Regulating Constraint-Following Bound for Fuzzy Mechanical Systems: Indirect Robust Control and Fuzzy Optimal Design

This article proposes an optimal indirect approach of constraint-following control for fuzzy mechanical systems. The system contains (possibly fast) time-varying uncertainty that lies in a fuzzy set. It aims at an optimal controller for the system to render bounded constraint-following error such that it can stay within a predetermined bound at all time and be sufficiently small eventually. First, for deterministic performance, the original system is transformed into a constructed system. A deterministic (not the usual IF-THEN rules-based) robust control is then designed for the constructed system to render it to be uniformly bounded and uniformly ultimately bounded, regardless of the uncertainty. Second, for optimal performance, a performance index, including the average fuzzy system performance and control effort, is proposed based on the fuzzy information. An optimal design problem associated with the control gain is then formulated and solved by minimizing the performance index. Finally, it is proved when the constructed system renders uniform boundedness and uniform ultimate boundedness, the original system achieves the desired performance of bounded constraint following.

Multiple Lyapunov Functions for Adaptive Neural Tracking Control of Switched Nonlinear Nonlower-Triangular Systems

In this paper, the problem of adaptive neural tracking control for a type of uncertain switched nonlinear nonlower-triangular system is considered. The innovations of this paper are summarized as follows: 1) input to state stability of unmodeled dynamics is removed, which is an indispensable assumption for the design of nonswitched unmodeled dynamic systems; 2) the design difficulties caused by the nonlower-triangular structure is handled by applying the universal approximation ability of radial basis function neural networks and the inherent properties of Gaussian functions, which avoids the restriction that the monotonously increasing bounding functions of the nonlower-triangular system functions must exist; and 3) multiple Lyapunov functions are utilized to develop a backstepping-like recursive design procedure such that the solvability of the adaptive neural tracking control issue of all subsystems is unnecessary. Based on the proposed controller design methods, it can be obtained that all signals in the closed-loop switched system remain bounded and the tracking error can eventually converge to a small neighborhood of the origin. In the simulation study, two examples are supplied to prove the practicability and feasibility of the developed design schemes.

Recursive fuzzy c-means clustering for recursive fuzzy identification of time-varying processes

In this paper we propose a new approach to on-line Takagi-Sugeno fuzzy model identification. It combines a recursive fuzzy c-means algorithm and recursive least squares. First the method is derived and than it is tested and compared on a benchmark problem of the Mackey-Glass time series with other established on-line identification methods. We showed that the developed algorithm gives a comparable degree of accuracy to other algorithms. The proposed algorithm can be used in a number of fields, including adaptive nonlinear control, model predictive control, fault detection, diagnostics and robotics. An example of identification based on a real data of the waste-water treatment process is also presented.