A new method for suboptimal control of a class of non-linear systems

In this paper, a new non-linear control synthesis technique (θ-D approximation) is discussed. This approach achieves suboptimal solutions to a class of non-linear optimal control problems characterized by a quadratic cost function and a plant model that is affine in control. An approximate solution to the Hamilton–Jacobi–Bellman equation is sought by adding perturbations to the cost function. By manipulating the perturbation terms both semi-global asymptotic stability and suboptimality properties are obtained. The new technique overcomes the large-control-for-large-initial-states problem that occurs in some other Taylor series expansion based methods. Also this method does not require excessive online computations like the recently popular state dependent Riccati equation technique. Furthermore, it provides a closed-form non-linear feedback controller if finite number of terms are taken in the series expansion. A scalar problem and a 2-D benchmark problem are investigated to demonstrate the effectiveness of this new technique. Both stability and convergence proofs are given.