Optimal control of nonlinear partially-unknown systems with unsymmetrical input constraints and its applications to the optimal UAV circumnavigation problem

Aimed at solving the optimal control problem for nonlinear systems with unsymmetrical input constraints, we present an online adaptive approach for partially unknown control systems/dynamics. The designed algorithm converges online to the optimal control solution without the knowledge of the internal system dynamics. The optimality of the obtained control policy and the stability for the closed-loop dynamic optimality are proved theoretically. The proposed method greatly relaxes the assumption on the form of the internal dynamics and input constraints in previous works. Besides, the control design framework proposed in this paper offers a new approach to solve the optimal circumnavigation problem involving a moving target for a fixed-wing unmanned aerial vehicle (UAV). The control performance of our method is compared with that of the existing circumnavigation control law in a numerical simulation and the simulation results validate the effectiveness of our algorithm

Supervisory observer for parameter and state estimation of nonlinear systems using the DIRECT algorithm

A supervisory observer is a multiple-model architecture, which estimates the parameters and the states of nonlinear systems. It consists of a bank of state observers, where each observer is designed for some nominal parameter values sampled in a known parameter set. A selection criterion is used to select a single observer at each time instant, which provides its state estimate and parameter value. The sampling of the parameter set plays a crucial role in this approach. Existing works require a sufficiently large number of parameter samples, but no explicit lower bound on this number is provided. The aim of this work is to overcome this limitation by sampling the parameter set automatically using an iterative global optimisation method, called DIviding RECTangles (DIRECT). Using this sampling policy, we start with 1 + 2np parameter samples where np is the dimension of the parameter set. Then, the algorithm iteratively adds samples to improve its estimation accuracy. Convergence guarantees are provided under the same assumptions as in previous works, which include a persistency of excitation condition. The efficacy of the supervisory observer with the DIRECT sampling policy is illustrated on a model of neural populations