Constructive Nonlinear Control

Constructive Nonlinear Control

Constructive Nonlinear Control

Constructive Nonlinear Control presents a broad repertoire of constructive nonlinear designs not available in other works by widening the class of systems and design tools. Several streams of nonlinear control theory are merged and directed towards a constructive solution of the feedback stabilization problem. Analysis, geometric and asymptotic concepts are assembled as design tools for a wide variety of nonlinear phenomena and structures. Geometry serves as a guide for the construction of design procedures whilst analysis provides the robustness which geometry lacks. New recursive designs remove earlier restrictions on feedback passivation. Recursive Lyapunov designs for feedback, feedforward and interlaced structures result in feedback systems with optimality properties and stability margins. The design-oriented approach will make this work a valuable tool for all those who have an interest in control theory.

Towards Constructive Nonlinear Control Systems Analysis and Design

This work presents a novel method to solve analysis and design problems for nonlinear control systems, the classical solutions of which rely on the solvability, or on the solution itself, of partial differential equations or inequalities. The first part of the thesis is dedicated to the analysis of nonlinear systems. The notion of Dynamic Lyapunov function is introduced. These functions allow to study stability properties of equilibrium points, similarly to standard Lyapunov functions. In the former, however, a positive definite function is combined with a dynamical system that render Dynamic Lyapunov functions easier to construct than Lyapunov functions. These ideas are then extended to characterize Dynamic Controllability and Observability functions, which are exploited in the model reduction problem for nonlinear systems. Constructive solutions to the L2-disturbance attenuation and the optimal control problems are proposed in the second part of the thesis. The key aspect of these solutions is the definition of Dynamic Value functions that, generalizing Dynamic Lyapunov functions, consist of a dynamical feedback and a positive definite function. In the last part of the thesis a similar approach is utilized to simplify the observer design problem via the Immersion and Invariance technique. Finally, the effectiveness of the methodologies is illustrated by means of several applications, including range estimation and the optimal robust control of mechanical systems, combustion engine test benches and the air path of a diesel engine.