Robust tracking control of non-linear systems with uncertain dynamics Part 1

An identification approach for linear and nonlinear time-variant structural systems via harmonic wavelets

MTN optimal control of MIMO non-affine nonlinear time-varying discrete systems for tracking only by output feedback

A nervous system consists of a large number of highly interconnected nerve cells. Nerve cells communicate by generation and transmission of short electrical pulses (action potential). In addition, membrane voltage is the only measurable state in nervous systems. A robust observer-based model reference tracking control is proposed for Hodgkin-Huxley (HH) neuron systems to generate a desired reference response in spite of environmental noises, uncertain initial values, and diffusion currents from other interconnected nerve cells. In order to simplify the robust tracking control design of nonlinear stochastic HH neuron systems, a fuzzy interpolation method is employed to interpolate several linear stochastic systems to approximate a nonlinear stochastic HH neuron system so that the nonlinear robust tracking control problem can be solved by the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. The proposed robust observer-based tracking control scheme can provide new methods for desired action potential generation, suppression of oscillations, and blockage of action potential transmission under environmental noise and diffusion currents. These new methods are useful for patients with different neuron system dysfunctions. Finally, three simulation examples of tracking control of nervous systems are given to illustrate the design procedure and confirm the tracking performance of the proposed method.

Robust tracking control of uncertain nonlinear systems with adaptive dynamic programming

The problems encountered in using a fuzzy logic-based single neuron controller (SNC) for the tracking control of nonlinear SISO systems are shown to be overcome by the use of a fuzzy inverse incremental model (FIIM) of the same process as the tracking controller. The proposed method of tracking control uses online tuning of the universe of discourse and online identification of the FIIM. Three different algorithms for the linguistic/fuzzy modeling of SISO systems are proposed. The comparative results of using these algorithms for the tracking control of some nonlinear systems are shown.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

EP-based adaptive tracker with observer and fault estimator for nonlinear time-varying sampled-data systems against actuator failures

The stability and behavior of continuous-time nonlinear time-varying (NTV), nonlinear time-invariant (NTI) and linear time-varying (LTV) systems are generally very difficult to ascertain using current analytical tools. This paper presents sufficient conditions under which a NTV system with a bounded system matrix, A(t,X), is globally exponentially stable (GES). The continuous-time NTV system is modeled as an uncertain polytopic system even though A(t,X) may be reasonably known. It is shown that if all polytope-vertex matrices are Hurwitz, then the system is GES. Also, a method for determining the boundary estimate of a NTV system state-trajectory norm is developed. Presented is a unified stability analysis approach for a large class of NTV, NTI, and LTV systems. Even for large systems, application of the GES theorem presented is straight forward using readily available software and computational power. Examples are given that illustrate the application of the theorem offered.

A general invariance principle is proposed from the output-to-state view-point for general nonlinear time-varying systems. A simple and intuitive criterion is proposed using an integral inequality involving the output function and a modified detectability condition. When applied to systems having a Lyapunov function, the well-known LaSalle's invariance principle can be deduces based on our approach. A similar criterion, called the integral invariance principle, was proposed by Byrnes and Martin for nonlinear time-invariant systems. In general, it can not be directly applied to time-varying systems. Our proposed method can be viewed as an extension of the integral invariance principle for time-invariance systems to time-varying systems. The extension is not trivial and can be used in divergence research area, including the adaptive control, the tracking control and the control of driftless systems. In particular, a globally tracking controller for 4-wheeled mobile robots is proposed based on the invariance principle derived in this paper. From this example, it can be seen that as LaSalle invariance principle is used in study the stability of time-invariant systems, our results can be also used to study the stability of time-varying systems along a similar argument.

Cooperative regulation based on virtual vector triangles asymptotically compressed in multidimensional space for time-varying nonlinear multi-agent systems.

State bounding for nonlinear time-varying systems with delay and disturbance

Interval state observer for nonlinear time varying systems

International audience

A novel neural network controller architecture is explored for the speed control of a DC motor-driven four bar linkage system which represents a class of time-varying nonlinear systems. Simulation and experimental implementation show the viability and effectiveness of this promising tool for nonlinear systems. Identification and control, as well as real-time implementation issues are considered. Comparative studies with two other neural network architectures are also reported. Importantly, they also perform well in real-time control studies for the system considered.

Learning-based robust output tracking control for unknown discrete-time nonlinear systems with dynamic uncertainty

The problem of controlling the suspension deflection of a quarter-car active suspension system using a robust tracking controller is proposed. The proposed robust asymptotic tracking and disturbance attenuation controller aims to keep the suspension deflection asymptotically to zero despite road disturbances and physical system uncertainties. The robust controller design technique is based on the respective results of Hurwitz invariability. The robust controller parameters are computed using an analytic algorithm. The effectiveness of the proposed controller is illustrated to an uncertain and disturbed environment.