Nonlinear Singular Control Systems Research Articles

Degrees of freedom analysis and parameter optimization of state feedback of first-order affine singular control for bioprocess systems

The state feedback optimization of first-order affine nonlinear singular control systems is formulated as a time-invariant parameter optimization problem. Degrees of freedom (DF) is applied to the differential balance equations with initial control or its time derivatives and switching times as parameters, and uncovered that the state feedback optimization problem has −2 DF, clarifying admissible singular control structures. Using these two novel concepts, we considered end-point optimization problems in fed-batch fermentation problem to illustrate the state feedback optimization of the feed flow rate.

A global canonical form for nonlinear singular control systems

In this paper, the concept of a global generalised characteristic number is defined and global zero dynamics algorithm is developed. Based on the feasibility of this algorithm, a global diffeomorphism is constructed, under which the original system can be put into a global canonical form. Sufficient conditions for the existence of the global diffeomorphism are provided.

Local disturbance decoupling of nonlinear singular systems

The problem of local disturbance decoupling is considered for a class of non-linear singular control systems. Assumptions are introduced, and an algorithm is developed such that the control system can be expressed in a simple form. A nonlinear feedback control law is then constructed, which ensures the closed-loop system has a unique solution without impulses, and its output is unaffected by disturbances. Sufficient and necessary conditions for the existence of such a feedback are derived. An example is provided to illustrate the results of the paper.

Feedback control of affine nonlinear singular control systems

This paper discusses feedback control problems for affine nonlinear singular systems. Namely, the problems of regularization (regular singular systems have for a particular initial state and input, a unique solution), non-interaction and exact linearization. First, an algorithm providing necessary and sufficient conditions for the regularizability of the affine nonlinear singular systems is introduced. This algorithm resembles the well-known constrained dynamics algorithm for affine nonlinear systems. For regularizable affine nonlinear singular systems, necessary and sufficient conditions for the solvability of the non-interacting control problem are derived. They are based on another algorithm producing a sequence of integers, the generalization of the well known notion of relative degree for usual affine nonlinear systems. Finally, the problem of feedback exact linearization of the dynamic part of singular systems is briefly addressed. An example is provided to illustrate the main results.