Case studies on the application of the stable manifold approach for nonlinear optimal control design

Nonlinear Luenberger observer design via invariant manifold computation

“…The C ω smoothness is necessary since they use the Taylor series approach. For the purpose of observer design, however, C 1 smoothness is sufficient and, as was mentioned in Introduction, the Taylor approach has serious drawbacks for solving nonlinear pdes (Sakamoto [2013a]). Generalizing their results requires to handle the cases where non-unique C r (r 1) solutions exist.…”

“…A detailed description and proof of its existence are presented in Kelley [1967]. The difficulty of using the Taylor expansion-based approach has been long recognized, an explicit example is shown in Sakamoto [2013a]. Recently, a method for finding the stable manifold based on iterative solution of certain differential equations appeared.…”

“…This method is suitable for solution of practical problems, optimal control of nonlinear systems among all. It is presented in Sakamoto and van der Schaft [2008], Sakamoto [2013a] and successfully extended to the construction of the center and center-stable manifolds in Sakamoto and Rehák [2011] with application to the optimal output regulation. The aim of this paper is to propose a framework for computing the invariant manifold that defines the systemobserver invariance relation based on the aforementioned method for computation of the center, unstable or centerunstable manifolds.…”

“…• The computation method for invariant manifolds is based on the flow approach for the manifolds (see Sakamoto and van der Schaft [2008], Sakamoto and Rehák [2011], Sakamoto [2013a]), which has been already applied to many actual systems with experimental verifications (see Fujimoto and Sakamoto [2011], Sakamoto [2013b]) and proven to be superior to the Taylor method from the viewpoints of accuracy and computational complexity.…”

Nonlinear Optimal Servo Control Design for PMSM with Inverter Voltage Norm Constraints

“…Anti-windup [1] (PMSM : Permanent Magnet Synchronous Motor) Hamilton-Jacobi [5] [6,7] Anti-windup [8,9] [10] . [11] Hamilton-Jacobi HamiltonJacobi PMSM …”