Sliding-Mode Control Design for Nonlinear Systems Using Probability Density Function Shaping

Abstract

In this paper, we propose a sliding-mode-based stochastic distribution control algorithm for nonlinear systems, where the sliding-mode controller is designed to stabilize the stochastic system and stochastic distribution control tries to shape the sliding surface as close as possible to the desired probability density function. Kullback-Leibler divergence is introduced to the stochastic distribution control, and the parameter of the stochastic distribution controller is updated at each sample interval rather than using a batch mode. It is shown that the estimated weight vector will converge to its ideal value and the system will be asymptotically stable under the rank-condition, which is much weaker than the persistent excitation condition. The effectiveness of the proposed algorithm is illustrated by simulation.

Globally neural-adaptive simultaneous position and torque variable structure tracking control for permanent magnet synchronous motors

“…Figures 6 and 7) is achieved as compared with previous studies (e.g., Wang et al., 2012; El-Sousy, 2013; Kayacan, et al., 2013; Chang and Chan, 2014; Mulero-Martínez, 2012; Chen et al., 2014; Wang et al., 2014) which are only semi-globally ultimately bounded. No persistent excitation (e.g., Liu et al., 2014; Chen et al., 2014; Dai et al., 2014) is required for the global convergence of system state (cf. Figure 6(a)).…”

“…Based on the result of Theorem 2 , two lumped uncertainties (15a) and (15b) in a compact subset D(Z), which is the union of two compact subsets Di(Zi),i=1,2, and ∀t≥0, are assumed to be continuous and approximated by the following two neural-network models (e.g., Huang, 2012; El-Sousy, 2013; Kayacan, et al., 2013; Chang and Chan, 2014; Liu et al., 2014; Dai et al., 2014) where Z1(t)=X(t),Z2 T(t)=[XT(t)ueq T(t)], W¯i∈ℜLi×1 are unknown constant matrices which are not necessarily unique; Φi(Z…”

“…For approximating these non-autonomous uncertainties, they are assumed to be absolutely bounded for time variable and relatively bounded for other variables, respectively. Without the requirement of persistent excitation (PE) (e.g., Liu et al., 2014; Chen et al., 2014; Dai et al., 2014), the proposed GNASPTVSTC for a class of PMSMs is accomplished. Although only the PMSM is considered, the proposed control can be extended to a class of highly nonlinear dynamic systems.…”

“…(v) It not only improves the steady state performance as compared with robust control (e.g., SPTVSTC, PID control), but also enhances the system stability in the face of excess uncertainties. (vi) No persistent excitation for the learning neural network (e.g., Mulero-Martínez, 2012; Liu et al., 2014; Chen et al., 2014; Dai et al., 2014) is required for the global tracking control.…”

Adaptive Recurrent Neural Network Enhanced Variable Structure Control for Nonlinear Discrete Mimo Systems

“…To improve the performance of DVSC, the lumped uncertainties caused by uncertain system functions and external disturbances are learned on‐line by a recurrent neural network (RNN) and then compensated such that the switching gain in the DVSC can be smaller to deal with the remaining uncertainties. It is known that the RNN is more suitable for dynamic mapping than the multilayer neural network or radial basis function neural network. An RNN can cope with time‐varying input or output through its own natural temporal operation.…”