Studies Of Multi-objective Optimal And Data-driven Controls Of Dynamical Systems

In recent years,nonlinear control has penetrated into all aspects of human society.Increased process variability in industries could result in complex controller tuning problems.Traditional controller tuning mainly focus on simple linear system,often helpless when meet the complicated nonlinear system.Consequently,how to effectively provide tuning rules with control theory and systems engineering,has become a very important issue that needs to be addressed.The aim of our work is to develop some tuning methods not only for system analysis,but also for nonlinear systems control.We first develop a tuning method of an under-actuated nonlinear system to validate the multi-objective optimal control design.The multi-objective optimal design of the nonlinear control involves four design parameters and six objective functions.We then develop the multi-objective particle swarm optimization algorithm is applied to find the Pareto set and Pareto front.Both numerical simulations and experiments are carried out to validate the control design.Next,we give a multi-objective optimal feedback control method for a multiple input and multiple output(MIMO)nonlinear system,which has strong nonlinear and coupling properties.In the first stage,we apply the nonlinear feed-forward term for the pitch angle compensates the gravitational torque.Then,the multi-objective optimal design method instead of the classical approaches are used to tune the control gains.Six objective functions are optimized with respect to eight control gains,resulting in a moderately high dimensional multi-objective optimization problem.In the second stage,an improved parallel simple cell mapping method with subdivision technique is developed to search the Pareto optimal designs of the control.Compared with the simple cell mapping,the improved hybrid method mimics the steepest descent search.Also,we present theoretical analysis,computer simulation and experiment results to demonstrate the feasibility.After that we present a direct output feedback linearization control with differential estimation method of the MIMO system.The proposed methodology requires only the measurement of two angular positions of the pitch and yaw motions and the voltage inputs to the pitch and yaw motors.Then an improved algebraic differential estimation approach is developed to compute the derivatives of the output signals.By qualitative and quantitative analysis,the output feedback linearization control with proposed algebraic differential estimation show large advantage in decreasing tracking error and reducing energy consumption.Traditional methods for analyzing and controlling the system,need to establish mathematical models.The last part of this thesis is a data-based model free control method for a class of nonlinear discrete-time systems,which have partial unknown mathematical models.This proposed MFC method is also based on some prior knowledge about the system.We first use the historical measured data to establish an ultra-model,which approximates the original system.Then,with this approximate model and the measured output data,we use a nonlinear programming method to estimate the corresponding matrix of tracking errors.The feedback controller is designed in real-time according to these errors matrices,which can drive the output signal to its desired value.Besides,the excellent performance shows that the MFC method has good application for difficult modeling system.