A method for suboptimal design of nonlinear feedback systems

Near-optimal feedback stabilization of a class of nonlinear singularly perturbed systems

“…Note that when z is not penalized in (2), that is when Q(x)=0, but R e U ( A 2)} < 0, then V2 i -s identically zero and u^ reduces to u^ of (10). Stabilizing properties of the composite control u^ are established in the next section.…”

“…Since system (1) is linear in z and J is quadratic in z, the optimal value function can be expanded as a power series in the components of z [2] . In addition, since z is the fast variable, the z terms in the optimal value function are multiplied by appropriate powers of [5] .…”

“…Realistic approaches to the difficult nonlinear feedback control problem usually exploit properties of special classes of systems to develop approximate methods [1,2]. The approach in this paper exploits multiple time scale properties of a class of nonlinear singularly perturbed systems [3,4] to achieve stabilization and near-optimality.…”

An analytical approximation method for the stabilizing solution of the Hamilton-Jacobi equation based on stable manifold theory

“…In [19], [11], [22], [12] various series expansion techniques are proposed to obtain approximate solutions of the Hamilton-Jacobi equation. With these methods, one can calculate sub-optimal solutions using a few terms for simple nonlinearities.…”

On approximate policy iteration for continuous-time systems

“…Due to its importance much time have been devoted to find such schemes. In [5], [10] the authors used various power series expansion strategies, with various assumptions, to obtain approximate solutions to the HJB-equation. These methods can sometimes be used to compute good local estimates, using only a few terms.…”