Inverse Optimal Control of Linear Distributed Parameter Systems

A constructive method is developed to design inverse optimal controllers for a class of linear distributed parameter systems (DPSs). Inverse optimality guarantees that the cost functional to be minimized is meaningful in the sense that the symmetric and positive definite weighting kernel matrix on the states is chosen after the control design instead of being specified at the start of the control design. Inverse optimal design enables that the Riccati nonlinear partial differential equation (PDE) can be simplified to a Bernoulli PDE, which can be solved analytically. The control design is based on a new Green matrix formula, a new unique and bounded solution of a linear PDE, and an analytical solution of a Bernoulli PDE. Both distributed and finite control problems are addressed. An example is given.