminal sliding mode, tracking | INTRODUCTIONSliding-mode control (SMC) is an efficient control scheme and has been widely applied in nonlinear systems. Sliding-mode control has many attractive features such as insensitivity to the model errors and parametric uncertainties.1,2 Given its advantages, SMC provides powerful techniques to complicated nonlinear dynamic systems for tracking control, including robotic manipulator systems, 3 active suspension vehicle systems, 4 induction motor drive systems, 5,6 power systems, 7 and spacecraft systems. The tracking problems using evolutionary optimization in complicated nonlinear systems attract much more attention. Evolutionary optimization algorithms are considered as a powerful optimization tool in solving nonlinear and complicated search spaces.9 Sliding-mode control combined with evolutionary optimization algorithms is presented to improve the tracking performances for complicated nonlinear systems, such as genetic algorithms 10 and particle swarm algorithms. 11,12 These methods have difficulty solving a class of nonlinear tracking problems of unknown system states with time-varying disturbances, which causes an impact on the convergence and stability of the tracking systems.In limited situations, the system states are unknown and needs to be estimated. Along with time-varying disturbances, the differential evolution (DE) optimization algorithm using an integral chain differentiator (ICD) proposed in

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The spine of mammals aids in the stability of locomotion. Central Pattern Generators (CPGs) located in spinal cord can rapidly provide a rhythmic output signal during loss of sensory feedback on the basis of a simulated quadruped agent. In this paper, active spine of quadruped robot is shown to be extremely effective in motion. An active spine model based on the Parallel Kinematic Mechanism (PKM) system and biological phenomena is described. The general principles involved in constructing a neural network coupled with limbs and spine to solve specific problems are discussed. A CPG mathematical model based on Hopf nonlinear oscillators produces rhythmic signal during locomotion is described, where many parameters to be solved must be formulated in terms of desired stability, often subject to vertical stability analysis. Our simulations demonstrate that active spine with setting reasonable CPG parameters can reduce unnecessary lateral displacement during trot gait, improving the stability of quadruped robot. In addition, we demonstrate that physical prototype mechanism provides a framework which shows correctness of simulation, and stability can thus be easily embodied within locomotion.