Nonlinear direct data-driven control for UAV formation flight system

This paper proposes the nonlinear direct data-driven control from theoretical analysis and practical engineering,i.e.,unmanned aerial vehicle(UAV)formation flight system.Firstly,from the theoretical point of view,consider one nonlinear closedloop system with a nonlinear plant and nonlinear feed-forward controller simultaneously.To avoid the complex identification process for that nonlinear plant,a nonlinear direct data-driven control strategy is proposed to design that nonlinear feed-forward controller only through the input-output measured data sequence directly,whose detailed explicit forms are model inverse method and approximated analysis method.Secondly,from the practical point of view,after reviewing the UAV formation flight system,nonlinear direct data-driven control is applied in designing the formation controller,so that the followers can track the leader’s desired trajectory during one small time instant only through solving one data fitting problem.Since most natural phenomena have nonlinear properties,the direct method must be the better one.Corresponding system identification and control algorithms are required to be proposed for those nonlinear systems,and the direct nonlinear controller design is the purpose of this paper.

Synthesis identification analysis for closed loop system

The existing theories for closed loop identification with the linear feedback controller are very mature.To apply the existed theories directly in the control field,we propose a new idea about replacing the original unknown and nonlinear feedback controller with one approximated linear controller,while guaranteeing the equivalent property for the obtained closed loop system.Based on some statistical correlation functions,one condition is derived to show the equivalent property between the approximated linear controller and the original nonlinear controller.The detailed explicit form,corresponding to the approximated linear controller,is also constructed.Furthermore,to give a complete analysis for closed loop identification,the cost function is rewritten as one extended expression,being convenient to understand.Then spectral estimation is introduced to identify the unknown plant in the closed loop system.Finally,the proposed theories are verified by one simulation example.

Introducing System Identification Strategy into Model Predictive Control

As system identification theory and model predictive control are belonged to two different research fields separately,so one gap exists between these two subjects.To alleviate this gap between them,one new idea proposed in this paper is to introduce system identification theory into model predictive control.As the most important element in model predictive control is the prediction of the output value for a nonlinear system,then the problem of deriving the prediction of the output value can be achieved by system identification theory.More specifically,a Bayesian approach is applied for the nonparametric estimation by modeling the prediction as realizations of zero mean random fields.Through comparing this kind of prediction corresponding to this Bayesian approach and the former direct weight optimization identification for nonlinear system,the authors see that if the unknown weights are chosen appropriately,these two approaches are equivalent to each other.Based on the obtained prediction of the output value,the authors substitute this prediction of the output value into one cost function of model predictive control,and then a quadratic programming problem with inequality constraints is formulated.When to solve this quadratic programming problem,a detailed process about how to derive its dual form is given.As the dual problem has a simple constraint set,it is amenable to the use of the common Gauss-Seidel algorithm,whose convergence can be shown easily.Finally,one simulation example confirms the proposed theoretical results.