Sub-Optimal Control for Nonlinear Heat Equations

This paper presents a successive approximation approach (SAA) designing optimal controllers for a class of nonlinear heat equations with a quadratic performance index. By using the SAA, the optimal control problem for nonlinear heat equations is transformed into a sequence of nonhomogeneous linear differential Riccati operator equations. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoin vector sequence. By using the finite-step iteration of the nonlinear compensation sequence, we can obtain a suboptimal control law.