Data-driven stabilization of unknown nonlinear dynamical systems using a cognition-based framework

• Published in: Nonlinear dynamics Vol. 86; no. 1; pp. 1 - 15
• Main Authors: Nowak, Xi, Söffker, Dirk
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-10-2016; Springer Nature B.V
• Subjects: Adaptive control; Automotive Engineering; Chaos theory; Classical Mechanics; Cognition; Control; Control stability; Control systems; Cost function; Dynamical Systems; Engineering; Lorenz system; Mechanical Engineering; MIMO (control systems); Modules; Motion stability; Nonlinear dynamics; Nonlinear systems; Nonlinearity; On-line systems; Optimal control; Original Paper; Stability criteria; State vectors; Vibration; High autonomy; Adaptive stabilizer; Cognitive; Data-driven approach; Unknown nonlinear dynamical MIMO system
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-016-2868-0

In this paper, a cognitive stabilizer concept is introduced. The framework acts as an adaptive discrete control approach. The aim of the cognitive stabilizer is to stabilize a specific class of unknown nonlinear MIMO systems. The cognitive stabilizer is able to gain useful local knowledge of the system assumed as unknown. The approach is able to define autonomously suitable control inputs to stabilize the system. The system class to be considered is described by the following assumptions: unknown input/output behavior, fully controllable, stable zero dynamics, and measured state vector. The cognitive stabilizer is realized by its four main modules: (1) “perception and interpretation” using system identifier for the system local dynamic online identification and multi-step-ahead prediction; (2) “expert knowledge” relating to the quadratic stability criterion to guarantee the stability of the considered motion of the controlled system; (3) “planning” to generate a suitable control input sequence according to a certain cost function; (4) “execution” to generate the optimal control input in a corresponding feedback form. Each module can be realized using different methods. Two realizations will be stated in this paper. Using the cognitive stabilizer, the control goal can be achieved efficiently without an individual control design process for different kinds of unknown systems. Numerical examples (e.g., a chaotic nonlinear MIMO system–Lorenz system) demonstrate the successful application of the proposed methods.