This paper concerns a study on the optimal control for Nonlinear systems. An appropriate alternative in order to alleviate the Nonlinearity of a system is the exact linearization approach. In this fashion, the Nonlinear system has been linearized using input-output feedback linearization (IOFL). Then, by utilizing the well developed optimal control theory of linear systems, the compensated Nonlinear system has been controlled. Thus, the structure of the objective function will be converted into a quadratic form which is qualitativly comparable with usual cost functions, and from operating viewpoint is more favorable. To qualify such a procedure, it has been applied to two minimum and nonminimum-phase chemical processes, and its performance is verified through computer simulations.

This paper gives a survey of the theory and practice of Nonlinear ABS methods including various types of generalizations and computer testing. We also show three applications to special problems, two of which are new.

In this paper, we first introduce the concepts of an equilibrium region and a stable equilibrium region. Then, we state and prove conditions under which a Nonlinear autonomous system has a stable equilibrium region. It will be shown that these concepts and stability conditions are generalizations of the corresponding concepts of equilibrium points and asymptotical stable equilibrium points and their stability conditions. Using these conditions and Poincare-Bendixson theorem, we discuss conditions for the existence of periodic solutions in a Nonlinear system of ordinary differential equations.

A QFT-type frequency-domain controller design technique is presented for multiple input-multiple ouput (MIMO) Nonlinear systems with significant structured (parametric) uncertainty. Hard time-domain constraints are imposed on the outputs and control inputs in response to step disturbances. The control design method is based on replacing the Nonlinear MIMO system with an equivalent diagonal MIMO linear uncertain plant using compact and convex sets of output functions. Then, a diagonal controller is designed for the equivalent linear system by transferring the time-domain constraints into the frequency-domain to obtain a series of allowable regions for the frequency responses of the nominal loop transfer functions. Next, a loop-shaping procedure is used to shape the nominal loop transfer function and hence the controller for each loop. Finally, Schauder"s fixed point theorem is utilized to show that the same controller will also work for the Nonlinear system. The proposed method is illustrated by an example.

In the several past years, Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) have became basic algorithm for state-variables and parameters estimation of discrete Nonlinear systems. The UKF has consistently outperformed for estimation. Sometimes least estimation error doesn't yield with UKF for the most Nonlinear systems. In this paper, we use a new approach for a two variable state Nonlinear systems which it is called Rotated UKF (R_UKF). R_UKF can be reduced estimation error and reached for least error in state estimation.

This paper presents a theoretical approach to implementation of the “Multi-realization of Nonlinear MIMO systems”. This method aims to find state-variable realization for a set of systems, sharing as many parameters as possible. In this paper a special Nonlinear multi-realization problem, namely the multi-realization of feedback linearizable Nonlinear systems is considered and an algorithm for achieving minimal stably-based multi-realization of a set of Nonlinear feedback linearizable systems is introduced. An example that illustrates this algorithm is also presented.

Singular systems behave more powerfully in terms of dynamical system modeling than ordinary state space systems. Since the algebraic equations in singular models can describe the systems constraints, Nonlinear singular systems can present a general method for modeling and controlling constrained dynamical systems. This paper discusses an adaptive control for Nonlinear singular systems which satisfy Lipschitz condition. Adaptive methods for singular systems are hardly ever investigated in literatures; however they are very useful methods in practice because the adaptive mechanism during the adaptive control can adjust the controller for a system with the unknown structures and parameters to improve the system performance. The presented controller is composed of a state feedback approach with adaptive gains and a mechanism to adjust the gains based on the Lyapunov stability theorem. First the controller is designed to stabilize the system, as a result, it is extended for the tracking problem. A simulation on a mobile robot singular model is provided to illustrate the effectiveness of the proposed control approach.