An Optimization Framework for Nonlinear Control Systems Design based on Multi-Constraints and Multi-Criteria

Classical control methods such as Pontryagin Maximum Principle and Bang-Bang Principle and other methods are not usually useful for solving opti-mal control systems (OCS) specially optimal control of nonlinear systems (OCNS). In this paper, we introduce a new approach for solving OCNS by using some combination of atomic measures. We define a criterion for controllability of lumped nonlinear control systems and when the system is nearly null controllable, we determine controls and states. Finally we use this criterion to solve some numerical examples.

Characteristic Phenomena and Model Problems in Nonlinear Control

International audience

Nonlinear [formula omitted]-gain verification for nonlinear systems

The bifurcation theory is applied to bifurcations and accompanying jump phenomena which appear in the frequency response of nonlinear feedback control systems. It is also shown by a numerical example that such complicated structures exist in the frequency response of a simple nonlinear feedback control system.

An LMI approach for designing an H/sup /spl infin// fuzzy controller for nonlinear dynamic systems is presented. The entire operating range for a nonlinear system is partitioned into several regimes. A local linear model with parameter uncertainties is identified for each region. These local models are integrated as the norm-bounded Tagaki-Sugeno (T-S) fuzzy model. The output feedback H/sup /spl infin// fuzzy controller design procedures are then investigated based on the T-S fuzzy model, therein the standard H/sup /spl infin// design problem is formulated as Linear Matrix Inequalities (LMIs). The necessary and sufficient conditions for the existence of an H/sup /spl infin// controller is derived. One numerical example is supplied, demonstrating the effectiveness of the proposed design procedures.

It is generally impossible to obtain the exact response of nonlinear control systems by the integral method. It is necessary, therefore, to use the approximate methods such as perturbation, iteration or others, when we intend to study the systems by the analytical method. The solution will be represented by infinite series, and the first several terms will afford an approximate solution. Then, the convergency of the solution and the accuracy of the approximate solution must be estimated, being compared with the numerical solution, which has a significant meaning in the theoretical study of nonlinear control systems. The author devised a modified Runge-Kutta method. He proved that the mcdified method is less troublesome in calculation with better accuracy than the conventional method in the illustrative analysis of the indicial response of gain-saturated second order servomechanism. He believes that the modified method will be superior to the conventional one in the general nonlinear gain systems or, moreover, in the general nonlinear control systems.

In this paper, a multiple generalized NARMA-L2 model is proposed for the identification and control of discrete nonlinear systems. It provides a global input-output representation for nonlinear systems by making use of the good local approximation property of NARMA-L2 model without encountering the curse of dimensionality problem. With the identified model, the control problem is then transformed into a constrained optimization problem based on the weighted one-step-ahead predictive control law. Simulation studies demonstrate the effectiveness of the proposed model structure.

Global optimal feedback control for general nonlinear systems with nonquadratic performance criteria

Theory of nonlinear control

The double inverted pendulum is a multivariable, nonlinear control system. The fuzzy controller of double inverted pendulum is studied in the paper. The mathematical model is gained by the Lagrange equation and the controllability of double inverted pendulum system in unstable equilibrium point is analyzed. On the base of above, the fuzzy controller for double inverted pendulum is designed by the fuzzy control theory. The dimensions and control rules of the fuzzy controller are depressed by designing a fusion function using the optimization control theory. Simulation and real-time control results prove that the fuzzy controller is effective and feasible.

An adaptive system for linear systems with unknown parameters is a nonlinear system. The analysis of such adaptive systems requires similar techniques to analyse nonlinear systems. Therefore it is natural to treat adaptive control as a part of nonlinear control systems. Nonlinear and Adaptive Control Systems treats nonlinear control and adaptive control in a unified framework, presenting the major results at a moderate mathematical level, suitable for MSc students and engineers with undergraduate degrees. Topics covered include introduction to nonlinear systems; state space models; describing functions for common nonlinear components; stability theory; feedback linearization; adaptive control; nonlinear observer design; backstepping design; disturbance rejection and output regulation; and control applications, including harmonic estimation and rejection in power distribution systems, observer and control design for circadian rhythms, and discrete-time implementation of continuous-time nonlinear control laws.

Linear stabilization of the programmed motions of non-linear controlled dynamical systems under parametric perturbations

This paper is focused on usability of multiestimation scheme approach in the area of identification and control of nonlinear systems. A multiestimation scheme is introduced and subsequently used for the adaptive control of real-time nonlinear system. The multiestimation scheme integrates on-line identification of suitable models of a controlled system and a controller synthesis on base of the identified model. The real-time testing has been carried out by the control of nonlinear laboratory model of interconnected tanks (DTS200 by Amira company).

This paper discusses the exact controllability of linear and nonlinear impulsive Caputo fractional systems. The exact controllability of a linear impulsive system is studied using the concept of generators and functional analysis. In contrast, the controllability of a nonlinear system is discussed using nonlinear functional analysis. An example is provided in the paper to support the results.