Constructive nonlinear control: a historical perspective

In the early days of nonlinear control theory most of the stability, optimality and uncertainty concepts were descriptive rather than constructive. This survey describes their ‘activation’ into design tools and constructive procedures. Structural properties of nonlinear systems, such as relative degree and zero dynamics, are connected to passivity, while dissipativity, as a finite L2-gain property, also appears in the disturbance attenuation problem, a nonlinear counterpart of robust linear control. Passivation-based designs exploit the connections between passivity and inverse optimality, and between Lyapunov functions and optimal value functions. Recursive design procedures, such as backstepping and forwarding, achieve certain optimal properties for important classes of nonlinear systems. The survey concludes with four representative applications. The selection of the topics and their interpretations are greatly influenced by the experience and personal views of the senior author.