Chapter II
The control of nonlinear lumped-parameter systems is considered with unknown random inputs and measurement noise. A scheme is developed whereby a nonlinear filter is included in the control loop to improve system performance. Pure time delays in the control loop are also examined. A computational example is presented for the proportional control on temperature of a CSTR subject to random disturbances, applying a nonlinear least square filter.
Chapter III
Least square filtering and interpolation algorithms are derived for states and parameters in nonlinear distributed systems with unknown additive volume, boundary and observation noises, and with volume and boundary dynamical inputs governed by stochastic ordinary differential equations. Observations are assumed to be made continuously in time at continuous or discrete spatial locations. Two methods are presentedfor derivation of the filter. One is the limiting procedure of the finite dimensional description of partial differential equation systems along the spatial axis, applying known filter equations in ordinary differential equation systems. The other is to define a least square estimation criterion and convert the estimation problem into an optimal control problem, using extended invariant imbedding technique inpartial differential equations. As an example, the derived filter is used to estimate the state and parameter in a nonlinear hyperbolic system describing a tubular plug flow chemical reactor. Also a heatconduction problem is studied with the filtering and interpolation algorithms.
Chapter IV
New necessary and sufficient conditions are presented for the observability of systems described by nonlinear ordinary differential equations with nonlinear observations. The conditions are based on extension of the necessary and sufficient conditions for observability of time-varying linear systems to the linearized trajectory of the nonlinear system. The result is that the local observability of any initial condition can be readily determined, and the observability of the entire initial domain can be computed. The observability of constant parameters appearing in the differential equations is also considered.
